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What is the Linear Discriminant Analysis (LDA) algorithm?

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Linear Discriminant Analysis, or LDA for short, is a machine learning algorithm that can help you reduce the dimensionality of your data while preserving the essential information. In this article, you will learn what LDA is, how it works, and what are its advantages and limitations.

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Shivani Paunikar, MSBA

Data Engineer @Tucson Police Department | ASU Grad Medallion | Full Stack Developer | Snowflake Certified | BGS Member
Samira Ghodratnama, PhD

Sr AI/ML Scientist | Research Fellow | NLP, Search, Generative AI
Iqra Bismi

Data Scientist at Salesforce || MS Data Analytics, San Jose State University

1 What is LDA?

LDA is a supervised learning technique that can be used for both classification and dimensionality reduction. The main idea of LDA is to find a linear combination of features that best separates the classes in the data. LDA assumes that the data follows a multivariate normal distribution and that the classes have equal covariance matrices. LDA tries to maximize the between-class variance and minimize the within-class variance of the projected data.

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Shivani Paunikar, MSBA

Data Engineer @Tucson Police Department | ASU Grad Medallion | Full Stack Developer | Snowflake Certified | BGS Member
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Imagine you have a basket of different fruits, including apples, and oranges. You want to find a way to tell these fruits apart based on their color and size. LDA is like using a smart tool that helps you figure out the best way to separate these fruits using their features, such as color and size. It not only helps you create clear boundaries between the different types of fruits but also helps you identify the key features that contribute the most to telling them apart. In simpler terms, It's a tool that can make it easier for you to understand and distinguish between different groups, just like telling apples from oranges and bananas based on their unique qualities.

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Samira Ghodratnama, PhD

Sr AI/ML Scientist | Research Fellow | NLP, Search, Generative AI
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Linear Discriminant Analysis (LDA) is a classification and dimensionality reduction technique. It aims to find the linear combination of features that best separate multiple classes. LDA does this by maximizing the distance between the means of different classes while minimizing the spread within each class. The process involves calculating eigenvalues and eigenvectors on the scatter matrices of the classes, and then transforming the features into a lower-dimensional space for classification or further analysis.

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2 How does LDA work?

LDA works by computing the mean and covariance of each class in the data, and then using them to calculate the between-class scatter matrix and the within-class scatter matrix. These matrices measure how much the classes differ from each other and how much they vary within themselves. LDA then finds the eigenvectors and eigenvalues of the matrix product of the inverse of the within-class scatter matrix and the between-class scatter matrix. The eigenvectors are the linear discriminants that define the direction of the projection, and the eigenvalues are the scalars that indicate the importance of each linear discriminant. LDA selects the eigenvectors with the highest eigenvalues as the new features for the reduced data.

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Iqra Bismi

Data Scientist at Salesforce || MS Data Analytics, San Jose State University
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Linear Discriminant Analysis (LDA) is a dimensionality reduction and classification technique. It works by finding linear combinations of features (dimensions) that maximize the separation between classes in a dataset. LDA aims to reduce the dimensionality while preserving class-specific information, making it suitable for classification tasks. It achieves this by maximizing the between-class scatter and minimizing the within-class scatter. The result is a set of linear discriminant functions that can be used for classification, reducing the data's dimensionality while maintaining class separability.

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3 What are the advantages of LDA?

LDA has several advantages as a dimensionality reduction technique. First, it can improve the classification performance by removing irrelevant or redundant features and enhancing the class separability. Second, it can reduce the computational cost and complexity of the subsequent models by using fewer features. Third, it can help with data visualization and interpretation by providing a lower-dimensional representation of the data that preserves the class structure.

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Iqra Bismi

Data Scientist at Salesforce || MS Data Analytics, San Jose State University
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Advantages of Linear Discriminant Analysis (LDA): Dimensionality Reduction: LDA reduces the dimensionality of data while preserving class separation, which can improve model training efficiency and reduce overfitting. Enhanced Classification: LDA is particularly effective for classification tasks, as it maximizes the separation between classes, leading to better discrimination. Interpretability: LDA provides insights into feature importance and their contributions to class separation, aiding in feature selection and model interpretability. Reduction of Multicollinearity: LDA can mitigate issues related to multicollinearity by transforming data into a lower-dimensional space, improving model stability.

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4 What are the limitations of LDA?

LDA also has some limitations that you should be aware of. First, it relies on some strong assumptions about the data distribution and the class covariance matrices, which may not hold in practice. Second, it can be sensitive to outliers and noise, which can affect the estimation of the mean and covariance of each class. Third, it can suffer from the small sample size problem, which occurs when the number of features is larger than the number of observations or when the classes are imbalanced. This can lead to a singular within-class scatter matrix and invalid results.

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Iqra Bismi

Data Scientist at Salesforce || MS Data Analytics, San Jose State University
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Limitations of Linear Discriminant Analysis (LDA): Assumption of Multivariate Normality: LDA assumes that the data in each class follows a multivariate normal distribution, which may not hold in some real-world datasets. Sensitivity to Outliers: LDA is sensitive to outliers, and the presence of outliers can significantly affect its performance. Requires Sufficient Data: LDA may not perform well with small sample sizes, leading to unreliable estimates of class separability. Linearity Assumption: LDA assumes linear relationships between features, which may not capture complex, nonlinear patterns in the data.

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5 How to use LDA in Python?

One way to use LDA in Python is to use the scikit-learn library, which provides a ready-made implementation of the algorithm. You can import the LinearDiscriminantAnalysis class from the sklearn.discriminant_analysis module and create an instance of it with the desired parameters. You can then fit the LDA model to your data using the fit method and transform your data to the lower-dimensional space using the transform method. Alternatively, you can use the fit_transform method to combine both steps. Here is an example of how to use LDA in Python:

#import the library
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
#create an instance of LDA
lda = LinearDiscriminantAnalysis(n_components=2)
#fit and transform the data
X_lda = lda.fit_transform(X, y)

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6 How to evaluate LDA?

To evaluate the performance of LDA, you can use various metrics and methods depending on your goal and context. For example, if you are using LDA for classification, you can use accuracy, precision, recall, F1-score, confusion matrix, or ROC curve to measure how well the LDA model predicts the class labels. If you are using LDA for dimensionality reduction, you can use explained variance ratio, reconstruction error, or visualization techniques to assess how much information is retained and how well the classes are separated in the lower-dimensional space.

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7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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What is the Linear Discriminant Analysis (LDA) algorithm?

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7

1 What is LDA?

2 How does LDA work?

3 What are the advantages of LDA?

4 What are the limitations of LDA?

5 How to use LDA in Python?

6 How to evaluate LDA?

7 Here’s what else to consider

Machine Learning

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What is the Linear Discriminant Analysis (LDA) algorithm?

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3

4

5

6

7

1 What is LDA?

2 How does LDA work?

3 What are the advantages of LDA?

4 What are the limitations of LDA?

5 How to use LDA in Python?

6 How to evaluate LDA?

7 Here’s what else to consider

Machine Learning

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