Non-linear dimension reduction with tangent bundle approximation

The problem of non-linear dimension reduction is relevant to many different areas of knowledge. While the linear case can be solved by variations of PCA, the non-linear case is more complex. Recent advances incorporate geometrical information by estimating a manifold that approximates the data. The paper follows that trend and tackles some limitations of existing approaches -arbitrary topology and curvature of the manifold, unknown intrinsic dimension and, for mixture models, unknown number of mixture components. An algorithm, designated TBA (tangent bundle approximation), is presented that addresses the enumerated difficulties and is faster than existing methods, in datasets of a few thousand points. The motivation behind TBA is to perform motion tracking in video sequences, but the algorithm can be applied in a wide class of problems. The paper starts with a brief review of related work and then describes the TBA approach in detail. The algorithm is then subjected to comparative evaluation.