Introduction to Linear Discriminant Analysis (LDA) Answers 1. What is one of the main advantages of using LDA in high-dimensional data? A. Increased computational cost B. Effective dimensionality reduction C. Sensitivity to outliers D. Requires large training sets Answer: Effective dimensionality reduction (B) LDA is effective in reducing dimensionality, which helps to improve algorithm performance. 2. Which assumption does LDA make about the class-conditional data distributions? A. They are Gaussian distributions B. They are uniform distributions C. They are binomial distributions D. They are Poisson distributions Answer: They are Gaussian distributions (A) LDA assumes that the class-conditional data distributions are Gaussian, impacting its performance if this assumption is incorrect. 3. How does LDA classify new data points? A. By calculating the distance to class means in the projected space B. By selecting the most distant class mean C. By averaging the features of all available classes D. By minimizing the sum of squared distances to all class means Answer: By calculating the distance to class means in the projected space (A) New data points are classified by calculating the distance to the class means in the projected space. 4. What is a significant drawback of using LDA? A. Assumes a linear relationship between features B. Does not perform well with missing data C. Sensitive to the scaling of features D. Requires normalized data Answer: Sensitive to the scaling of features (C) LDA is sensitive to feature scaling, making it important to scale features properly to avoid undue influence on the results. 5. In what context is LDA commonly applied? A. Unsupervised learning B. Time series analysis C. Regression problems D. Image recognition tasks Answer: Image recognition tasks (D) LDA is used in classification tasks including image recognition, making it versatile for various applications. 6. How does QDA differ from LDA? A. QDA uses a single covariance matrix for all classes B. QDA is a non-probabilistic method C. QDA allows for varying covariance matrices between classes D. QDA is fundamentally simpler to implement Answer: QDA allows for varying covariance matrices between classes (C) QDA differs from LDA by allowing different covariance matrices for each class, improving performance in certain scenarios. 7. What is the primary focus of LDA as opposed to linear regression? A. Class separation and discrimination B. Estimating class probabilities C. Identifying relationships between variables D. Predicting continuous outcomes Answer: Class separation and discrimination (A) LDA focuses on class separation while linear regression aims to identify relationships between variables. 8. What aspect of data do LDA methodologies help to highlight during feature selection? A. Features that are least related to outcomes B. Outliers that mislead classifications C. Redundant features with high variance D. Features that discriminate effectively between classes Answer: Features that discriminate effectively between classes (D) LDA highlights features that most effectively discriminate between different classes, aiding in feature selection. 9. What is the primary goal of Linear Discriminant Analysis (LDA)? A. To create new classes based on hidden patterns in the data B. To identify nonlinear relationships between features C. To maximize separation between different classes and minimize variance within classes D. To maximize variance within each class Answer: To maximize separation between different classes and minimize variance within classes (C) The main aim of LDA is to maximize the separation between different classes while minimizing the variance within each class. 10. Which method does LDA often utilize for estimating its parameters? A. Ordinary least squares B. Gradient descent C. Bayesian inference D. Maximum likelihood estimation Answer: Maximum likelihood estimation (D) LDA parameters are commonly estimated using maximum likelihood estimation, which fits the data according to a probability model. 11. Which of the following is an assumption of LDA? A. Equal covariance matrices for each class B. Classes have different measurement scales C. Data follows a binomial distribution D. Classes have unequal means Answer: Equal covariance matrices for each class (A) One of LDA's assumptions is that each class has an equal covariance matrix, which simplifies calculations. 12. What role does Fisher's Linear Discriminant play in LDA? A. It defines the class probabilities after transformation B. It measures the total variance of the dataset C. It calculates the eigenvalues of the covariance matrices D. It determines the transformation direction to maximize class separation Answer: It determines the transformation direction to maximize class separation (D) Fisher's Linear Discriminant is used to find the optimal projection that maximizes the separation between class means. 13. What does LDA use to handle the dispersion within classes during calculation? A. Class distribution matrix B. Within-class scatter matrix C. Between-class centroid matrix D. Total variance matrix Answer: Within-class scatter matrix (B) LDA first calculates the within-class scatter matrix, which represents the spread of data points within each class. 14. How does LDA approach dimensionality reduction? A. By eliminating features with high multicollinearity B. By clustering similar data points together C. By averaging feature values across all classes D. By projecting data points into lower-dimensional space using optimal directions Answer: By projecting data points into lower-dimensional space using optimal directions (D) LDA reduces dimensionality by finding optimal directions that best separate classes and projecting data into a lower-dimensional space. 15. In what manner can LDA also function aside from dimensionality reduction? A. As a probabilistic classification model B. As a regression model to predict continuous outcomes C. As an unsupervised clustering algorithm D. As a feature selection method Answer: As a probabilistic classification model (A) LDA can function as a classification model by calculating class probabilities to classify new data points after transformation. 16. What does the between-class scatter matrix represent in LDA? A. Overall variance across all classes combined B. Measurement of data points that fall outside expected ranges C. Dispersion within individual classes D. Separation between multiple classes based on their means Answer: Separation between multiple classes based on their means (D) The between-class scatter matrix in LDA is calculated based on the overall means of the classes and represents the separation between them.