Success TrackerSuccess Tracker
Log inSign up

GATE DA 2025 Set 1 — Question 55

Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.
MSQ+2 / -0MediumEuclidean Distance & MetricsVector AlgebraLinear AlgebraClassificationMachine Learning

Linear Algebra → Classification → Euclidean Distance & Metrics

Last updated

Question

Consider a two-class problem in Rd\mathbb{R}^d with class labels red and green. Let μred\mu_{red} and μgreen\mu_{green} be the means of the two classes. Given test sample x∈Rdx \in \mathbb{R}^d, a classifier calculates the squared Euclidean distance (denoted by ∥⋅∥2\| \cdot \|^2) between xx and the means of the two classes and assigns the class label that the sample xx is closest to. That is, the classifier computesf(x)=∥μred−x∥2−∥μgreen−x∥2f(x) = \|\mu_{red} - x\|^2 - \|\mu_{green} - x\|^2and assigns the label red to xx if f(x)<0f(x) < 0, and green otherwise. Which of the following statements is/are correct?
Your answer

Select all that apply, 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 Classification

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…