Question

Which of the following statements about Principal Component Analysis (PCA) is CORRECT?

• A. \( \text{A two-dimensional data set can have up to four principal components} \)
• B. \( \text{The first principal component accounts for the majority of conceivable data variation} \)
• C. \( \text{The second principal component attempts to encapsulate the mode of the data} \)
• D. \( \text{The transformed principal components are non-linear combinations of the original variables} \)

Hint:

Remember that PCA aims to find the directions (principal components) that explain the most spread in the data.

Answer 1

The Correct Option is B

Principal Component Analysis (PCA) is a dimensionality reduction technique. \begin{itemize} \item The number of principal components that can be extracted from a dataset is equal to the number of its original variables (or the number of samples, whichever is smaller). Thus, a two-dimensional dataset can have up to two principal components. \item The first principal component is derived in such a way that it captures the largest possible variance in the dataset. Subsequent principal components capture the remaining variance in decreasing order. \item The second principal component captures the next largest variance, orthogonal to the first. It doesn't specifically target the 'mode' of the data. \item Principal components are linear combinations of the original variables, with coefficients (eigenvectors) that determine the contribution of each original variable to each principal component. \end{itemize}