Question-3

Which of the following is the most appropriate description of the method used in PCA to achieve dimensionality reduction?

• PCA achieves this by discarding a random subset of features in the dataset
• PCA achieves this by selecting those features in the dataset along which the variance of the dataset is maximised
• PCA achieves this by looking for those directions in the feature space along which the variance of the dataset is maximised
• PCA achieves this by retaining the those features in the dataset along which the variance of the dataset is minimised

Answer

• PCA achieves this by discarding a random subset of features in the dataset
• PCA achieves this by selecting those features in the dataset along which the variance of the dataset is maximised
• PCA achieves this by looking for those directions in the feature space along which the variance of the dataset is maximised
• PCA achieves this by retaining the those features in the dataset along which the variance of the dataset is minimised

Solution

PCA looks for a new set of directions in feature space such that the first few directions capture the maximum variance in the data. It does this by re-orienting the feature axes, which can be thought of as rotating the axes in the feature space.