Angular Decomposition
Dengdi Sun, Chris Ding, Bin Luo and Jin Tang
Dimensionality reduction plays a vital rule in pattern recognition. However, for normalized vector data, existing methods do not utilize the fact that data is normalized. In this paper, we propose Angular Decomposition of the normalized vector data which corresponds to embedding them on a unit surface. On graph data for similarity/kernel matrix with constant diagonal elements, we propose Angular Decomposition of the similarity matrix which corresponds to embedding objects on a unit sphere. In these angular embeddings, Euclidean space is equivalent to cosine similarity. Thus data structures best described in cosine similarity and data structures best captured by Euclidean distance can both be effectively detected in our angular embedding. We provide theoretical analysis, derive the computational algorithm, and evaluate the angular embedding on several datasets. Experiments on data clustering demonstrate that our method can provide a more discriminative subspace.