Success TrackerSuccess Tracker
Log inSign up

GATE DA 2024 Set 1 — Question 22

Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.
MCQ+1 / -0.33MediumLinear Discriminant Analysis (LDA)Dimensionality ReductionMachine LearningEigenvalue ComputationEigenvalues & EigenvectorsLinear Algebra

Linear Algebra → Dimensionality Reduction → Eigenvalue Computation

Last updated

Question

For any binary classification dataset, let SB∈Rd×dS_B \in \mathbb{R}^{d \times d} and SW∈Rd×dS_W \in \mathbb{R}^{d \times d} be the between-class and within-class scatter (covariance) matrices, respectively. The Fisher linear discriminant is defined by u∗∈Rdu^* \in \mathbb{R}^d, that maximizes J(u)=uTSBuuTSWuJ(u) = \frac{u^T S_B u}{u^T S_W u}If λ=J(u∗)\lambda = J(u^*), SWS_W is non-singular and SB≠0S_B \neq 0, then (u∗,λ)(u^*, \lambda) must satisfy which ONE of the following equations?
Note: R\mathbb{R} denotes the set of real numbers.
Your answer

Choose one option, then check your answer.

The solution stays hidden until you check.

Continue learning with Success Tracker

A step still unclear? Work through it with support

Use Success Tracker to ask about the reasoning, then try another GATE DA question to check your understanding.

AI-powered practice· Unlimited practice on eligible plans
PYQs with solutions
Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
Practice that adapts
Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
AI doubt support
Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.

Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.

Start with a free accountView plans and allowances

This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.

More questions on Dimensionality Reduction

2026 Set 1 Q11For a classification problem, Principal Component Analysis (PCA) has been used to reduce the…2026 Set 1 Q12Consider that you are training a classifier for a 10-class classification problem. Each input is…2026 Set 1 Q21Let M=(cos⁡θ−sin⁡θsin⁡θcos⁡θ)M = \begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix} be…2026 Set 1 Q22Consider a set S1={x=(x1,x2,x3)T∈R3∣xTx≤16}S_1 = \{x = (x_1, x_2, x_3)^T \in \mathbb{R}^3 \mid x^T x \leq 16\}. Let S2S_2 be…2026 Set 1 Q23In the following table, the Task column lists a few tasks related to machine learning. The…