Semi-supervised subspace segmentation

Subspace segmentation methods usually rely on the raw explicit feature vectors in an unsupervised manner. In many applications, it is cheap to obtain some pairwise link information that tells whether two data points are in the same subspace or not. Though partially available, such link information serves as some kind of high-level semantics, which can be further used as a constraint to improve the segmentation accuracy. By constructing a link matrix and using it as a regularizer, we propose a semi-supervised subspace segmentation model where the partially observed subspace membership prior can be encoded. Specificly, under the common linear representation assumption, we enforce the representational coefficient to be consistent with the link matrix. Thus the low-level and high-level information about the data can be integrated to produce more precise segmentation results. We then develop an effective algorithm to optimize our model in an alternating minimization way. Experimental results for both motion segmentation and face clustering validate that incorporating such link information is helpful to assist and bias the unsupervised subspace segmentation methods.