How does the term "principal component analysis" (PCA) contribute to dimensionality reduction in data analysis?By clustering similar data points togetherBy transforming features into a lower-dimensional spaceBy creating new features based on existing onesBy evaluating feature importance

Principal Component Analysis (PCA) contributes to dimensionality reduction in data analysis primarily by transforming features into a lower-dimensional space. Here's a step-by-step explanation:

1. Standardization: PCA starts by standardizing the range of the continuous initial variables so that each one of them contributes equally to the analysis.

2. Covariance Matrix computation: PCA then constructs a covariance matrix that measures the correlation between different variables.

3. Computation of Eigenvectors and Eigenvalues: The next step involves computing the eigenvectors and eigenvalues of the covariance matrix. Eigenvectors represent the directions or components for the reduced subspace of the dataset, whereas eigenvalues represent the magnitude for the directions.

4. Sorting and selecting k eigenvectors: The eigenvectors are then sorted by decreasing eigenvalues and choose the first k eigenvectors, which results in a k-dimensional data space (k < n).

5. Transforming the original dataset: Finally, PCA transforms the original n-dimensional data set to a new k-dimensional data set.

So, PCA does not cluster similar data points together, create new features based on existing ones, or evaluate feature importance. Instead, it transforms the original high-dimensional data into a lower-dimensional space, making it easier to analyze and visualize.