An experimental evaluation of K-nn for linear transforms of positive data

We present an experimented evaluation of the subspaces obtained on positive data using the Principal Component Analysis (PCA), Non-negative Matrix Factorization (NMF) and Weighted Non-negative Matrix Factorization (WNMF) techniques in order to compare which technique provides a subspace that mantains the neighbourhood structure of the original space. Different distance metrics are used both in the original and the projected spaces in order to find which one is more adapted to our data. Results demonstrate that for our positive data (color histograms) a good candidate that preserves the original neighbourhood is NMF in conjunction with L1 distance metric when the χ2 metric is used in the original space. Since this is the most widely used distance metric when having histogram representations, our initial results seem to be relevant. © Springer-Verlag Berlin Heidelberg 2003.