is a data-mining technique used for classifying a set of observations into predefined classes.

Question

BlackTom AI · Accepted Answer

Discriminant analysis separates predefined groups by finding one or more linear combinations of predictor variables that best discriminate between the classes.

Relevant concepts:
- Supervised classification: assigning observations to known classes based on predictors.
- Discriminant functions: linear (LDA) or quadratic (QDA) combinations of predictors that maximize between-class separation relative to within-class variation.
- Key assumptions of classical LDA: multivariate normality and (for LDA) equal covariance matrices across classes.

Step-by-step reasoning and method (mathematical form):
1. For each class k compute the class mean vector μ_k and the pooled within-class covariance matrix S_w = Σ_k Σ_i (x_i - μ_k)(x_i - μ_k)^T.
2. Compute the between-class scatter S_b = Σ_k n_k (μ_k - μ)(μ_k - μ)^T, where μ is the overall mean and n_k are class sizes.
3. Solve the generalized eigenvalue problem S_b w = λ S_w w; for two classes this simplifies to w ∝ S_w^-1 (μ_1 - μ_2). This w is the discriminant vector.
4. Project an observation x onto w: y = w^T x. Classify x by comparing y to a threshold (often based on class priors and projected class means).
These steps show how discriminant analysis constructs explicit decision boundaries to classify observations into predefined groups.

Why the correct answer is correct:
- Discriminant analysis is explicitly designed to classify observations into known categories by maximizing separation between classes; it provides discriminant functions and decision rules directly tied to predefined classes.

Why other options are not correct:
- Logistic regression: also a classification technique modeling class probabilities via a logit link; but the question asks specifically for the data-mining technique conventionally described as classifying via discriminant functions—“Discriminant analysis” is the textbook answer. Logistic regression differs in approach (probability modeling rather than discriminant functions) and is not named “discriminant analysis.”
- k-Nearest Neighbors: a non-parametric instance-based classifier; it assigns class by neighborhood voting rather than constructing discriminant functions, so it’s not what the phrase typically denotes.
- Linear regression: predicts continuous outcomes, not classification into predefined classes, so it’s incorrect.

Conclusion: The correct choice is Discriminant analysis, as given.

is a data-mining technique used for classifying a set of observations into predefined classes.单项选择题

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