This paper considers the problem of dimensionality reduction by orthogonal projection techniques. The main feature of the proposed techniques is that they attempt to preserve both the intrinsic neighborhood geometry of the data samples and the global geometry. In particular we propose a method, named Orthogonal Neighborhood Preserving Projections, which works by first building an "affinity" graph for the data, in a way that is similar to the method of Locally Linear Embedding (LLE). However, in contrast with the standard LLE where the mapping between the input and the reduced spaces is implicit, ONPP employs an explicit linear mapping between the two. As a result, handling new data samples becomes straightforward, as this amounts to a simple linear transformation.We show how to define kernel variants of ONPP, as well as how to apply the method in a supervised setting. Numerical experiments are reported to illustrate the performance of ONPP and to compare it with a few competing methods.
|Original language||English (US)|
|Number of pages||14|
|Journal||IEEE Transactions on Pattern Analysis and Machine Intelligence|
|State||Published - Dec 2007|
Bibliographical noteFunding Information:
The authors are grateful to Professor D. Boley for his valuable help and insightful discussions on various aspects of the paper. This work was supported by the US National Science Foundation under grant DMS 0510131 and by the Minnesota Supercomputing Institute.
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