{
  "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."
    }
  ]
}