Orthogonal neighborhood preserving projections

Orthogonal Neighborhood Preserving Projections (ONPP) is a linear dimensionality reduction technique which attempts to preserve both the intrinsic neighborhood geometry of the data samples and the global geometry. The proposed technique constructs a weighted data graph where the weights are constructed in a data-driven fashion, similarly to Locally Linear Embedding (LLE). A major difference with the standard LLE where the mapping between the input and the reduced spaces is implicit, is that ONPP employs an explicit linear mapping between the two. As a result, and in contrast with LLE, handling new data samples becomes straightforward, as this amounts to a simple linear transformation. ONPP shares some of the properties of Locality Preserving Projections (LPP). Both ONPP and LPP rely on a k-nearest neighbor graph in order to capture the data topology. However, our algorithm inherits the characteristics of LLE in preserving the structure of local neighborhoods, while LPP aims at preserving only locality without specifically aiming at preserving the geometric structure. This feature makes ONPP an effective method for data visualization. We provide ample experimental evidence to demonstrate the advantageous characteristics of ONPP, using well known synthetic test cases as well as real life data from computational biology and computer vision.