# Updating the partial singular value decomposition in latent semantic indexing

*29-Sep-2018 23:43*

Below is an example of the iris dataset, which is comprised of 4 features, projected on the 2 dimensions that explain most variance: It is often interesting to project data to a lower-dimensional space that preserves most of the variance, by dropping the singular vector of components associated with lower singular values.For instance, if we work with 64x64 pixel gray-level pictures for face recognition, the dimensionality of the data is 4096 and it is slow to train an RBF support vector machine on such wide data.makes it possible to project the data onto the singular space while scaling each component to unit variance.This is often useful if the models down-stream make strong assumptions on the isotropy of the signal: this is for example the case for Support Vector Machines with the RBF kernel and the K-Means clustering algorithm., but differs in that it works on sample matrices directly instead of their covariance matrices.When the columnwise (per-feature) means of are subtracted from the feature values, truncated SVD on the resulting matrix is equivalent to PCA.It can be seen how the regularization term induces many zeros.Furthermore, the natural structure of the data causes the non-zero coefficients to be vertically adjacent.

The degree of penalization (and thus sparsity) can be adjusted through the hyperparameter implements a variant of singular value decomposition (SVD) that only computes the largest singular values, where is a user-specified parameter.The PCA algorithm can be used to linearly transform the data while both reducing the dimensionality and preserve most of the explained variance at the same time.