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What is LDA: Linear Discriminant Analysis for Machine Learning

Linear Discriminant Analysis or LDA is a dimensionality reduction technique. It is used as a pre-processing step in Machine Learning and applications of pattern classification. The goal of LDA is to project the features in higher dimensional space onto a lower-dimensional space in order to avoid the curse of dimensionality and also reduce resources and dimensional costs.The original technique was developed in the year 1936 by Ronald A. Fisher and was named Linear Discriminant or Fisher's Discriminant Analysis. The original Linear Discriminant was described as a two-class technique. The multi-class version was later generalized by C.R Rao as Multiple Discriminant Analysis. They are all simply referred to as the Linear Discriminant Analysis.LDA is a supervised classification technique that is considered a part of crafting competitive machine learning models. This category of dimensionality reduction is used in areas like image recognition and predictive analysis in marketing.What is Dimensionality Reduction?The techniques of dimensionality reduction are important in applications of Machine Learning, Data Mining, Bioinformatics, and Information Retrieval. The main agenda is to remove the redundant and dependent features by changing the dataset onto a lower-dimensional space.In simple terms, they reduce the dimensions (i.e. variables) in a particular dataset while retaining most of the data.Multi-dimensional data comprises multiple features having a correlation with one another. You can plot multi-dimensional data in just 2 or 3 dimensions with dimensionality reduction. It allows the data to be presented in an explicit manner which can be easily understood by a layman.What are the limitations of Logistic Regression?Logistic Regression is a simple and powerful linear classification algorithm. However, it has some disadvantages which have led to alternate classification algorithms like LDA. Some of the limitations of Logistic Regression are as follows:Two-class problems – Logistic Regression is traditionally used for two-class and binary classification problems. Though it can be extrapolated and used in multi-class classification, this is rarely performed. On the other hand, Linear Discriminant Analysis is considered a better choice whenever multi-class classification is required and in the case of binary classifications, both logistic regression and LDA are applied.Unstable with Well-Separated classes – Logistic Regression can lack stability when the classes are well-separated. This is where LDA comes in.Unstable with few examples – If there are few examples from which the parameters are to be estimated, logistic regression becomes unstable. However, Linear Discriminant Analysis is a better option because it tends to be stable even in such cases.How to have a practical approach to an LDA model?Consider a situation where you have plotted the relationship between two variables where each color represents a different class. One is shown with a red color and the other with blue.If you are willing to reduce the number of dimensions to 1, you can just project everything to the x-axis as shown below: This approach neglects any helpful information provided by the second feature. However, you can use LDA to plot it. The advantage of LDA is that it uses information from both the features to create a new axis which in turn minimizes the variance and maximizes the class distance of the two variables.How does LDA work?LDA focuses primarily on projecting the features in higher dimension space to lower dimensions. You can achieve this in three steps:Firstly, you need to calculate the separability between classes which is the distance between the mean of different classes. This is called the between-class variance.Secondly, calculate the distance between the mean and sample of each class. It is also called the within-class variance.Finally, construct the lower-dimensional space which maximizes the between-class variance and minimizes the within-class variance. P is considered as the lower-dimensional space projection, also called Fisher’s criterion.How are LDA models represented?The representation of LDA is pretty straight-forward. The model consists of the statistical properties of your data that has been calculated for each class. The same properties are calculated over the multivariate Gaussian in the case of multiple variables. The multivariates are means and covariate matrix.Predictions are made by providing the statistical properties into the LDA equation. The properties are estimated from your data. Finally, the model values are saved to file to create the LDA model.How do LDA models learn?The assumptions made by an LDA model about your data:Each variable in the data is shaped in the form of a bell curve when plotted,i.e. Gaussian.The values of each variable vary around the mean by the same amount on the average,i.e. each attribute has the same variance.The LDA model is able to estimate the mean and variance from your data for each class with the help of these assumptions.The mean value of each input for each of the classes can be calculated by dividing the sum of values by the total number of values:Mean =Sum(x)/Nkwhere Mean = mean value of x for class           N = number of           k = number of           Sum(x) = sum of values of each input x.The variance is computed across all the classes as the average of the square of the difference of each value from the mean:Σ²=Sum((x - M)²)/(N - k)where  Σ² = Variance across all inputs x.            N = number of instances.            k = number of classes.            Sum((x - M)²) = Sum of values of all (x - M)².            M = mean for input x.How does an LDA model make predictions?LDA models use Bayes’ Theorem to estimate probabilities. They make predictions based upon the probability that a new input dataset belongs to each class. The class which has the highest probability is considered the output class and then the LDA makes a prediction.  The prediction is made simply by the use of Bayes’ Theorem which estimates the probability of the output class given the input. They also make use of the probability of each class and the probability of the data belonging to each class:P(Y=x|X=x)  = [(Plk * fk(x))] / [(sum(PlI * fl(x))]Where x = input.            k = output class.            Plk = Nk/n or base probability of each class observed in the training data. It is also called prior probability in Bayes’ Theorem.            fk(x) = estimated probability of x belonging to class k.The f(x) is plotted using a Gaussian Distribution function and then it is plugged into the equation above and the result we get is the equation as follows:Dk(x) = x∗(mean/Σ²) – (mean²/(2*Σ²)) + ln(PIk)The Dk(x) is called the discriminant function for class k given input x, mean,  Σ² and Plk are all estimated from the data and the class is calculated as having the largest value, will be considered in the output classification.  How to prepare data from LDA?Some suggestions you should keep in mind while preparing your data to build your LDA model:LDA is mainly used in classification problems where you have a categorical output variable. It allows both binary classification and multi-class classification.The standard LDA model makes use of the Gaussian Distribution of the input variables. You should check the univariate distributions of each attribute and transform them into a more Gaussian-looking distribution. For example, for the exponential distribution, use log and root function and for skewed distributions use BoxCox.Outliers can skew the primitive statistics used to separate classes in LDA, so it is preferable to remove them.Since LDA assumes that each input variable has the same variance, it is always better to standardize your data before using an LDA model. Keep the mean to be 0 and the standard deviation to be 1.How to implement an LDA model from scratch?You can implement a Linear Discriminant Analysis model from scratch using Python. Let’s start by importing the libraries that are required for the model:from sklearn.datasets import load_wine import pandas as pd import numpy as np np.set_printoptions(precision=4) from matplotlib import pyplot as plt import seaborn as sns sns.set() from sklearn.preprocessing import LabelEncoder from sklearn.tree import DecisionTreeClassifier from sklearn.model_selection import train_test_split from sklearn.metrics import confusion_matrixSince we will work with the wine dataset, you can obtain it from the UCI machine learning repository. The scikit-learn library in Python provides a wrapper function for downloading it:wine_info = load_wine() X = pd.DataFrame(wine_info.data, columns=wine_info.feature_names) y = pd.Categorical.from_codes(wine_info.target, wine_info.target_names)The wine dataset comprises of 178 rows of 13 columns each:X.shape(178, 13)The attributes of the wine dataset comprise of various characteristics such as alcohol content of the wine, magnesium content, color intensity, hue and many more:X.head()The wine dataset contains three different kinds of wine:wine_info.target_names array(['class_0', 'class_1', 'class_2'], dtype='<U7')Now we create a DataFrame which will contain both the features and the content of the dataset:df = X.join(pd.Series(y, name='class'))We can divide the process of Linear Discriminant Analysis into 5 steps as follows:Step 1 - Computing the within-class and between-class scatter matrices.Step 2 - Computing the eigenvectors and their corresponding eigenvalues for the scatter matrices.Step 3 - Sorting the eigenvalues and selecting the top k.Step 4 - Creating a new matrix that will contain the eigenvectors mapped to the k eigenvalues.Step 5 - Obtaining new features by taking the dot product of the data and the matrix from Step 4.Within-class scatter matrixTo calculate the within-class scatter matrix, you can use the following mathematical expression:where, c = total number of distinct classes andwhere, x = a sample (i.e. a row).            n = total number of samples within a given class.Now we create a vector with the mean values of each feature:feature_means1 = pd.DataFrame(columns=wine_info.target_names) for c, rows in df.groupby('class'): feature_means1[c] = rows.mean() feature_means1The mean vectors (mi ) are now plugged into the above equations to obtain the within-class scatter matrix:withinclass_scatter_matrix = np.zeros((13,13)) for c, rows in df.groupby('class'): rows = rows.drop(['class'], axis=1) s = np.zeros((13,13)) for index, row in rows.iterrows(): x, mc = row.values.reshape(13,1), feature_means1[c].values.reshape(13,1) s += (x - mc).dot((x - mc).T) withinclass_scatter_matrix += sBetween-class scatter matrixWe can calculate the between-class scatter matrix using the following mathematical expression:where,andfeature_means2 = df.mean() betweenclass_scatter_matrix = np.zeros((13,13)) for c in feature_means1:        n = len(df.loc[df['class'] == c].index)    mc, m = feature_means1[c].values.reshape(13,1), feature_means2.values.reshape(13,1) betweenclass_scatter_matrix += n * (mc - m).dot((mc - m).T)Now we will solve the generalized eigenvalue problem to obtain the linear discriminants for:eigen_values, eigen_vectors = np.linalg.eig(np.linalg.inv(withinclass_scatter_matrix).dot(betweenclass_scatter_matrix))We will sort the eigenvalues from the highest to the lowest since the eigenvalues with the highest values carry the most information about the distribution of data is done. Next, we will first k eigenvectors. Finally, we will place the eigenvalues in a temporary array to make sure the eigenvalues map to the same eigenvectors after the sorting is done:eigen_pairs = [(np.abs(eigen_values[i]), eigen_vectors[:,i]) for i in range(len(eigen_values))] eigen_pairs = sorted(eigen_pairs, key=lambda x: x[0], reverse=True) for pair in eigen_pairs: print(pair[0])237.46123198302251 46.98285938758684 1.4317197551638386e-14 1.2141209883217706e-14 1.2141209883217706e-14 8.279823065850476e-15 7.105427357601002e-15 6.0293733655173466e-15 6.0293733655173466e-15 4.737608877108813e-15 4.737608877108813e-15 2.4737196789039026e-15 9.84629525010022e-16Now we will transform the values into percentage since it is difficult to understand how much of the variance is explained by each component.sum_of_eigen_values = sum(eigen_values) print('Explained Variance') for i, pair in enumerate(eigen_pairs):    print('Eigenvector {}: {}'.format(i, (pair[0]/sum_of_eigen_values).real))Explained Variance Eigenvector 0: 0.8348256799387275 Eigenvector 1: 0.1651743200612724 Eigenvector 2: 5.033396012077518e-17 Eigenvector 3: 4.268399397827047e-17 Eigenvector 4: 4.268399397827047e-17 Eigenvector 5: 2.9108789097898625e-17 Eigenvector 6: 2.498004906118145e-17 Eigenvector 7: 2.119704204950956e-17 Eigenvector 8: 2.119704204950956e-17 Eigenvector 9: 1.665567688286435e-17 Eigenvector 10: 1.665567688286435e-17 Eigenvector 11: 8.696681541121664e-18 Eigenvector 12: 3.4615924706522496e-18First, we will create a new matrix W using the first two eigenvectors:W_matrix = np.hstack((eigen_pairs[0][1].reshape(13,1), eigen_pairs[1][1].reshape(13,1))).realNext, we will save the dot product of X and W into a new matrix Y:Y = X∗Wwhere, X = n x d matrix with n sample and d dimensions.            Y = n x k matrix with n sample and k dimensions.In simple terms, Y is the new matrix or the new feature space.X_lda = np.array(X.dot(W_matrix))Our next work is to encode every class a member in order to incorporate the class labels into our plot. This is done because matplotlib cannot handle categorical variables directly.Finally, we plot the data as a function of the two LDA components using different color for each class:plt.xlabel('LDA1') plt.ylabel('LDA2') plt.scatter( X_lda[:,0], X_lda[:,1], c=y, cmap='rainbow', alpha=0.7, edgecolors='b' )<matplotlib.collections.PathCollection at 0x7fd08a20e908>How to implement LDA using scikit-learn?For implementing LDA using scikit-learn, let’s work with the same wine dataset. You can also obtain it from the  UCI machine learning repository. You can use the predefined class LinearDiscriminant Analysis made available to us by the scikit-learn library to implement LDA rather than implementing from scratch every time:from sklearn.discriminant_analysis import LinearDiscriminantAnalysis lda_model = LinearDiscriminantAnalysis() X_lda = lda_model.fit_transform(X, y)To obtain the variance corresponding to each component, you can access the following property:lda.explained_variance_ratio_array([0.6875, 0.3125])Again, we will plot the two LDA components just like we did before:plt.xlabel('LDA1') plt.ylabel('LDA2') plt.scatter( X_lda[:,0], X_lda[:,1],    c=y, cmap='rainbow',    alpha=0.7, edgecolors='b' )<matplotlib.collections.PathCollection at 0x7fd089f60358>Linear Discriminant Analysis vs PCABelow are the differences between LDA and PCA:PCA ignores class labels and focuses on finding the principal components that maximizes the variance in a given data. Thus it is an unsupervised algorithm. On the other hand, LDA is a supervised algorithm that intends to find the linear discriminants that represents those axes which maximize separation between different classes.LDA performs better multi-class classification tasks than PCA. However, PCA performs better when the sample size is comparatively small. An example would be comparisons between classification accuracies that are used in image classification.Both LDA and PCA are used in case of dimensionality reduction. PCA is first followed by LDA.Let us create and fit an instance of the PCA class:from sklearn.decomposition import PCA pca_class = PCA(n_components=2) X_pca = pca.fit_transform(X, y)Again, to view the values in percentage for a better understanding, we will access the explained_variance_ratio_ property:pca.explained_variance_ratio_array([0.9981, 0.0017])Clearly, PCA selected the components which will be able to retain the most information and ignores the ones which maximize the separation between classes.plt.xlabel('PCA1') plt.ylabel('PCA2') plt.scatter( X_pca[:,0], X_pca[:,1],    c=y, cmap='rainbow',    alpha=0.7, edgecolors='bNow to create a classification model using the LDA components as features, we will divide the data into training datasets and testing datasets:X_train, X_test, y_train, y_test = train_test_split(X_lda, y, random_state=1)The next thing we will do is create a Decision Tree. Then, we will predict the category of each sample test and create a confusion matrix to evaluate the LDA model’s performance:data = DecisionTreeClassifier() data.fit(X_train, y_train) y_pred = data.predict(X_test) confusion_matrix(y_test, y_pred)array([[18,  0,  0],  [ 0, 17,  0],  [ 0,  0, 10]])So it is clear that the Decision Tree Classifier has correctly classified everything in the test dataset.What are the extensions to LDA?LDA is considered to be a very simple and effective method, especially for classification techniques. Since it is simple and well understood, so it has a lot of extensions and variations:Quadratic Discriminant Analysis(QDA) – When there are multiple input variables, each of the class uses its own estimate of variance and covariance.Flexible Discriminant Analysis(FDA) – This technique is performed when a non-linear combination of inputs is used as splines.Regularized Discriminant Analysis(RDA) – It moderates the influence of various variables in LDA by regularizing the estimate of the covariance.Real-Life Applications of LDASome of the practical applications of LDA are listed below:Face Recognition – LDA is used in face recognition to reduce the number of attributes to a more manageable number before the actual classification. The dimensions that are generated are a linear combination of pixels that forms a template. These are called Fisher’s faces.Medical – You can use LDA to classify the patient disease as mild, moderate or severe. The classification is done upon the various parameters of the patient and his medical trajectory. Customer Identification – You can obtain the features of customers by performing a simple question and answer survey. LDA helps in identifying and selecting which describes the properties of a group of customers who are most likely to buy a particular item in a shopping mall. SummaryLet us take a look at the topics we have covered in this article: Dimensionality Reduction and need for LDA Working of an LDA model Representation, Learning, Prediction and preparing data in LDA Implementation of an LDA model Implementation of LDA using scikit-learn LDA vs PCA Extensions and Applications of LDA The Linear Discriminant Analysis in Python is a very simple and well-understood approach of classification in machine learning. Though there are other dimensionality reduction techniques like Logistic Regression or PCA, but LDA is preferred in many special classification cases. If you want to be an expert in machine learning, knowledge of Linear Discriminant Analysis would lead you to that position effortlessly. Enrol in our  Data Science and Machine Learning Courses for more lucrative career options in this landscape and become a certified Data Scientist.

What is LDA: Linear Discriminant Analysis for Machine Learning

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What is LDA: Linear Discriminant Analysis for Machine Learning

Linear Discriminant Analysis or LDA is a dimensionality reduction technique. It is used as a pre-processing step in Machine Learning and applications of pattern classification. The goal of LDA is to project the features in higher dimensional space onto a lower-dimensional space in order to avoid the curse of dimensionality and also reduce resources and dimensional costs.

The original technique was developed in the year 1936 by Ronald A. Fisher and was named Linear Discriminant or Fisher's Discriminant Analysis. The original Linear Discriminant was described as a two-class technique. The multi-class version was later generalized by C.R Rao as Multiple Discriminant Analysis. They are all simply referred to as the Linear Discriminant Analysis.

LDA is a supervised classification technique that is considered a part of crafting competitive machine learning models. This category of dimensionality reduction is used in areas like image recognition and predictive analysis in marketing.

What is Dimensionality Reduction?

The techniques of dimensionality reduction are important in applications of Machine Learning, Data Mining, Bioinformatics, and Information Retrieval. The main agenda is to remove the redundant and dependent features by changing the dataset onto a lower-dimensional space.

In simple terms, they reduce the dimensions (i.e. variables) in a particular dataset while retaining most of the data.

Multi-dimensional data comprises multiple features having a correlation with one another. You can plot multi-dimensional data in just 2 or 3 dimensions with dimensionality reduction. It allows the data to be presented in an explicit manner which can be easily understood by a layman.

What are the limitations of Logistic Regression?

Logistic Regression is a simple and powerful linear classification algorithm. However, it has some disadvantages which have led to alternate classification algorithms like LDA. Some of the limitations of Logistic Regression are as follows:

  • Two-class problems – Logistic Regression is traditionally used for two-class and binary classification problems. Though it can be extrapolated and used in multi-class classification, this is rarely performed. On the other hand, Linear Discriminant Analysis is considered a better choice whenever multi-class classification is required and in the case of binary classifications, both logistic regression and LDA are applied.
  • Unstable with Well-Separated classes – Logistic Regression can lack stability when the classes are well-separated. This is where LDA comes in.
  • Unstable with few examples – If there are few examples from which the parameters are to be estimated, logistic regression becomes unstable. However, Linear Discriminant Analysis is a better option because it tends to be stable even in such cases.

How to have a practical approach to an LDA model?

Consider a situation where you have plotted the relationship between two variables where each color represents a different class. One is shown with a red color and the other with blue.

How to have a practical approach to an LDA model?

If you are willing to reduce the number of dimensions to 1, you can just project everything to the x-axis as shown below: 

How to have a practical approach to an LDA model?

How to have a practical approach to an LDA model?

This approach neglects any helpful information provided by the second feature. However, you can use LDA to plot it. The advantage of LDA is that it uses information from both the features to create a new axis which in turn minimizes the variance and maximizes the class distance of the two variables.

How to have a practical approach to an LDA model?

How to have a practical approach to an LDA model?

How does LDA work?

LDA focuses primarily on projecting the features in higher dimension space to lower dimensions. You can achieve this in three steps:

  • Firstly, you need to calculate the separability between classes which is the distance between the mean of different classes. This is called the between-class variance.

How does LDA work?

  • Secondly, calculate the distance between the mean and sample of each class. It is also called the within-class variance.

How does LDA work?

  • Finally, construct the lower-dimensional space which maximizes the between-class variance and minimizes the within-class variance. P is considered as the lower-dimensional space projection, also called Fisher’s criterion.

How does LDA work?

How are LDA models represented?

The representation of LDA is pretty straight-forward. The model consists of the statistical properties of your data that has been calculated for each class. The same properties are calculated over the multivariate Gaussian in the case of multiple variables. The multivariates are means and covariate matrix.

Predictions are made by providing the statistical properties into the LDA equation. The properties are estimated from your data. Finally, the model values are saved to file to create the LDA model.

How do LDA models learn?

The assumptions made by an LDA model about your data:

  • Each variable in the data is shaped in the form of a bell curve when plotted,i.e. Gaussian.
  • The values of each variable vary around the mean by the same amount on the average,i.e. each attribute has the same variance.

The LDA model is able to estimate the mean and variance from your data for each class with the help of these assumptions.

The mean value of each input for each of the classes can be calculated by dividing the sum of values by the total number of values:

Mean =Sum(x)/Nk

where Mean = mean value of x for class
           N = number of
           k = number of
           Sum(x) = sum of values of each input x.

The variance is computed across all the classes as the average of the square of the difference of each value from the mean:

Σ²=Sum((x - M)²)/(N - k)

where  Σ² = Variance across all inputs x.
            N = number of instances.
            k = number of classes.
            Sum((x - M)²) = Sum of values of all (x - M)².
            M = mean for input x.

How does an LDA model make predictions?

LDA models use Bayes’ Theorem to estimate probabilities. They make predictions based upon the probability that a new input dataset belongs to each class. The class which has the highest probability is considered the output class and then the LDA makes a prediction.  

The prediction is made simply by the use of Bayes’ Theorem which estimates the probability of the output class given the input. They also make use of the probability of each class and the probability of the data belonging to each class:

P(Y=x|X=x)  = [(Plk * fk(x))] / [(sum(PlI * fl(x))]

Where x = input.
            k = output class.
            Plk = Nk/n or base probability of each class observed in the training data. It is also called prior probability in Bayes’ Theorem.
            fk(x) = estimated probability of x belonging to class k.

The f(x) is plotted using a Gaussian Distribution function and then it is plugged into the equation above and the result we get is the equation as follows:

Dk(x) = x∗(mean/Σ²) – (mean²/(2*Σ²)) + ln(PIk)

The Dk(x) is called the discriminant function for class k given input x, mean,  Σ² and Plk are all estimated from the data and the class is calculated as having the largest value, will be considered in the output classification.  

How to prepare data from LDA?

Some suggestions you should keep in mind while preparing your data to build your LDA model:

  • LDA is mainly used in classification problems where you have a categorical output variable. It allows both binary classification and multi-class classification.
  • The standard LDA model makes use of the Gaussian Distribution of the input variables. You should check the univariate distributions of each attribute and transform them into a more Gaussian-looking distribution. For example, for the exponential distribution, use log and root function and for skewed distributions use BoxCox.
  • Outliers can skew the primitive statistics used to separate classes in LDA, so it is preferable to remove them.
  • Since LDA assumes that each input variable has the same variance, it is always better to standardize your data before using an LDA model. Keep the mean to be 0 and the standard deviation to be 1.

How to implement an LDA model from scratch?

You can implement a Linear Discriminant Analysis model from scratch using Python. Let’s start by importing the libraries that are required for the model:

from sklearn.datasets import load_wine
import pandas as pd
import numpy as np
np.set_printoptions(precision=4)
from matplotlib import pyplot as plt
import seaborn as sns
sns.set()
from sklearn.preprocessing import LabelEncoder
from sklearn.tree import DecisionTreeClassifier
from sklearn.model_selection import train_test_split
from sklearn.metrics import confusion_matrix

Since we will work with the wine dataset, you can obtain it from the UCI machine learning repository. The scikit-learn library in Python provides a wrapper function for downloading it:

wine_info = load_wine()
X = pd.DataFrame(wine_info.data, columns=wine_info.feature_names)
y = pd.Categorical.from_codes(wine_info.target, wine_info.target_names)

The wine dataset comprises of 178 rows of 13 columns each:

X.shape
(178, 13)

The attributes of the wine dataset comprise of various characteristics such as alcohol content of the wine, magnesium content, color intensity, hue and many more:

X.head()

How to implement an LDA model from scratch?

The wine dataset contains three different kinds of wine:

wine_info.target_names 
array(['class_0', 'class_1', 'class_2'], dtype='<U7')

Now we create a DataFrame which will contain both the features and the content of the dataset:

df = X.join(pd.Series(y, name='class'))

We can divide the process of Linear Discriminant Analysis into 5 steps as follows:

Step 1 - Computing the within-class and between-class scatter matrices.
Step 2 - Computing the eigenvectors and their corresponding eigenvalues for the scatter matrices.
Step 3 - Sorting the eigenvalues and selecting the top k.
Step 4 - Creating a new matrix that will contain the eigenvectors mapped to the k eigenvalues.
Step 5 - Obtaining new features by taking the dot product of the data and the matrix from Step 4.

Within-class scatter matrix

To calculate the within-class scatter matrix, you can use the following mathematical expression:

Within-class scatter matrix

where, c = total number of distinct classes and

Within-class scatter matrix

Within-class scatter matrix

where, x = a sample (i.e. a row).
            n = total number of samples within a given class.

Now we create a vector with the mean values of each feature:

feature_means1 = pd.DataFrame(columns=wine_info.target_names)
for c, rows in df.groupby('class'):
feature_means1[c] = rows.mean()
feature_means1

Within-class scatter matrix

The mean vectors (mi ) are now plugged into the above equations to obtain the within-class scatter matrix:

withinclass_scatter_matrix = np.zeros((13,13))
for c, rows in df.groupby('class'):
rows = rows.drop(['class'], axis=1)

s = np.zeros((13,13))
for index, row in rows.iterrows():
x, mc = row.values.reshape(13,1),
feature_means1[c].values.reshape(13,1)

s += (x - mc).dot((x - mc).T)

withinclass_scatter_matrix += s

Between-class scatter matrix

We can calculate the between-class scatter matrix using the following mathematical expression:

Between-class scatter matrix

where,

Between-class scatter matrix

and

Between-class scatter matrix

feature_means2 = df.mean()
betweenclass_scatter_matrix = np.zeros((13,13))
for c in feature_means1:    
   n = len(df.loc[df['class'] == c].index)
   mc, m = feature_means1[c].values.reshape(13,1), 
feature_means2.values.reshape(13,1)
betweenclass_scatter_matrix += n * (mc - m).dot((mc - m).T)

Now we will solve the generalized eigenvalue problem to obtain the linear discriminants for:

eigen_values, eigen_vectors = 
np.linalg.eig(np.linalg.inv(withinclass_scatter_matrix).dot(betweenclass_scatter_matrix))

We will sort the eigenvalues from the highest to the lowest since the eigenvalues with the highest values carry the most information about the distribution of data is done. Next, we will first k eigenvectors. Finally, we will place the eigenvalues in a temporary array to make sure the eigenvalues map to the same eigenvectors after the sorting is done:

eigen_pairs = [(np.abs(eigen_values[i]), eigen_vectors[:,i]) for i in range(len(eigen_values))]
eigen_pairs = sorted(eigen_pairs, key=lambda x: x[0], reverse=True)
for pair in eigen_pairs:
print(pair[0])
237.46123198302251
46.98285938758684
1.4317197551638386e-14
1.2141209883217706e-14
1.2141209883217706e-14
8.279823065850476e-15
7.105427357601002e-15
6.0293733655173466e-15
6.0293733655173466e-15
4.737608877108813e-15
4.737608877108813e-15
2.4737196789039026e-15
9.84629525010022e-16

Now we will transform the values into percentage since it is difficult to understand how much of the variance is explained by each component.

sum_of_eigen_values = sum(eigen_values)
print('Explained Variance')
for i, pair in enumerate(eigen_pairs):
   print('Eigenvector {}: {}'.format(i, (pair[0]/sum_of_eigen_values).real))
Explained Variance
Eigenvector 0: 0.8348256799387275
Eigenvector 1: 0.1651743200612724
Eigenvector 2: 5.033396012077518e-17
Eigenvector 3: 4.268399397827047e-17
Eigenvector 4: 4.268399397827047e-17
Eigenvector 5: 2.9108789097898625e-17
Eigenvector 6: 2.498004906118145e-17
Eigenvector 7: 2.119704204950956e-17
Eigenvector 8: 2.119704204950956e-17
Eigenvector 9: 1.665567688286435e-17
Eigenvector 10: 1.665567688286435e-17
Eigenvector 11: 8.696681541121664e-18
Eigenvector 12: 3.4615924706522496e-18

First, we will create a new matrix W using the first two eigenvectors:

W_matrix = np.hstack((eigen_pairs[0][1].reshape(13,1), eigen_pairs[1][1].reshape(13,1))).real

Next, we will save the dot product of X and W into a new matrix Y:

Y = X∗W

where, X = n x d matrix with n sample and d dimensions.
            Y = n x k matrix with n sample and k dimensions.

In simple terms, Y is the new matrix or the new feature space.

X_lda = np.array(X.dot(W_matrix))

Our next work is to encode every class a member in order to incorporate the class labels into our plot. This is done because matplotlib cannot handle categorical variables directly.

Finally, we plot the data as a function of the two LDA components using different color for each class:

plt.xlabel('LDA1')
plt.ylabel('LDA2')
plt.scatter(
X_lda[:,0],
X_lda[:,1],
c=y,
cmap='rainbow',
alpha=0.7,
edgecolors='b'
)
<matplotlib.collections.PathCollection at 0x7fd08a20e908>

Between-class scatter matrix

How to implement LDA using scikit-learn?

For implementing LDA using scikit-learn, let’s work with the same wine dataset. You can also obtain it from the  UCI machine learning repository. 

You can use the predefined class LinearDiscriminant Analysis made available to us by the scikit-learn library to implement LDA rather than implementing from scratch every time:

from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
lda_model = LinearDiscriminantAnalysis()
X_lda = lda_model.fit_transform(X, y)

To obtain the variance corresponding to each component, you can access the following property:

lda.explained_variance_ratio_
array([0.6875, 0.3125])

Again, we will plot the two LDA components just like we did before:

plt.xlabel('LDA1')
plt.ylabel('LDA2')
plt.scatter(
X_lda[:,0],
X_lda[:,1],
   c=y,
cmap='rainbow',
   alpha=0.7,
edgecolors='b'
)
<matplotlib.collections.PathCollection at 0x7fd089f60358>

How to implement LDA using scikit-learn?

Linear Discriminant Analysis vs PCA

Below are the differences between LDA and PCA:

  • PCA ignores class labels and focuses on finding the principal components that maximizes the variance in a given data. Thus it is an unsupervised algorithm. On the other hand, LDA is a supervised algorithm that intends to find the linear discriminants that represents those axes which maximize separation between different classes.
  • LDA performs better multi-class classification tasks than PCA. However, PCA performs better when the sample size is comparatively small. An example would be comparisons between classification accuracies that are used in image classification.
  • Both LDA and PCA are used in case of dimensionality reduction. PCA is first followed by LDA.

Linear Discriminant Analysis vs PCA

Let us create and fit an instance of the PCA class:

from sklearn.decomposition import PCA
pca_class = PCA(n_components=2)
X_pca = pca.fit_transform(X, y)

Again, to view the values in percentage for a better understanding, we will access the explained_variance_ratio_ property:

pca.explained_variance_ratio_
array([0.9981, 0.0017])

Clearly, PCA selected the components which will be able to retain the most information and ignores the ones which maximize the separation between classes.

plt.xlabel('PCA1')
plt.ylabel('PCA2')
plt.scatter(
   X_pca[:,0],
   X_pca[:,1],
   c=y,
   cmap='rainbow',
   alpha=0.7,
   edgecolors='b

Linear Discriminant Analysis vs PCA

Now to create a classification model using the LDA components as features, we will divide the data into training datasets and testing datasets:

X_train, X_test, y_train, y_test = train_test_split(X_lda, y, random_state=1)

The next thing we will do is create a Decision Tree. Then, we will predict the category of each sample test and create a confusion matrix to evaluate the LDA model’s performance:

data = DecisionTreeClassifier()
data.fit(X_train, y_train)
y_pred = data.predict(X_test)
confusion_matrix(y_test, y_pred)
array([[18,  0,  0], 
       [ 0, 17,  0], 
       [ 0,  0, 10]])

So it is clear that the Decision Tree Classifier has correctly classified everything in the test dataset.

What are the extensions to LDA?

LDA is considered to be a very simple and effective method, especially for classification techniques. Since it is simple and well understood, so it has a lot of extensions and variations:

  • Quadratic Discriminant Analysis(QDA) – When there are multiple input variables, each of the class uses its own estimate of variance and covariance.
  • Flexible Discriminant Analysis(FDA) – This technique is performed when a non-linear combination of inputs is used as splines.
  • Regularized Discriminant Analysis(RDA) – It moderates the influence of various variables in LDA by regularizing the estimate of the covariance.

Real-Life Applications of LDA

Some of the practical applications of LDA are listed below:

  • Face Recognition – LDA is used in face recognition to reduce the number of attributes to a more manageable number before the actual classification. The dimensions that are generated are a linear combination of pixels that forms a template. These are called Fisher’s faces.
  • Medical – You can use LDA to classify the patient disease as mild, moderate or severe. The classification is done upon the various parameters of the patient and his medical trajectory. 
  • Customer Identification – You can obtain the features of customers by performing a simple question and answer survey. LDA helps in identifying and selecting which describes the properties of a group of customers who are most likely to buy a particular item in a shopping mall. 

Summary

Let us take a look at the topics we have covered in this article: 

  • Dimensionality Reduction and need for LDA 
  • Working of an LDA model 
  • Representation, Learning, Prediction and preparing data in LDA 
  • Implementation of an LDA model 
  • Implementation of LDA using scikit-learn 
  • LDA vs PCA 
  • Extensions and Applications of LDA 

The Linear Discriminant Analysis in Python is a very simple and well-understood approach of classification in machine learning. Though there are other dimensionality reduction techniques like Logistic Regression or PCA, but LDA is preferred in many special classification cases. If you want to be an expert in machine learning, knowledge of Linear Discriminant Analysis would lead you to that position effortlessly. Enrol in our  Data Science and Machine Learning Courses for more lucrative career options in this landscape and become a certified Data Scientist.

Priyankur

Priyankur Sarkar

Data Science Enthusiast

Priyankur Sarkar loves to play with data and get insightful results out of it, then turn those data insights and results in business growth. He is an electronics engineer with a versatile experience as an individual contributor and leading teams, and has actively worked towards building Machine Learning capabilities for organizations.

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Types of Probability Distributions Every Data Science Expert Should know

Data Science has become one of the most popular interdisciplinary fields. It uses scientific approaches, methods, algorithms, and operations to obtain facts and insights from unstructured, semi-structured, and structured datasets. Organizations use these collected facts and insights for efficient production, business growth, and to predict user requirements. Probability distribution plays a significant role in performing data analysis equipping a dataset for training a model. In this article, you will learn about the types of Probability Distribution, random variables, types of discrete distributions, and continuous distribution.  What is Probability Distribution? A Probability Distribution is a statistical method that determines all the probable values and possibilities that a random variable can deliver from a particular range. This range of values will have a lower bound and an upper bound, which we call the minimum and the maximum possible values.  Various factors on which plotting of a value depends are standard deviation, mean (or average), skewness, and kurtosis. All of these play a significant role in Data science as well. We can use probability distribution in physics, engineering, finance, data analysis, machine learning, etc. Significance of Probability distributions in Data Science In a way, most of the data science and machine learning operations are dependent on several assumptions about the probability of your data. Probability distribution allows a skilled data analyst to recognize and comprehend patterns from large data sets; that is, otherwise, entirely random variables and values. Thus, it makes probability distribution a toolkit based on which we can summarize a large data set. The density function and distribution techniques can also help in plotting data, thus supporting data analysts to visualize data and extract meaning. General Properties of Probability Distributions Probability distribution determines the likelihood of any outcome. The mathematical expression takes a specific value of x and shows the possibility of a random variable with p(x). Some general properties of the probability distribution are – The total of all probabilities for any possible value becomes equal to 1. In a probability distribution, the possibility of finding any specific value or a range of values must lie between 0 and 1. Probability distributions tell us the dispersal of the values from the random variable. Consequently, the type of variable also helps determine the type of probability distribution.Common Data Types Before jumping directly into explaining the different probability distributions, let us first understand the different types of probability distributions or the main categories of the probability distribution. Data analysts and data engineers have to deal with a broad spectrum of data, such as text, numerical, image, audio, voice, and many more. Each of these have a specific means to be represented and analyzed. Data in a probability distribution can either be discrete or continuous. Numerical data especially takes one of the two forms. Discrete data: They take specific values where the outcome of the data remains fixed. Like, for example, the consequence of rolling two dice or the number of overs in a T-20 match. In the first case, the result lies between 2 and 12. In the second case, the event will be less than 20. Different types of discrete distributions that use discrete data are: Binomial Distribution Hypergeometric Distribution Geometric Distribution Poisson Distribution Negative Binomial Distribution Multinomial Distribution  Continuous data: It can obtain any value irrespective of bound or limit. Example: weight, height, any trigonometric value, age, etc. Different types of continuous distributions that use continuous data are: Beta distribution Cauchy distribution Exponential distribution Gamma distribution Logistic distribution Weibull distribution Types of Probability Distribution explained Here are some of the popular types of Probability distributions used by data science professionals. (Try all the code using Jupyter Notebook) Normal Distribution: It is also known as Gaussian distribution. It is one of the simplest types of continuous distribution. This probability distribution is symmetrical around its mean value. It also shows that data at close proximity of the mean is frequently occurring, compared to data that is away from it. Here, mean = 0, variance = finite valueHere, you can see 0 at the center is the Normal Distribution for different mean and variance values. Here is a code example showing the use of Normal Distribution: from scipy.stats import norm  import matplotlib.pyplot as mpl  import numpy as np  def normalDist() -> None:      fig, ax = mpl.subplots(1, 1)      mean, var, skew, kurt = norm.stats(moments = 'mvsk')      x = np.linspace(norm.ppf(0.01),  norm.ppf(0.99), 100)      ax.plot(x, norm.pdf(x),          'r-', lw = 5, alpha = 0.6, label = 'norm pdf')      ax.plot(x, norm.cdf(x),          'b-', lw = 5, alpha = 0.6, label = 'norm cdf')      vals = norm.ppf([0.001, 0.5, 0.999])      np.allclose([0.001, 0.5, 0.999], norm.cdf(vals))      r = norm.rvs(size = 1000)      ax.hist(r, normed = True, histtype = 'stepfilled', alpha = 0.2)      ax.legend(loc = 'best', frameon = False)      mpl.show()  normalDist() Output: Bernoulli Distribution: It is the simplest type of probability distribution. It is a particular case of Binomial distribution, where n=1. It means a binomial distribution takes 'n' number of trials, where n > 1 whereas, the Bernoulli distribution takes only a single trial.   Probability Mass Function of a Bernoulli’s Distribution is:  where p = probability of success and q = probability of failureHere is a code example showing the use of Bernoulli Distribution: from scipy.stats import bernoulli  import seaborn as sb    def bernoulliDist():      data_bern = bernoulli.rvs(size=1200, p = 0.7)      ax = sb.distplot(          data_bern,           kde = True,           color = 'g',           hist_kws = {'alpha' : 1},          kde_kws = {'color': 'y', 'lw': 3, 'label': 'KDE'})      ax.set(xlabel = 'Bernouli Values', ylabel = 'Frequency Distribution')  bernoulliDist() Output:Continuous Uniform Distribution: In this type of continuous distribution, all outcomes are equally possible; each variable gets the same probability of hit as a consequence. This symmetric probabilistic distribution has random variables at an equal interval, with the probability of 1/(b-a). Here is a code example showing the use of Uniform Distribution: from numpy import random  import matplotlib.pyplot as mpl  import seaborn as sb  def uniformDist():      sb.distplot(random.uniform(size = 1200), hist = True)      mpl.show()  uniformDist() Output: Log-Normal Distribution: A Log-Normal distribution is another type of continuous distribution of logarithmic values that form a normal distribution. We can transform a log-normal distribution into a normal distribution. Here is a code example showing the use of Log-Normal Distribution import matplotlib.pyplot as mpl  def lognormalDist():      muu, sig = 3, 1      s = np.random.lognormal(muu, sig, 1000)      cnt, bins, ignored = mpl.hist(s, 80, normed = True, align ='mid', color = 'y')      x = np.linspace(min(bins), max(bins), 10000)      calc = (np.exp( -(np.log(x) - muu) **2 / (2 * sig**2))             / (x * sig * np.sqrt(2 * np.pi)))      mpl.plot(x, calc, linewidth = 2.5, color = 'g')      mpl.axis('tight')      mpl.show()  lognormalDist() Output: Pareto Distribution: It is one of the most critical types of continuous distribution. The Pareto Distribution is a skewed statistical distribution that uses power-law to describe quality control, scientific, social, geophysical, actuarial, and many other types of observable phenomena. The distribution shows slow or heavy-decaying tails in the plot, where much of the data reside at its extreme end. Here is a code example showing the use of Pareto Distribution – import numpy as np  from matplotlib import pyplot as plt  from scipy.stats import pareto  def paretoDist():      xm = 1.5        alp = [2, 4, 6]       x = np.linspace(0, 4, 800)      output = np.array([pareto.pdf(x, scale = xm, b = a) for a in alp])      plt.plot(x, output.T)      plt.show()  paretoDist() Output:Exponential Distribution: It is a type of continuous distribution that determines the time elapsed between events (in a Poisson process). Let’s suppose, that you have the Poisson distribution model that holds the number of events happening in a given period. We can model the time between each birth using an exponential distribution.Here is a code example showing the use of Pareto Distribution – from numpy import random  import matplotlib.pyplot as mpl  import seaborn as sb  def expDist():      sb.distplot(random.exponential(size = 1200), hist = True)      mpl.show()   expDist()Output:Types of the Discrete probability distribution – There are various types of Discrete Probability Distribution a Data science aspirant should know about. Some of them are – Binomial Distribution: It is one of the popular discrete distributions that determine the probability of x success in the 'n' trial. We can use Binomial distribution in situations where we want to extract the probability of SUCCESS or FAILURE from an experiment or survey which went through multiple repetitions. A Binomial distribution holds a fixed number of trials. Also, a binomial event should be independent, and the probability of obtaining failure or success should remain the same. Here is a code example showing the use of Binomial Distribution – from numpy import random  import matplotlib.pyplot as mpl  import seaborn as sb    def binomialDist():      sb.distplot(random.normal(loc = 50, scale = 6, size = 1200), hist = False, label = 'normal')      sb.distplot(random.binomial(n = 100, p = 0.6, size = 1200), hist = False, label = 'binomial')      plt.show()    binomialDist() Output:Geometric Distribution: The geometric probability distribution is one of the crucial types of continuous distributions that determine the probability of any event having likelihood ‘p’ and will happen (occur) after 'n' number of Bernoulli trials. Here 'n' is a discrete random variable. In this distribution, the experiment goes on until we encounter either a success or a failure. The experiment does not depend on the number of trials. Here is a code example showing the use of Geometric Distribution – import matplotlib.pyplot as mpl  def probability_to_occur_at(attempt, probability):      return (1-p)**(attempt - 1) * probability  p = 0.3  attempt = 4  attempts_to_show = range(21)[1:]  print('Possibility that this event will occur on the 7th try: ', probability_to_occur_at(attempt, p))  mpl.xlabel('Number of Trials')  mpl.ylabel('Probability of the Event')  barlist = mpl.bar(attempts_to_show, height=[probability_to_occur_at(x, p) for x in attempts_to_show], tick_label=attempts_to_show)  barlist[attempt].set_color('g')  mpl.show() Output:Poisson Distribution: Poisson distribution is one of the popular types of discrete distribution that shows how many times an event has the possibility of occurrence in a specific set of time. We can obtain this by limiting the Bernoulli distribution from 0 to infinity. Data analysts often use the Poisson distributions to comprehend independent events occurring at a steady rate in a given time interval. Here is a code example showing the use of Poisson Distribution from scipy.stats import poisson  import seaborn as sb  import numpy as np  import matplotlib.pyplot as mpl  def poissonDist():       mpl.figure(figsize = (10, 10))      data_binom = poisson.rvs(mu = 3, size = 5000)      ax = sb.distplot(data_binom, kde=True, color = 'g',                       bins=np.arange(data_binom.min(), data_binom.max() + 1),                       kde_kws={'color': 'y', 'lw': 4, 'label': 'KDE'})      ax.set(xlabel = 'Poisson Distribution', ylabel='Data Frequency')      mpl.show()      poissonDist() Output:Multinomial Distribution: A multinomial distribution is another popular type of discrete probability distribution that calculates the outcome of an event having two or more variables. The term multi means more than one. The Binomial distribution is a particular type of multinomial distribution with two possible outcomes - true/false or heads/tails. Here is a code example showing the use of Multinomial Distribution – import numpy as np  import matplotlib.pyplot as mpl  np.random.seed(99)   n = 12                      pvalue = [0.3, 0.46, 0.22]     s = []  p = []     for size in np.logspace(2, 3):      outcomes = np.random.multinomial(n, pvalue, size=int(size))        prob = sum((outcomes[:,0] == 7) & (outcomes[:,1] == 2) & (outcomes[:,2] == 3))/len(outcomes)      p.append(prob)      s.append(int(size))  fig1 = mpl.figure()  mpl.plot(s, p, 'o-')  mpl.plot(s, [0.0248]*len(s), '--r')  mpl.grid()  mpl.xlim(xmin = 0)  mpl.xlabel('Number of Events')  mpl.ylabel('Function p(X = K)') Output:Negative Binomial Distribution: It is also a type of discrete probability distribution for random variables having negative binomial events. It is also known as the Pascal distribution, where the random variable tells us the number of repeated trials produced during a specific number of experiments.  Here is a code example showing the use of Negative Binomial Distribution – import matplotlib.pyplot as mpl   import numpy as np   from scipy.stats import nbinom    x = np.linspace(0, 6, 70)   gr, kr = 0.3, 0.7        g = nbinom.ppf(x, gr, kr)   s = nbinom.pmf(x, gr, kr)   mpl.plot(x, g, "*", x, s, "r--") Output: Apart from these mentioned distribution types, various other types of probability distributions exist that data science professionals can use to extract reliable datasets. In the next topic, we will understand some interconnections & relationships between various types of probability distributions. Relationship between various Probability distributions – It is surprising to see that different types of probability distributions are interconnected. In the chart shown below, the dashed line is for limited connections between two families of distribution, whereas the solid lines show the exact relationship between them in terms of transformation, variable, type, etc. Conclusion  Probability distributions are prevalent among data analysts and data science professionals because of their wide usage. Today, companies and enterprises hire data science professionals in many sectors, namely, computer science, health, insurance, engineering, and even social science, where probability distributions appear as fundamental tools for application. It is essential for Data analysts and data scientists. to know the core of statistics. Probability Distributions perform a requisite role in analyzing data and cooking a dataset to train the algorithms efficiently. If you want to learn more about data science - particularly probability distributions and their uses, check out KnowledgeHut's comprehensive Data science course. 
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Top Data Analytics Certifications

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The field of data Analytics has grown more than 50 times from the early 2000s to 2021. Companies specialising in banking, healthcare, fraud detection, e-commerce, telecommunication, infrastructure and risk management hire data analysts and professionals every year in huge numbers.Need for certification:Skills are the first and foremost criteria for a job, but these skills need to be validated and recognised by reputed organisations for them to impress a potential employer. In the field of Data Analytics, it is pretty crucial to show your certifications. Hence, an employer knows you have hands-on experience in the field and can handle the workload of a real-world setting beyond just theoretical knowledge. 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SAS Academy for Data Science is a viable institute for those who want to receive proper training for the exam and use this as a basis for their career.  Prerequisites: To earn this credential, one needs to pass 5 exams, two from the SAS Certified Big Data Professional credential and three exams from the SAS Certified Advanced Analytics Professional Credential. Exam Fee: The cost for each exam is $180. (Source) An exception is Predictive Modelling using the SAS Enterprise Miner, costing $250, This exam can be taken in the English language. One can join the SAS Academy for Data Science and also take a practice exam beforehand. Salary: You can get a job as a SAS Data Analyst that pays up to $90,000 per year! (Source) 5. IBM Data Science Professional CertificateWhenever someone studies the history of a computer, IBM (International Business Machines) is the first brand that comes up. IBM is still alive and kicking, now having forayed into and becoming a major player in the Big Data segment. The IBM Data Science Professional certificate is one of the beginner-level certificates if you want to sink your hands into the world of data analysis. It shows a candidate's skills in various topics pertaining to data sciences, including various open-source tools, Python databases, SWL, data visualisation, and data methodologies.  One needs to complete nine courses to earn the certificate. It takes around three months if one works twelve hours per week. It also involves the completion of various hands-on assignments and building a portfolio. A candidate earns the Professional certificate from Coursera and a badge from IBM that recognises a candidate's proficiency in the area. Prerequisites: It is the optimal course for freshers since it requires no requisite programming knowledge or proficiency in Analytics. Exam Fee: It costs $39 per month (Source) to access the course materials and the certificate. The course is handled by the Coursera organisation. Expected Salary: This certification can earn you the title of IBM Data Scientist and help you earn a salary of $134,846 per annum. (Source) 6. Microsoft Certified Azure Data Scientist AssociateIt's one of the most well-known certifications for newcomers to step into the field of Big Data and Data analytics. This credential is offered by the leader in the industry, Microsoft Azure. This credential validates a candidate's ability to work with Microsoft Azure developing environment and proficiency in analysing big data, preparing data for the modelling process, and then progressing to designing models. One advantage of this credential is that it has no expiry date and does not need renewal; it also authorises the candidate’s extensive knowledge in predictive Analytics. Prerequisites: knowledge and experience in data science and using Azure Machine Learning and Azure Databricks. Exam Fee: It costs $165 to (Source) register for the exam. One advantage is that there is no need to attend proxy institutions to prepare for this exam, as Microsoft offers free training materials as well as an instructor-led course that is paid. There is a comprehensive collection of resources available to a candidate. Expected Salary: The job title typically offered is Microsoft Data Scientist and it typically fetches a yearly pay of $130,993.(Source) Why be a Data Analytics professional? For those already working in the field of data, being a Data Analyst is one of the most viable options. The salary of a data analyst ranges from $65,000 to $85,000 depending on number of years of experience. This lucrative salary makes it worth the investment to get a certification and advance your skills to the next level so that you can work for multinational companies by interpreting and organising data and using this analysis to accelerate businesses. These certificates demonstrate that you have the required knowledge needed to operate data models of the volumes needed by big organizations. 1. Demand is more than supply With the advent of the Information Age, there has been a huge boom in companies that either entirely or partially deal with IT. For many companies IT forms the core of their business. Every business has to deal with data, and it is crucial to get accurate insights from this data and use it to further business interests and expand profits. The interpretation of data also aims to guide them in the future to make the best business decisions.  Complex business intelligence algorithms are in place these days. They need trained professionals to operate them; since this field is relatively new, there is a shortage of experts. Thus, there are vacancies for data analyst positions with lucrative pay if one is qualified enough.2. Good pay with benefitsA data analyst is an extremely lucrative profession, with an average base pay of $71,909 (Source), employee benefits, a good work-home balance, and other perks. It has been consistently rated as being among the hottest careers of the decade and allows professionals to have a long and satisfying career.   Companies Hiring Certified Data Analytics Professionals Oracle A California based brand, Oracle is a software company that is most famous for its data solutions. With over 130000 employees and a revenue of 39 billion, it is surely one of the bigger players in Data Analytics.  MicroStrategy   Unlike its name, this company is anything but micro, with more than 400 million worth of revenue. It provides a suite of analytical products along with business mobility solutions. It is a key player in the mobile space, working natively with Android and iOS.   SAS   One of the companies in the list which provides certifications and is also without a doubt one of the largest names in the field of Big Data, machine learning and Data Analytics, is SAS. The name SAS is derived from Statistical Analysis System. This company is trusted and has a solid reputation. It is also behind the SAS Institute for Data Science. Hence, SAS is the organisation you would want to go to if you're aiming for a long-term career in data science.    Conclusion To conclude, big data and data Analytics are a field of endless opportunities. By investing in the right credential, one can pave the way to a viable and lucrative career path. Beware though, there are lots of companies that provide certifications, but only recognised and reputed credentials will give you the opportunities you are seeking. Hiring companies look for these certifications as a mark of authenticity of your hands-on experience and the amount of work you can handle effectively. Therefore, the credential you choose for yourself plays a vital role in the career you can have in the field of Data analytics.  Happy learning!    
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Top Data Analytics Certifications

What is data analytics?In the world of IT, every s... Read More

Why Should You Start a Career in Machine Learning?

If you are even remotely interested in technology you would have heard of machine learning. In fact machine learning is now a buzzword and there are dozens of articles and research papers dedicated to it.  Machine learning is a technique which makes the machine learn from past experiences. Complex domain problems can be resolved quickly and efficiently using Machine Learning techniques.  We are living in an age where huge amounts of data are produced every second. This explosion of data has led to creation of machine learning models which can be used to analyse data and to benefit businesses.  This article tries to answer a few important concepts related to Machine Learning and informs you about the career path in this prestigious and important domain.What is Machine Learning?So, here’s your introduction to Machine Learning. This term was coined in the year 1997. “A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at the tasks improves with the experiences.”, as defined in the book on ML written by Mitchell in 1997. The difference between a traditional programming and programming using Machine Learning is depicted here, the first Approach (a) is a traditional approach, and second approach (b) is a Machine Learning based approach.Machine Learning encompasses the techniques in AI which allow the system to learn automatically looking at the data available. While learning, the system tries to improve the experience without making any explicit efforts in programming. Any machine learning application follows the following steps broadlySelecting the training datasetAs the definition indicates, machine learning algorithms require past experience, that is data, for learning. So, selection of appropriate data is the key for any machine learning application.Preparing the dataset by preprocessing the dataOnce the decision about the data is made, it needs to be prepared for use. Machine learning algorithms are very susceptible to the small changes in data. To get the right insights, data must be preprocessed which includes data cleaning and data transformation.  Exploring the basic statistics and properties of dataTo understand what the data wishes to convey, the data engineer or Machine Learning engineer needs to understand the properties of data in detail. These details are understood by studying the statistical properties of data. Visualization is an important process to understand the data in detail.Selecting the appropriate algorithm to apply on the datasetOnce the data is ready and understood in detail, then appropriate Machine Learning algorithms or models are selected. The choice of algorithm depends on characteristics of data as well as type of task to be performed on the data. The choice also depends on what kind of output is required from the data.Checking the performance and fine-tuning the parameters of the algorithmThe model or algorithm chosen is fine-tuned to get improved performance. If multiple models are applied, then they are weighed against the performance. The final algorithm is again fine-tuned to get appropriate output and performance.Why Pursue a Career in Machine Learning in 2021?A recent survey has estimated that the jobs in AI and ML have grown by more than 300%. Even before the pandemic struck, Machine Learning skills were in high demand and the demand is expected to increase two-fold in the near future.A career in machine learning gives you the opportunity to make significant contributions in AI, the future of technology. All the big and small businesses are adopting Machine Learning models to improve their bottom-line margins and return on investment.  The use of Machine Learning has gone beyond just technology and it is now used in diverse industries including healthcare, automobile, manufacturing, government and more. This has greatly enhanced the value of Machine Learning experts who can earn an average salary of $112,000.  Huge numbers of jobs are expected to be created in the coming years.  Here are a few reasons why one should pursue a career in Machine Learning:The global machine learning market is expected to touch $20.83B in 2024, according to Forbes.  We are living in a digital age and this explosion of data has made the use of machine learning models a necessity. Machine Learning is the only way to extract meaning out of data and businesses need Machine Learning engineers to analyze huge data and gain insights from them to improve their businesses.If you like numbers, if you like research, if you like to read and test and if you have a passion to analyse, then machine learning is the career for you. Learning the right tools and programming languages will help you use machine learning to provide appropriate solutions to complex problems, overcome challenges and grow the business.Machine Learning is a great career option for those interested in computer science and mathematics. They can come up with new Machine Learning algorithms and techniques to cater to the needs of various business domains.As explained above, a career in machine learning is both rewarding and lucrative. There are huge number of opportunities available if you have the right expertise and knowledge. On an average, Machine Learning engineers get higher salaries, than other software developers.Years of experience in the Machine Learning domain, helps you break into data scientist roles, which is not just among the hottest careers of our generation but also a highly respected and lucrative career. Right skills in the right business domain helps you progress and make a mark for yourself in your organization. For example, if you have expertise in pharmaceutical industries and experience working in Machine learning, then you may land job roles as a data scientist consultant in big pharmaceutical companies.Statistics on Machine learning growth and the industries that use MLAccording to a research paper in AI Multiple (https://research.aimultiple.com/ml-stats/), the Machine Learning market will grow to 9 Billion USD by the end of 2022. There are various areas where Machine Learning models and solutions are getting deployed, and businesses see an overall increase of 44% investments in this area. North America is one of the leading regions in the adoption of Machine Learning followed by Asia.The Global Machine Learning market will grow by 42% which is evident from the following graph. Image sourceThere is a huge demand for Machine Learning modelling because of the large use of Cloud Based Applications and Services. The pandemic has changed the face of businesses, making them heavily dependent on Cloud and AI based services. Google, IBM, and Amazon are just some of the companies that have invested heavily in AI and Machine Learning based application development, to provide robust solutions for problems faced by small to large scale businesses. Machine Learning and Cloud based solutions are scalable and secure for all types of business.ML analyses and interprets data patterns, computing and developing algorithms for various business purposes.Advantages of Machine Learning courseNow that we have established the advantages of perusing a career in Machine Learning, let’s understand from where to start our machine learning journey. The best option would be to start with a Machine Learning course. There are various platforms which offer popular Machine Learning courses. One can always start with an online course which is both effective and safe in these COVID times.These courses start with an introduction to Machine Learning and then slowly help you to build your skills in the domain. Many courses even start with the basics of programming languages such as Python, which are important for building Machine Learning models. Courses from reputed institutions will hand hold you through the basics. Once the basics are clear, you may switch to an offline course and get the required certification.Online certifications have the same value as offline classes. They are a great way to clear your doubts and get personalized help to grow your knowledge. These courses can be completed along with your normal job or education, as most are self-paced and can be taken at a time of your convenience. There are plenty of online blogs and articles to aid you in completion of your certification.Machine Learning courses include many real time case studies which help you in understanding the basics and application aspects. Learning and applying are both important and are covered in good Machine Learning Courses. So, do your research and pick an online tutorial that is from a reputable institute.What Does the Career Path in Machine Learning Look Like?One can start their career in Machine Learning domain as a developer or application programmer. But the acquisition of the right skills and experience can lead you to various career paths. Following are some of the career options in Machine Learning (not an exhaustive list):Data ScientistA data scientist is a person with rich experience in a particular business field. A person who has a knowledge of domain, as well as machine learning modelling, is a data scientist. Data Scientists’ job is to study the data carefully and suggest accurate models to improve the business.AI and Machine Learning EngineerAn AI engineer is responsible for choosing the proper Machine Learning Algorithm based on natural language processing and neural network. They are responsible for applying it in AI applications like personalized advertising.  A Machine Learning Engineer is responsible for creating the appropriate models for improvement of the businessData EngineerA Data Engineer, as the name suggests, is responsible to collect data and make it ready for the application of Machine Learning models. Identification of the right data and making it ready for extraction of further insights is the main work of a data engineer.Business AnalystA person who studies the business and analyzes the data to get insights from it is a Business Analyst. He or she is responsible for extracting the insights from the data at hand.Business Intelligence (BI) DeveloperA BI developer uses Machine Learning and Data Analytics techniques to work on a large amount of data. Proper representation of data to suit business decisions, using the latest tools for creation of intuitive dashboards is the role of a BI developer.  Human Machine Interface learning engineerCreating tools using machine learning techniques to ease the human machine interaction or automate decisions, is the role of a Human Machine Interface learning engineer. This person helps in generating choices for users to ease their work.Natural Language Processing (NLP) engineer or developerAs the name suggests, this person develops various techniques to process Natural Language constructs. Building applications or systems using machine learning techniques to build Natural Language based applications is their main task. They create multilingual Chatbots for use in websites and other applications.Why are Machine Learning Roles so popular?As mentioned above, the market growth of AI and ML has increased tremendously over the past years. The Machine Learning Techniques are applied in every domain including marketing, sales, product recommendations, brand retention, creating advertising, understanding the sentiments of customer, security, banking and more. Machine learning algorithms are also used in emails to ease the users work. This says a lot, and proves that a career in Machine Learning is in high demand as all businesses are incorporating various machine learning techniques and are improving their business.One can harness this popularity by skilling up with Machine Learning skills. Machine Learning models are now being used by every company, irrespective of their size--small or big, to get insights on their data and use these insights to improve the business. As every company wishes to grow faster, they are deploying more machine learning engineers to get their work done on time. Also, the migration of businesses to Cloud services for better security and scalability, has increased their requirement for more Machine Learning algorithms and models to cater to their needs.Introducing the Machine learning techniques and solutions has brought huge returns for businesses.  Machine Learning solution providers like Google, IBM, Microsoft etc. are investing in human resources for development of Machine Learning models and algorithms. The tools developed by them are popularly used by businesses to get early returns. It has been observed that there is significant increase in patents in Machine Learning domains since the past few years, indicating the quantum of work happening in this domain.Machine Learning SkillsLet’s visit a few important skills one must acquire to work in the domain of Machine Learning.Programming languagesKnowledge of programming is very important for a career in Machine Learning. Languages like Python and R are popularly used to develop applications using Machine Learning models and algorithms. Python, being the simplest and most flexible language, is very popular for AI and Machine Learning applications. These languages provide rich support of libraries for implementation of Machine Learning Algorithms. A person who is good in programming can work very efficiently in this domain.Mathematics and StatisticsThe base for Machine Learning is mathematics and statistics. Statistics applied to data help in understanding it in micro detail. Many machine learning models are based on the probability theory and require knowledge of linear algebra, transformations etc. A good understanding of statistics and probability increases the early adoption to Machine Learning domain.Analytical toolsA plethora of analytical tools are available where machine learning models are already implemented and made available for use. Also, these tools are very good for visualization purposes. Tools like IBM Cognos, PowerBI, Tableue etc are important to pursue a career as a  Machine Learning engineer.Machine Learning Algorithms and librariesTo become a master in this domain, one must master the libraries which are provided with various programming languages. The basic understanding of how machine learning algorithms work and are implemented is crucial.Data Modelling for Machine Learning based systemsData lies at the core of any Machine Learning application. So, modelling the data to suit the application of Machine Learning algorithms is an important task. Data modelling experts are the heart of development teams that develop machine learning based systems. SQL based solutions like Oracle, SQL Server, and NoSQL solutions are important for modelling data required for Machine Learning applications. MongoDB, DynamoDB, Riak are some important NOSQL based solutions available to process unstructured data for Machine Learning applications.Other than these skills, there are two other skills that may prove to be beneficial for those planning on a career in the Machine Learning domain:Natural Language processing techniquesFor E-commerce sites, customer feedback is very important and crucial in determining the roadmap of future products. Many customers give reviews for the products that they have used or give suggestions for improvement. These feedbacks and opinions are analyzed to gain more insights about the customers buying habits as well as about the products. This is part of natural language processing using Machine Learning. The likes of Google, Facebook, Twitter are developing machine learning algorithms for Natural Language Processing and are constantly working on improving their solutions. Knowledge of basics of Natural Language Processing techniques and libraries is must in the domain of Machine Learning.Image ProcessingKnowledge of Image and Video processing is very crucial when a solution is required to be developed in the area of security, weather forecasting, crop prediction etc. Machine Learning based solutions are very effective in these domains. Tools like Matlab, Octave, OpenCV are some important tools available to develop Machine Learning based solutions which require image or video processing.ConclusionMachine Learning is a technique to automate the tasks based on past experiences. This is among the most lucrative career choices right now and will continue to remain so in the future. Job opportunities are increasing day by day in this domain. Acquiring the right skills by opting for a proper Machine Learning course is important to grow in this domain. You can have an impressive career trajectory as a machine learning expert, provided you have the right skills and expertise.
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Why Should You Start a Career in Machine Learning?

If you are even remotely interested in technology ... Read More