Goal: to reduce feature dimensions
How dimensionality reduction: base change (original feature depends yl group is converted into a new group group group group change, also the original characteristics of the transform becomes yl group).
How to determine the new base group: variance transformed the bigger the better (the more original information retained), while the group covariance-based group to 0 (covariance measure of the degree of correlation between variables, covariance is 0 the two variables not relevant, i.e. are orthogonal to each group group group, expressed as geometric vertical).
With the new standard-yl group, how to calculate the new group Group: covariance matrix (variance is on the diagonal, the rest position of the covariance, the matrix is a symmetric matrix), because the real symmetric matrix be able to find a positive unit post eigenvectors, covariance matrices so find eigenvalues and eigenvectors corresponding Diagonalization (PubMed mathematics).
Relationship with the feature vector of dimension reduction: the selected feature vectors can be achieved by multiplying the original data of the original data dimension reduction. For example, 150 pieces of data having four feature (150 4) multiplying two feature vectors (added 4 2), the raw data reduction to 2 * 150, 2-dimensional feature dimensions reduced.
So how to choose the number of feature vectors and the feature vector does what particular: a characteristic value of the standard, the larger feature value, the more important the representative feature vectors corresponding to the feature value. Characteristic values in descending order, according to pre-specified number of feature dimensionality reduction (e.g., 2), selecting the eigenvector corresponding to the top two eigenvalues.
