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Title: Minimal sample subspace learning Authors:  Yuqing Xia - National University of Singapore (Singapore) [presenting]
Zhenyue Zhang - Zhejiang University (China)
Abstract: Given a collection of data points sampled from a union of several unknown low-dimensional subspaces, the subspace learning aims to partition these points into several segments according to the underlying subspaces they belong to. Current work on subspace learning will be introduced which is challenging, especially when the underlying subspaces are heavily intersected. To define the canonical segmentation one could expect to learn, we introduce the concept of minimal subspace segmentation and build a mapping from the minimal segmentation to the self-expressive matrix with fixed rank. Theoretical analysis guarantees such mapping is one-to-one under some week conditions. An optimization is then proposed to capture the self-expressive matrix, along with an alternative algorithm based on manifold conjugate gradient method and spectral clustering. The reported simulation shows the strong ability of our proposed method on retrieving the minimal subspace segmentation, even when the underlying subspaces are heavily intersected.