Domain Adaptive Subspace Clustering

Many practical applications in image processing and computer vision require one to analyze and process high-dimensional data. It has been observed that these high-dimensional data can be represented by a lowdimensional subspace. As a result, the collection of data from different classes can be viewed as samples from a union of low-dimensional subspaces. In subspace clustering, given the data from a union of subspaces, the objective is to find the number of subspaces, their dimensions, and the segmentation of the data and a basis for each subspace. In many applications, one has to deal with heterogeneous data. For example, when clustering digits, one may have to process both computer generated as well as handwritten digits. Similarly, when clustering face images collected in the wild, one may have to cluster images of the same individual collected using different cameras and possibly under different resolution and lighting conditions. Clustering of heterogeneous data is difficult because it is not meaningful to directly compare the heterogenous samples with different distributions which may span different feature spaces. In recent years, various domain adaptation methods have been developed to deal with the distributional changes that occur after learning a classifier for supervised and semi-supervised learning [3]. However, to the best of our knowledge, these methods have not been developed for clustering heterogeneous data that lie in a union of low-dimensional subspaces.