Explain Principal Component Analysis. What are its disadvantages?

Question Analysis

The question asks you to explain Principal Component Analysis (PCA), which is a fundamental technique in machine learning and statistics. It also requires you to identify and explain the disadvantages of PCA. This indicates that the interviewer is assessing your understanding of PCA, its applications, and its limitations. A solid answer should cover what PCA is, how it works, and end with a discussion on its disadvantages.

Answer

Principal Component Analysis (PCA):

• Definition: PCA is a dimensionality reduction technique used to reduce the number of variables in a dataset while preserving as much variance as possible.
• How it Works:
  • Step 1: Standardize the data if variables have different units or scales.
  • Step 2: Compute the covariance matrix to understand how variables relate to each other.
  • Step 3: Calculate the eigenvalues and eigenvectors of the covariance matrix to identify the principal components.
  • Step 4: Sort the eigenvectors by decreasing eigenvalues and choose the top k eigenvectors to form a new feature space.
  • Step 5: Transform the original data into this new feature space, reducing the dimensionality.

Disadvantages of PCA:

• Interpretability: PCA can make data interpretation more difficult because the new principal components are linear combinations of the original variables, which may not have a clear meaning.
• Linear Assumption: PCA assumes linear relationships among variables, limiting its application to data with non-linear relationships.
• Data Scaling: PCA is sensitive to the relative scaling of the original variables, which may necessitate careful data preprocessing.
• Information Loss: While PCA aims to preserve variance, some information is inevitably lost, particularly if a large reduction in dimensionality is performed.
• Sensitivity to Outliers: PCA is sensitive to outliers, which can significantly affect the principal components.

In summary, PCA is a powerful tool for reducing dimensionality, but one must be aware of its limitations and ensure it is suitable for the specific dataset and analysis goals.