Suppose we have some data with n dimensions, and we perform kernel PCA on this data using a suitable kernel. Is the dimensionality of the data after kernel PCA necessarily less than n? Justify your...

Suppose we have some data with n dimensions, and we perform kernel PCA on this data using a suitable kernel. Is the dimensionality of the data after kernel PCA necessarily less than n? Justify your answer.

Calculate the LDA class scatter matrices (between-class, withinclass, and total scatter matrices) for the dataset in matrix X below. The dataset contains two classes, “yes” and “no.”