In Principal Components Analysis, each new component is constructed to be uncorrelated with the previous ones.

In Principal Components Analysis, each new component is constructed to be uncorrelated with the previous ones.

• A. Orthogonality
• B. Principal Components Analysis (PCA)
• C. Data Transformation
• D. Normalization (Min-Max)

Answer: (B)

The main idea is that PCA constructs new variables that are uncorrelated by projecting the data onto orthogonal directions. These directions, or principal components, are obtained as eigenvectors of the data's covariance matrix, so they are orthogonal to each other. Because the directions are orthogonal and the data are centered (and often scaled), the covariance between different principal components is zero, which means they are uncorrelated. This is why the method itself is the best fit here: PCA is specifically designed to produce uncorrelated components by using those orthogonal, variance-ordered directions. Orthogonality describes the resulting property, not the method; normalization is just scaling, and data transformation is too broad to capture the specific uncorrelated-component goal.

The main idea is that PCA constructs new variables that are uncorrelated by projecting the data onto orthogonal directions. These directions, or principal components, are obtained as eigenvectors of the data's covariance matrix, so they are orthogonal to each other. Because the directions are orthogonal and the data are centered (and often scaled), the covariance between different principal components is zero, which means they are uncorrelated. This is why the method itself is the best fit here: PCA is specifically designed to produce uncorrelated components by using those orthogonal, variance-ordered directions. Orthogonality describes the resulting property, not the method; normalization is just scaling, and data transformation is too broad to capture the specific uncorrelated-component goal.