The correct answer is: A. transform data to zero mean.
PCA (Principal Component Analysis) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. The number of principal components is less than or equal to the number of original variables.
SVD (Singular Value Decomposition) is a mathematical technique that decomposes a matrix into three matrices: a unitary matrix, a diagonal matrix of singular values, and another unitary matrix. The singular values are non-negative real numbers, and they are arranged in decreasing order.
The first principal component of a data set is the projection of the data onto the direction of the largest singular value of the covariance matrix of the data. The second principal component is the projection of the data onto the direction of the second largest singular value of the covariance matrix of the data, and so on.
In order to get the same projection as SVD in PCA, we need to transform the data to zero mean. This is because the covariance matrix of the data is equal to the correlation matrix of the data plus the identity matrix times the variance of the data. The variance of the data is equal to the sum of the squares of the singular values of the covariance matrix of the data.
If we transform the data to zero mean, then the covariance matrix of the data will be equal to the correlation matrix of the data. This means that the first principal component of the data will be the projection of the data onto the direction of the largest singular value of the correlation matrix of the data. The second principal component of the data will be the projection of the data onto the direction of the second largest singular value of the correlation matrix of the data, and so on.
The following are brief explanations of each option:
- Option A: transform data to zero mean. This is the correct answer.
- Option B: transform data to zero median. This is not the correct answer. The median is not a measure of central tendency that is used in PCA.
- Option C: not possible. This is not the correct answer. It is possible to get the same projection as SVD in PCA by transforming the data to zero mean.
- Option D: none of these. This is not the correct answer. Option A is the correct answer.