Non-negative matrix factorization, NMF, is an alternative to PCA when the elements of the matrix are non-negative. NMF can be used to cluster row and columns of the matrix. NMF is driven by the large values in the matrix. Often small values are important too. For example, genes can be up regulated or down regulated. Our idea is to build a new matrix that can be analyzed by NMF. Our idea is to normalize the data, e.g. by subtracting the row/column means, and split the matrix into positive and negative parts. NMF clustering applied to the concatenated data, “PosNegNMF” [3], gives equal weight to large and small values.A key advantage of NMF over PCA is that the variables, loadings, point to specific mechanisms rather than adsorbing maximum variability.
