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{
"title": "Linear Discriminant Analysis Mastery: 100 MCQs",
"description": "A comprehensive set of 100 multiple-choice questions to test and deepen your understanding of Linear Discriminant Analysis (LDA), covering fundamental concepts, assumptions, discriminant functions, and applications in classification tasks.",
"questions": [
{
"id": 1,
"questionText": "What is the primary goal of Linear Discriminant Analysis (LDA)?",
"options": [
"To cluster unlabeled data",
"To find correlations between variables",
"To reduce the dimensionality of a dataset while retaining most variance",
"To fit a regression line"
],
"correctAnswerIndex": 2,
"explanation": "LDA aims to reduce dimensionality and maximize separability between known classes by projecting data onto a lower-dimensional space."
},
{
"id": 2,
"questionText": "LDA assumes that the data in each class:",
"options": [
"Has equal number of samples per class",
"Follows a Gaussian (normal) distribution",
"Has no correlation between features",
"Is uniformly distributed"
],
"correctAnswerIndex": 1,
"explanation": "LDA assumes normally distributed features for each class, which allows it to compute class-specific mean and covariance matrices for optimal separation."
},
{
"id": 3,
"questionText": "In LDA, the discriminant function is used to:",
"options": [
"Normalize the data",
"Compute the correlation between features",
"Reduce the number of features",
"Assign a class label to a sample"
],
"correctAnswerIndex": 3,
"explanation": "Discriminant functions are computed for each class, and a sample is assigned to the class with the highest score."
},
{
"id": 4,
"questionText": "Scenario: You have two classes in 3D space. LDA reduces the data to 1D. Why?",
"options": [
"Because LDA always reduces to 1D",
"To normalize the data",
"To eliminate one feature randomly",
"Because maximum class separability can be achieved in a line"
],
"correctAnswerIndex": 3,
"explanation": "LDA projects the data to a subspace that maximizes the ratio of between-class variance to within-class variance. For two classes, a 1D projection suffices."
},
{
"id": 5,
"questionText": "LDA works best when classes:",
"options": [
"Have distinct means and similar covariance matrices",
"Are highly skewed",
"Have identical data points",
"Are non-Gaussian"
],
"correctAnswerIndex": 0,
"explanation": "LDA assumes Gaussian distributions with equal covariances; distinct means allow for better class separation."
},
{
"id": 6,
"questionText": "Scenario: Two features are highly correlated. What is a likely effect on LDA?",
"options": [
"May cause redundancy but LDA can still compute projection",
"Algorithm fails",
"Produces random results",
"Features will be removed automatically"
],
"correctAnswerIndex": 0,
"explanation": "Highly correlated features can reduce LDA effectiveness slightly but the algorithm can still compute the optimal projection."
},
{
"id": 7,
"questionText": "The number of linear discriminants in LDA is at most:",
"options": [
"Number of samples",
"Number of features minus one",
"Number of features",
"Number of classes minus one"
],
"correctAnswerIndex": 3,
"explanation": "For c classes, LDA can produce at most c−1 discriminant axes."
},
{
"id": 8,
"questionText": "Scenario: LDA projection separates classes poorly. Possible reason?",
"options": [
"Output dimension is 1D",
"Too many features",
"Classes have overlapping distributions or unequal covariances",
"Data is normalized"
],
"correctAnswerIndex": 2,
"explanation": "If the assumptions of Gaussian distribution with equal covariance are violated, class separation by LDA can be poor."
},
{
"id": 9,
"questionText": "LDA is commonly used for:",
"options": [
"Classification tasks",
"Clustering",
"Regression tasks",
"Time series forecasting"
],
"correctAnswerIndex": 0,
"explanation": "LDA is primarily a classification algorithm, although it can also be used for dimensionality reduction."
},
{
"id": 10,
"questionText": "Scenario: You have 3 classes and 5 features. Maximum LDA dimensions?",
"options": [
"5",
"2",
"3",
"1"
],
"correctAnswerIndex": 1,
"explanation": "Maximum number of linear discriminants is c−1 = 3−1 = 2."
},
{
"id": 11,
"questionText": "LDA computes projections by maximizing:",
"options": [
"Sum of all variances",
"Mean of features",
"Ratio of between-class variance to within-class variance",
"Correlation coefficient"
],
"correctAnswerIndex": 2,
"explanation": "The objective of LDA is to find a projection that increases class separability, which is measured by the ratio of between-class to within-class variance."
},
{
"id": 12,
"questionText": "Scenario: You have highly overlapping classes. LDA output may be:",
"options": [
"Perfect classification",
"Normalized projections",
"Poor classification",
"Automatic clustering"
],
"correctAnswerIndex": 2,
"explanation": "When class distributions overlap significantly, LDA cannot separate them well, resulting in misclassification."
},
{
"id": 13,
"questionText": "Which of these is an assumption of LDA?",
"options": [
"Features are normally distributed per class",
"Data has missing values",
"Classes have different covariance matrices",
"Data is categorical only"
],
"correctAnswerIndex": 0,
"explanation": "LDA assumes Gaussian features for each class to compute the optimal linear projection."
},
{
"id": 14,
"questionText": "Scenario: Two features have vastly different scales. What to do before LDA?",
"options": [
"Use log transform only",
"Leave them as is",
"Standardize or normalize features",
"Remove the smaller scale feature"
],
"correctAnswerIndex": 2,
"explanation": "Scaling ensures that features contribute equally to the discriminant function."
},
{
"id": 15,
"questionText": "LDA vs PCA: key difference?",
"options": [
"Both are unsupervised",
"LDA reduces features; PCA increases features",
"Both require class labels",
"LDA is supervised; PCA is unsupervised"
],
"correctAnswerIndex": 3,
"explanation": "PCA ignores class labels and maximizes variance; LDA uses class labels to maximize separability."
},
{
"id": 16,
"questionText": "Scenario: You have two classes with very different variances. How does it affect LDA?",
"options": [
"May reduce classification performance since LDA assumes equal covariance",
"Automatically scales variances",
"Classes will merge",
"Does not affect LDA"
],
"correctAnswerIndex": 0,
"explanation": "LDA assumes equal covariance matrices for classes; large differences can reduce separability and classification accuracy."
},
{
"id": 17,
"questionText": "LDA projects data onto a lower-dimensional space using:",
"options": [
"Linear combinations of original features",
"Polynomial transformations",
"Kernel functions only",
"Random feature selection"
],
"correctAnswerIndex": 0,
"explanation": "LDA computes linear combinations of features to maximize class separability."
},
{
"id": 18,
"questionText": "Scenario: After applying LDA, one feature dominates the discriminant. Likely reason?",
"options": [
"Feature is categorical",
"Feature has much larger variance than others",
"Random initialization",
"Algorithm error"
],
"correctAnswerIndex": 1,
"explanation": "Features with larger variance can dominate projections if data is not scaled."
},
{
"id": 19,
"questionText": "Number of discriminant axes depends on:",
"options": [
"Number of samples",
"Number of features minus one",
"Number of zero-variance features",
"Number of classes minus one"
],
"correctAnswerIndex": 3,
"explanation": "Maximum number of discriminants is c−1 for c classes."
},
{
"id": 20,
"questionText": "Scenario: You have three classes with very similar means. LDA may:",
"options": [
"Perfectly separate classes",
"Remove features automatically",
"Struggle to separate classes",
"Convert data to 1D"
],
"correctAnswerIndex": 2,
"explanation": "When class means are very close, LDA finds it difficult to achieve good separability."
},
{
"id": 21,
"questionText": "In LDA, 'within-class scatter matrix' represents:",
"options": [
"Mean differences between classes",
"Variability of samples within each class",
"Distance to origin",
"Covariance of features across all samples"
],
"correctAnswerIndex": 1,
"explanation": "Within-class scatter measures how data points of the same class vary around their mean."
},
{
"id": 22,
"questionText": "In LDA, 'between-class scatter matrix' represents:",
"options": [
"Within-class variance",
"Random noise",
"Sum of all features",
"Variability of class means relative to overall mean"
],
"correctAnswerIndex": 3,
"explanation": "Between-class scatter captures how distinct the class centers are from the global mean."
},
{
"id": 23,
"questionText": "Scenario: You want to classify 4 classes. Maximum LDA dimensions?",
"options": [
"4",
"1",
"3",
"5"
],
"correctAnswerIndex": 2,
"explanation": "For c classes, maximum discriminant axes = c−1 = 4−1 = 3."
},
{
"id": 24,
"questionText": "LDA vs QDA: main difference?",
"options": [
"LDA allows nonlinear separation; QDA is linear",
"Both are unsupervised",
"QDA allows different covariance matrices per class; LDA assumes equal",
"QDA uses PCA internally"
],
"correctAnswerIndex": 2,
"explanation": "LDA assumes equal covariance matrices; QDA allows class-specific covariances for more flexible separation."
},
{
"id": 25,
"questionText": "Scenario: You have 100 features and 3 classes. LDA may:",
"options": [
"Reduce data to at most 2 dimensions",
"Fail if features exceed 50",
"Increase dimensionality",
"Remove random features"
],
"correctAnswerIndex": 0,
"explanation": "Number of LDA axes = c−1 = 2, regardless of the number of features."
},
{
"id": 26,
"questionText": "Scenario: LDA applied to two classes with equal means. Expected outcome?",
"options": [
"Cannot separate classes",
"Data transformed to zero",
"Perfect separation",
"Automatic feature selection"
],
"correctAnswerIndex": 0,
"explanation": "If class means are identical, LDA has no discriminative power to separate them."
},
{
"id": 27,
"questionText": "LDA projection maximizes:",
"options": [
"Sum of variances",
"Correlation of features",
"Between-class variance / within-class variance",
"Eigenvectors only"
],
"correctAnswerIndex": 2,
"explanation": "LDA selects projections that maximize separability measured by the ratio of between-class to within-class variance."
},
{
"id": 28,
"questionText": "Scenario: LDA applied to skewed data. Suggested preprocessing?",
"options": [
"Use raw data",
"Normalize or transform data to approximate Gaussian",
"Reduce classes to 2",
"Remove features randomly"
],
"correctAnswerIndex": 1,
"explanation": "LDA assumes Gaussian features; transforming skewed data helps satisfy assumptions."
},
{
"id": 29,
"questionText": "LDA is mainly classified as:",
"options": [
"Regression algorithm",
"Reinforcement learning",
"Supervised dimensionality reduction",
"Unsupervised clustering"
],
"correctAnswerIndex": 2,
"explanation": "LDA uses class labels to reduce dimensions while preserving class separability."
},
{
"id": 30,
"questionText": "Scenario: After LDA projection, some data points are misclassified. Likely reason?",
"options": [
"Output dimension too high",
"Overlapping distributions or violated assumptions",
"Algorithm failure",
"Features removed automatically"
],
"correctAnswerIndex": 1,
"explanation": "Misclassification occurs when class distributions overlap or LDA assumptions (normality, equal covariance) are violated."
},
{
"id": 31,
"questionText": "Scenario: You have 3 classes of flowers with 4 features each. Before applying LDA, why is standardization important?",
"options": [
"To ensure all features contribute equally to the discriminant function",
"To increase between-class variance",
"To reduce the number of classes automatically",
"To make LDA nonlinear"
],
"correctAnswerIndex": 0,
"explanation": "Standardizing features ensures that features with larger scales do not dominate the linear discriminant function."
},
{
"id": 32,
"questionText": "Scenario: You want to reduce 10-dimensional data to 2D using LDA for 3 classes. Maximum dimensions achievable?",
"options": [
"1",
"10",
"2",
"3"
],
"correctAnswerIndex": 2,
"explanation": "Maximum LDA dimensions = c−1 = 3−1 = 2."
},
{
"id": 33,
"questionText": "Scenario: Two classes with similar means but different covariances. LDA may:",
"options": [
"Reduce dimensionality to 1D",
"Perfectly separate them",
"Fail to separate classes effectively",
"Automatically detect clusters"
],
"correctAnswerIndex": 2,
"explanation": "LDA assumes equal covariances; different covariances violate this assumption and may reduce separation."
},
{
"id": 34,
"questionText": "Which matrix in LDA captures variance within each class?",
"options": [
"Between-class scatter matrix",
"Within-class scatter matrix",
"Covariance of all features",
"Correlation matrix"
],
"correctAnswerIndex": 1,
"explanation": "Within-class scatter matrix measures how samples vary within their respective classes."
},
{
"id": 35,
"questionText": "Scenario: You applied LDA and classes still overlap. Possible remedies?",
"options": [
"Reduce output dimension to 1",
"Check for assumptions violations, consider QDA or kernel LDA",
"Ignore overlapping points",
"Remove classes randomly"
],
"correctAnswerIndex": 1,
"explanation": "If assumptions are violated, alternatives like QDA or kernel LDA can handle unequal covariances or nonlinear separation."
},
{
"id": 36,
"questionText": "Scenario: LDA applied to customer data with categorical features. How to proceed?",
"options": [
"Ignore categorical features",
"Reduce classes to 2 only",
"Use raw text",
"Encode categorical features numerically before applying LDA"
],
"correctAnswerIndex": 3,
"explanation": "Categorical variables must be numerically encoded to be included in LDA."
},
{
"id": 37,
"questionText": "LDA maximizes the ratio of:",
"options": [
"Eigenvalue magnitude",
"Between-class variance to within-class variance",
"Correlation of features",
"Within-class variance to total variance"
],
"correctAnswerIndex": 1,
"explanation": "This ratio ensures optimal class separability in the projected space."
},
{
"id": 38,
"questionText": "Scenario: LDA projection of 4-class dataset onto 3D space. Number of axes used?",
"options": [
"4",
"2",
"1",
"3"
],
"correctAnswerIndex": 3,
"explanation": "For c classes, maximum LDA axes = c−1 = 4−1 = 3."
},
{
"id": 39,
"questionText": "Scenario: You observe one feature dominates LDA axis. Solution?",
"options": [
"Remove other features",
"Standardize features",
"Increase number of classes",
"Reduce output dimension"
],
"correctAnswerIndex": 1,
"explanation": "Standardization ensures all features contribute equally to discriminant axes."
},
{
"id": 40,
"questionText": "Scenario: After LDA, misclassification occurs. Likely causes?",
"options": [
"Overlapping classes, unequal covariances, or noisy data",
"LDA failure",
"Too few features",
"Too many classes"
],
"correctAnswerIndex": 0,
"explanation": "Violation of LDA assumptions or overlapping class distributions can cause misclassification."
},
{
"id": 41,
"questionText": "Scenario: You want to visualize class separation after LDA. Suggested output dimensions?",
"options": [
"At most c−1 dimensions",
"Number of samples",
"Equal to number of features",
"1D only"
],
"correctAnswerIndex": 0,
"explanation": "LDA can produce at most c−1 discriminant axes for c classes, suitable for visualization."
},
{
"id": 42,
"questionText": "Scenario: LDA is applied to a dataset with overlapping covariances. What is recommended?",
"options": [
"Consider QDA or kernel LDA for nonlinear separation",
"Reduce dataset size",
"Ignore overlapping samples",
"Use PCA instead"
],
"correctAnswerIndex": 0,
"explanation": "QDA allows different class covariances and kernel LDA can handle nonlinear separability."
},
{
"id": 43,
"questionText": "Scenario: Dataset has 1000 features and 4 classes. How many LDA axes?",
"options": [
"1000",
"2",
"3",
"4"
],
"correctAnswerIndex": 2,
"explanation": "Maximum axes = c−1 = 4−1 = 3, independent of feature count."
},
{
"id": 44,
"questionText": "Scenario: You want LDA for classification on skewed data. Recommended preprocessing?",
"options": [
"Use raw skewed data",
"Remove skewed features",
"Normalize or transform data to approximate Gaussian",
"Reduce number of classes"
],
"correctAnswerIndex": 2,
"explanation": "LDA assumes Gaussian distributions; transformation improves performance."
},
{
"id": 45,
"questionText": "Scenario: You have missing values in features. LDA requires:",
"options": [
"Leave them as NaN",
"Ignore affected samples in testing only",
"Random replacement with 0",
"Imputation or removal before applying LDA"
],
"correctAnswerIndex": 3,
"explanation": "Missing values must be handled because LDA computations require complete data."
},
{
"id": 46,
"questionText": "Scenario: LDA applied to two classes with equal means. Projection result?",
"options": [
"Perfect separation",
"No separation possible",
"Random projection",
"Automatic clustering"
],
"correctAnswerIndex": 1,
"explanation": "If class means are identical, discriminant axis cannot separate classes."
},
{
"id": 47,
"questionText": "Scenario: High-dimensional data with many features but few samples. Risk in LDA?",
"options": [
"Singular scatter matrices and overfitting",
"Perfect separation",
"Automatic feature removal",
"No impact"
],
"correctAnswerIndex": 0,
"explanation": "Few samples relative to features can make within-class scatter matrix singular, causing numerical issues."
},
{
"id": 48,
"questionText": "Scenario: You want nonlinear class separation. Standard LDA may:",
"options": [
"Work perfectly",
"Fail to separate classes; consider kernel LDA",
"Reduce output dimension to 1D",
"Automatically create new features"
],
"correctAnswerIndex": 1,
"explanation": "Standard LDA is linear; kernel LDA extends it for nonlinear boundaries."
},
{
"id": 49,
"questionText": "Scenario: Two features are highly correlated. LDA may:",
"options": [
"Merge features automatically",
"Fail completely",
"Ignore one feature",
"Produce redundant axes but still work"
],
"correctAnswerIndex": 3,
"explanation": "Highly correlated features may not add new information, but LDA can still compute discriminants."
},
{
"id": 50,
"questionText": "Scenario: You apply LDA and notice one class dominates projections. Likely cause?",
"options": [
"Class imbalance in sample sizes",
"Output dimension too high",
"Too few classes",
"Too many features"
],
"correctAnswerIndex": 0,
"explanation": "LDA assumes equal class priors; imbalance can bias the projection toward larger classes."
},
{
"id": 51,
"questionText": "Scenario: You have 5 classes, LDA reduces data to 4D. You want to visualize in 2D. Recommended approach?",
"options": [
"Reduce classes to 2",
"Use PCA instead of LDA",
"Select first two discriminant axes",
"Randomly select features"
],
"correctAnswerIndex": 2,
"explanation": "Selecting the top discriminant axes allows visualization while preserving maximum class separability."
},
{
"id": 52,
"questionText": "Scenario: Features have different units (e.g., meters and kilograms). LDA requires:",
"options": [
"Remove large-unit features",
"Convert all features to meters",
"Leave features as is",
"Standardization to make features comparable"
],
"correctAnswerIndex": 3,
"explanation": "Standardization ensures all features contribute proportionally to discriminant functions."
},
{
"id": 53,
"questionText": "Scenario: LDA misclassifies samples near class boundaries. Likely reason?",
"options": [
"Overlap in class distributions",
"Output dimension too high",
"Too few features",
"Algorithm failure"
],
"correctAnswerIndex": 0,
"explanation": "LDA cannot perfectly classify points in overlapping regions."
},
{
"id": 54,
"questionText": "Scenario: LDA applied to a dataset with nonlinear boundaries. Best alternative?",
"options": [
"QDA",
"Kernel LDA",
"PCA",
"Standard LDA"
],
"correctAnswerIndex": 1,
"explanation": "Kernel LDA handles nonlinear separations by mapping data to higher-dimensional space."
},
{
"id": 55,
"questionText": "Scenario: You want to classify emails as spam or not. Why LDA may be suitable?",
"options": [
"It ignores class labels",
"It clusters data automatically",
"It reduces dimensionality and maximizes separation of two known classes",
"It predicts numeric values"
],
"correctAnswerIndex": 2,
"explanation": "LDA is supervised and can be used for two-class classification while reducing dimensionality."
},
{
"id": 56,
"questionText": "Scenario: You have two classes with different priors. How to handle in LDA?",
"options": [
"Use class priors in discriminant function",
"Standardize features only",
"Ignore class priors",
"Reduce number of classes"
],
"correctAnswerIndex": 0,
"explanation": "Incorporating class priors prevents bias toward larger classes."
},
{
"id": 57,
"questionText": "Scenario: LDA applied after PCA pre-reduction. Advantage?",
"options": [
"Randomly removes features",
"Automatically adds classes",
"Reduces noise and computational cost while preserving discriminative features",
"Increases variance"
],
"correctAnswerIndex": 2,
"explanation": "PCA pre-reduction simplifies LDA computations and can improve stability on high-dimensional data."
},
{
"id": 58,
"questionText": "Scenario: LDA misclassifies samples at class edges. Likely cause?",
"options": [
"Output dimension too low",
"Too many features",
"Algorithm error",
"Overlap in distributions or violation of assumptions"
],
"correctAnswerIndex": 3,
"explanation": "Misclassification occurs where distributions overlap or assumptions are violated."
},
{
"id": 59,
"questionText": "Scenario: LDA applied to gene expression data with thousands of features. Recommended step?",
"options": [
"Use raw data directly",
"Reduce classes to 2",
"Remove high-expression genes only",
"Dimensionality reduction with PCA before LDA"
],
"correctAnswerIndex": 3,
"explanation": "PCA reduces high-dimensional noise and makes LDA computation feasible."
},
{
"id": 60,
"questionText": "Scenario: LDA projections differ between runs. Likely cause?",
"options": [
"Random initialization in eigen decomposition",
"Features not scaled",
"Algorithm failure",
"Too few classes"
],
"correctAnswerIndex": 0,
"explanation": "Random numerical processes in LDA can lead to slightly different projections across runs."
},
{
"id": 61,
"questionText": "Scenario: Two features perfectly correlated. LDA result?",
"options": [
"Cannot compute projection",
"Redundant axis; still works",
"Algorithm fails",
"Removes one feature automatically"
],
"correctAnswerIndex": 1,
"explanation": "Perfect correlation introduces redundancy but LDA can still compute the discriminant axis."
},
{
"id": 62,
"questionText": "Scenario: Class distributions are heavily skewed. LDA assumption?",
"options": [
"Automatic transformation occurs",
"Skewed data improves separation",
"LDA ignores distribution",
"Assumes Gaussian distributions; skewness can reduce accuracy"
],
"correctAnswerIndex": 3,
"explanation": "Skewed distributions violate the Gaussian assumption, potentially reducing LDA effectiveness."
},
{
"id": 63,
"questionText": "Scenario: LDA output used for visualization. How to select axes?",
"options": [
"Top discriminant axes based on eigenvalues",
"All features",
"First features only",
"Random axes"
],
"correctAnswerIndex": 0,
"explanation": "Eigenvalues indicate discriminative power; top axes preserve maximum class separation."
},
{
"id": 64,
"questionText": "Scenario: LDA applied on imbalanced dataset. How to improve performance?",
"options": [
"Remove smaller classes",
"Ignore imbalance",
"Use class priors or resample data",
"Reduce output dimensions"
],
"correctAnswerIndex": 2,
"explanation": "Incorporating priors or balancing data prevents bias toward larger classes."
},
{
"id": 65,
"questionText": "Scenario: LDA applied to text data (TF-IDF vectors). Recommended preprocessing?",
"options": [
"Use raw counts without scaling",
"Remove class labels",
"Feature scaling or normalization",
"Randomly select words"
],
"correctAnswerIndex": 2,
"explanation": "Scaling ensures different term frequencies contribute proportionally to discriminant function."
},
{
"id": 66,
"questionText": "Scenario: LDA for multi-class image classification. Which is true?",
"options": [
"LDA increases feature dimensions",
"Maximum axes = c−1; use top axes for visualization or classifier",
"Automatically converts to binary classes",
"Does not require labels"
],
"correctAnswerIndex": 1,
"explanation": "LDA produces at most c−1 axes; top axes can be used for classification or visualization."
},
{
"id": 67,
"questionText": "Scenario: After LDA, two classes overlap. Which action helps?",
"options": [
"Reduce output dimensions",
"Check assumptions, consider kernel LDA or QDA",
"Remove overlapping points",
"Use PCA only"
],
"correctAnswerIndex": 1,
"explanation": "Violations of LDA assumptions may require alternative methods like kernel LDA or QDA."
},
{
"id": 68,
"questionText": "Scenario: LDA applied to numeric data only. Why?",
"options": [
"Categorical data works directly",
"Algorithm ignores numeric values",
"LDA requires numeric input for linear combination computation",
"LDA converts numeric to categorical automatically"
],
"correctAnswerIndex": 2,
"explanation": "Linear combinations require numeric values; categorical features must be encoded numerically."
},
{
"id": 69,
"questionText": "Scenario: LDA applied to overlapping classes. Performance metric?",
"options": [
"Scatter plot only",
"Variance only",
"Eigenvalues only",
"Classification accuracy, confusion matrix, or F1-score"
],
"correctAnswerIndex": 3,
"explanation": "Use standard classification metrics to evaluate LDA performance on overlapping classes."
},
{
"id": 70,
"questionText": "Scenario: LDA applied on high-dimensional dataset with noisy features. Suggested approach?",
"options": [
"Increase output dimensions",
"Apply PCA before LDA to reduce noise and dimensionality",
"Use raw data directly",
"Remove labels"
],
"correctAnswerIndex": 1,
"explanation": "PCA helps reduce noise and computational complexity before applying LDA on high-dimensional data."
},
{
"id": 71,
"questionText": "Scenario: You apply LDA on a dataset with 5 classes, but class 4 has only 2 samples. Likely issue?",
"options": [
"Within-class scatter matrix may become singular, causing numerical instability",
"LDA perfectly separates all classes",
"Algorithm will automatically remove the class",
"No impact since LDA ignores class size"
],
"correctAnswerIndex": 0,
"explanation": "Very few samples in a class can make the within-class scatter matrix singular, leading to computation problems."
},
{
"id": 72,
"questionText": "Scenario: After LDA, two classes are misclassified even though they have distinct means. Possible reason?",
"options": [
"Algorithm failed randomly",
"Too many features",
"Overlap in covariance structure violates LDA assumptions",
"Output dimensions too high"
],
"correctAnswerIndex": 2,
"explanation": "Distinct means alone do not guarantee separation; LDA assumes equal covariance matrices across classes."
},
{
"id": 73,
"questionText": "Scenario: You want to classify high-dimensional gene expression data with 3 classes. LDA fails. Recommended approach?",
"options": [
"Use LDA directly without preprocessing",
"Reduce the number of classes to 2",
"Apply PCA first to reduce dimensionality, then LDA",
"Remove high-variance genes only"
],
"correctAnswerIndex": 2,
"explanation": "High-dimensional data can lead to singular matrices; PCA reduces dimensionality and noise, stabilizing LDA."
},
{
"id": 74,
"questionText": "Scenario: Two classes with similar means but different covariance. LDA vs QDA?",
"options": [
"LDA is better since it assumes equal covariance",
"Both perform equally",
"QDA will perform better as it allows class-specific covariances",
"Neither works"
],
"correctAnswerIndex": 2,
"explanation": "QDA handles unequal covariances, whereas LDA assumes equality, which may cause misclassification."
},
{
"id": 75,
"questionText": "Scenario: You apply LDA to image data and notice one axis dominates classification. Likely cause?",
"options": [
"Feature variance imbalance; need normalization",
"Too many classes",
"Algorithm failure",
"Output dimension too low"
],
"correctAnswerIndex": 0,
"explanation": "Features with larger variance dominate projections if data is not scaled."
},
{
"id": 76,
"questionText": "Scenario: Applying LDA to text classification with sparse TF-IDF features. Recommended preprocessing?",
"options": [
"Dimensionality reduction (PCA or SVD) before LDA",
"Use raw sparse data",
"Remove class labels",
"Randomly sample features"
],
"correctAnswerIndex": 0,
"explanation": "Sparse high-dimensional data can cause numerical instability; PCA or SVD reduces dimensions before LDA."
},
{
"id": 77,
"questionText": "Scenario: After LDA, some minority class samples are misclassified. How to improve?",
"options": [
"Ignore minority class",
"Increase output dimensions",
"Use class priors or resampling techniques",
"Randomly merge classes"
],
"correctAnswerIndex": 2,
"explanation": "Incorporating class priors or oversampling minority class balances the discriminant function."
},
{
"id": 78,
"questionText": "Scenario: Two classes perfectly linearly separable. How does LDA behave?",
"options": [
"Cannot compute scatter matrices",
"Fails since overlap is zero",
"Finds the optimal linear projection maximizing separation",
"Randomly assigns projections"
],
"correctAnswerIndex": 2,
"explanation": "LDA works best when linear separation exists; it identifies a projection that maximizes separation."
},
{
"id": 79,
"questionText": "Scenario: You have four classes and high feature correlation. LDA produces redundant axes. Solution?",
"options": [
"Use raw features",
"Apply PCA before LDA to remove redundancy",
"Randomly remove features",
"Reduce number of classes"
],
"correctAnswerIndex": 1,
"explanation": "PCA can decorrelate features, reducing redundancy and improving LDA projections."
},
{
"id": 80,
"questionText": "Scenario: LDA applied to dataset with skewed distributions. Result?",
"options": [
"Reduced accuracy due to violated Gaussian assumption",
"Perfect classification",
"Automatic feature scaling",
"Increased dimensionality"
],
"correctAnswerIndex": 0,
"explanation": "LDA assumes normal distribution; skewness violates this, affecting performance."
},
{
"id": 81,
"questionText": "Scenario: LDA applied to two classes, but one feature is categorical with three levels. How to proceed?",
"options": [
"Use raw categorical values",
"Ignore the categorical feature",
"Encode categorical feature numerically before LDA",
"Remove class labels"
],
"correctAnswerIndex": 2,
"explanation": "Categorical features must be numerically encoded to compute linear combinations in LDA."
},
{
"id": 82,
"questionText": "Scenario: Applying LDA to imbalanced dataset causes bias toward majority class. Fix?",
"options": [
"Increase output dimensions",
"Reduce features",
"Use class priors or resample minority classes",
"Ignore imbalance"
],
"correctAnswerIndex": 2,
"explanation": "Adjusting priors or balancing data prevents biased projections."
},
{
"id": 83,
"questionText": "Scenario: You want nonlinear boundaries between classes. Standard LDA?",
"options": [
"Fails; consider kernel LDA or QDA",
"Reduces dimensions automatically",
"Performs perfectly",
"Removes overlapping points"
],
"correctAnswerIndex": 0,
"explanation": "Standard LDA is linear; kernel LDA extends it to nonlinear separations."
},
{
"id": 84,
"questionText": "Scenario: After LDA, eigenvalues of some discriminant axes are near zero. Interpretation?",
"options": [
"Remove features randomly",
"Axis contributes little to class separation",
"Algorithm failure",
"Data has missing values"
],
"correctAnswerIndex": 1,
"explanation": "Low eigenvalue axes have low discriminative power and may be ignored."
},
{
"id": 85,
"questionText": "Scenario: You have 10 classes and 1000 features. LDA reduces to 9D. You want 2D visualization. How?",
"options": [
"Randomly select 2 axes",
"Use PCA only",
"Reduce classes to 2",
"Select top 2 discriminant axes based on eigenvalues"
],
"correctAnswerIndex": 3,
"explanation": "Top eigenvalue axes preserve maximum class separation in reduced dimensions."
},
{
"id": 86,
"questionText": "Scenario: LDA misclassifies boundary samples consistently. Cause?",
"options": [
"Output dimension too high",
"Too many features",
"Overlap in class distributions",
"Algorithm error"
],
"correctAnswerIndex": 2,
"explanation": "Misclassification occurs where class distributions overlap."
},
{
"id": 87,
"questionText": "Scenario: High-dimensional LDA suffers from singular within-class scatter matrix. Solution?",
"options": [
"Increase sample size only",
"Apply PCA or regularization before LDA",
"Remove features randomly",
"Reduce number of classes"
],
"correctAnswerIndex": 1,
"explanation": "Dimensionality reduction or regularization stabilizes matrix inversion."
},
{
"id": 88,
"questionText": "Scenario: After LDA, two classes overlap in projection. Next step?",
"options": [
"Ignore problem",
"Increase output dimension",
"Remove overlapping points",
"Check assumptions, consider kernel LDA or QDA"
],
"correctAnswerIndex": 3,
"explanation": "Alternative methods handle unequal covariance or nonlinear separability."
},
{
"id": 89,
"questionText": "Scenario: LDA applied to numeric and binary features. Action?",
"options": [
"Remove numeric features",
"Apply PCA only",
"Ignore binary features",
"Standardize numeric features, encode binary features numerically"
],
"correctAnswerIndex": 3,
"explanation": "All features must be numeric to compute linear discriminant functions."
},
{
"id": 90,
"questionText": "Scenario: LDA applied to a 3-class dataset. Number of discriminant axes?",
"options": [
"Depends on features",
"3",
"2",
"1"
],
"correctAnswerIndex": 2,
"explanation": "Maximum axes = c−1 = 3−1 = 2."
},
{
"id": 91,
"questionText": "Scenario: LDA applied with noisy features. Best practice?",
"options": [
"Use raw features",
"Remove minority classes",
"Increase output dimension",
"Apply PCA or feature selection before LDA"
],
"correctAnswerIndex": 3,
"explanation": "Reducing noise and dimensionality improves LDA stability."
},
{
"id": 92,
"questionText": "Scenario: Two classes with identical covariances and means. LDA outcome?",
"options": [
"Perfect separation",
"Cannot separate classes",
"Random projections",
"Removes features automatically"
],
"correctAnswerIndex": 1,
"explanation": "No difference in mean or covariance means LDA has no discriminative power."
},
{
"id": 93,
"questionText": "Scenario: LDA applied on imbalanced dataset with rare class. How to handle?",
"options": [
"Ignore imbalance",
"Remove majority class",
"Reduce number of classes",
"Use class priors or oversample rare class"
],
"correctAnswerIndex": 3,
"explanation": "Balancing class sizes prevents biased discriminant functions."
},
{
"id": 94,
"questionText": "Scenario: After LDA, projections of classes are not aligned with original features. Why?",
"options": [
"Normalization failed",
"Discriminant axes are linear combinations, not original features",
"Algorithm error",
"Random initialization"
],
"correctAnswerIndex": 1,
"explanation": "LDA axes are combinations of features to maximize separability."
},
{
"id": 95,
"questionText": "Scenario: LDA applied to high-dimensional text dataset. Why PCA first?",
"options": [
"Convert text to binary",
"Remove labels",
"Increase class separation automatically",
"Reduce noise and dimensionality, improve numerical stability"
],
"correctAnswerIndex": 3,
"explanation": "High-dimensional sparse data can cause singular matrices; PCA helps."
},
{
"id": 96,
"questionText": "Scenario: LDA applied to two classes with unequal priors. How to proceed?",
"options": [
"Ignore priors",
"Remove minority class",
"Reduce output dimensions",
"Incorporate priors in discriminant function"
],
"correctAnswerIndex": 3,
"explanation": "Incorporating priors prevents bias toward larger class."
},
{
"id": 97,
"questionText": "Scenario: You want to visualize 5-class dataset in 2D using LDA. Max axes?",
"options": [
"4 axes; select top 2 for visualization",
"Depends on features",
"5 axes",
"2 axes only"
],
"correctAnswerIndex": 0,
"explanation": "Maximum axes = c−1 = 5−1 = 4; top 2 axes can be used for visualization."
},
{
"id": 98,
"questionText": "Scenario: LDA misclassifies samples near overlapping region. Best evaluation metric?",
"options": [
"Eigenvalue magnitude",
"Scatter plot",
"Variance only",
"Confusion matrix, precision, recall, or F1-score"
],
"correctAnswerIndex": 3,
"explanation": "Classification metrics are needed to evaluate performance on overlapping regions."
},
{
"id": 99,
"questionText": "Scenario: LDA applied on dataset with outliers. Recommended step?",
"options": [
"Ignore outliers",
"Increase number of classes",
"Reduce output dimensions",
"Detect and remove or transform outliers before LDA"
],
"correctAnswerIndex": 3,
"explanation": "Outliers can distort mean and covariance, affecting discriminant functions."
},
{
"id": 100,
"questionText": "Scenario: LDA applied to 3-class dataset with 50 features. Within-class scatter matrix is singular. Cause?",
"options": [
"Features too independent",
"Number of features > number of samples per class",
"Output dimension too high",
"Algorithm error"
],
"correctAnswerIndex": 1,
"explanation": "When features exceed sample count, the within-class scatter matrix becomes singular, requiring dimensionality reduction or regularization."
}
]
}
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