![]() ![]() If the data are not normalized, the patterns that are extracted are often specific to the samples with the higher values, rather than being typical of the data as a whole.Īny g × n matrix M can be decomposed into 3 matrices U, D, V where For sequencing data, the pseudo-counts computed by multiplying the actual counts by the normalization factors are used to normalize the samples to an equivalent library size. For microarray data, the values will be the usual normalized data. It is important to use the normalized values when using these dimension reduction methods. ![]() (I will assume here that g>n but if not, the matrix can be transposed.) The features might be genes or protein binding sites, and the values are the normalized expression values. Our data consist of n samples and g feature values arranged as a g × n matrix which I will call M. However in computer science and machine learning, SVD is one of the most important computational methods. ![]() Oddly, statisticians don't seem to know much about this (although we use a related method, principal components analysis, very frequently). The most fundamental dimension reduction method is called the singular value decomposition or SVD. ![]()
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