Projecting a multi-dimensional dataset onto which vector has the greatest variance?

The correct answer is A. first principal component. The method based on principal component analysis (PCA) evaluates the features according to the projection of the largest eigenvector of the correlation matrix on the initial dimensions, the method based on Fisher's linear discriminant analysis evaluates. Them according to the…

Feature Engineering and Dimensionality Reduction

Question

Options

Afirst principal component
Bfirst eigenvector
Cnot enough information given to answer
Dsecond eigenvector
Esecond principal component

How the community answered

(41 responses)

A
80% (33)
B
10% (4)
C
5% (2)
D
2% (1)
E
2% (1)

Explanation

The method based on principal component analysis (PCA) evaluates the features according to the projection of the largest eigenvector of the correlation matrix on the initial dimensions, the method based on Fisher's linear discriminant analysis evaluates. Them according to the magnitude of the components of the discriminant vector. The first principal component corresponds to the greatest variance in the data, by definition. If we project the data onto the first principal component line, the data is more spread out (higher variance) than if projected onto any other line, including other principal components.

Topics

#PCA#principal components#dimensionality reduction#variance maximization

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