Pca
Maximize the sensitivity of individual dimensions and reduce the impact between dimensions. Differentiated measures: Variance dimension Effects: Covariance is thus represented by a matrix as the eigenvalues and eigenvectors of the covariance matrix. 1. Construct The matrix. 2. Find the covariance matrix of the Matrix. 3. Find the eigenvalues and eigenvectors of the covariance matrix, which are invariant in these directions. 4. Select a few of these directions to compare the full representation of all vectors. 5. Calculate the coordinates on the new axis
The key of ref:http://www.cnblogs.com/cbdoctor/archive/2011/10/29/2228756.html covariance matrix--PCA. The purpose of PCA is to "de-noising" and "de-redundancy". The purpose of "noise reduction" is to make the relationship between the retained dimensions as small as possible, while the purpose of "de-redundancy" is to make the remaining dimensions contain the "energy", i.e. the variance as large as possible. First of all, we need to know the correlations between the dimensions and the variance on each dimension! What data structure can simultaneously show the correlation between different dimensions and the variance of each dimension? Natural non-covariance matrix is the genus. Recalling the contents of the covariance matrix, the covariance matrix measures the relationship between dimensions and dimensions, not between samples. The elements on the main diagonal of the covariance matrix are the variances (that is, the energy) on each dimension, and the other elements are the covariance (that is, the correlation) between the 22 dimensions. We want to have the covariance matrix all have, first look at "noise reduction", so that the relationship between the different dimensions are kept as small as possible, that is, the covariance matrix non-diagonal elements are basically zero. The way to achieve this is naturally needless to say, the line generation is very clear--matrix diagonalization. The diagonal matrix, which is the eigenvalues of the covariance matrix, has two identities: first, it is also the new variance on each dimension, and secondly, it is the energy that each dimension should own (the concept of energy accompanies the eigenvalues). This is why we call "variance" as "energy" in the front. Perhaps the 2nd question may be in doubt, but we should be aware of the fact that, through diagonalization, the correlation between the remaining dimensions has been reduced to the weakest and has no longer been affected by "noise", so the energy should be larger than before. After reading the "noise reduction", our "redundant" is not finished yet. The diagonal covariance matrix, where the smaller new variance on the diagonal corresponds to those dimensions that are removed. So we only take those dimensions that contain larger energies (eigenvalues), and the rest of them are dropped. The essence of PCA is actually the diagonalization covariance matrix. The essence of PCA is the diagonalization covariance matrix, which is designed to minimize the correlation between dimensions (noise reduction) and to retain the maximum energy of the dimension (de-redundancy).
Http://www.cnblogs.com/zh ngchaoyang/articles/2222048.html
Http://www.cnblogs.com/tornadomeet/archive/2012/12/30/2839615.htmlmatlab
2015.8.17 PCA
