text: In this paper we present Collaborative Low-Rank Subspace Clustering. Given multiple observations of a phenomenon we learn a unified representation matrix. This unified matrix incorporates the features from all the observations, thus increasing the discriminative power compared with learning the representation matrix on each observation separately. Experimental evaluation shows that our method outperforms subspace clustering on separate observations and the state of the art collaborative learning algorithm.
  @cite_41: We describe two recently proposed randomized algorithms for the construction of low-rank approximations to matrices, and demonstrate their application (inter alia) to the evaluation of the singular value decompositions of numerically low-rank matrices. Being probabilistic, the schemes described here have a finite probability of failure; in most cases, this probability is rather negligible (10−17 is a typical value). In many situations, the new procedures are considerably more efficient and reliable than the classical (deterministic) ones; they also parallelize naturally. We present several numerical examples to illustrate the performance of the schemes.
summary: The work most closely related and which inspires our work is the so called Multi-Task Low-rank Affinity Pursuit (MLAP) @cite_41 . MLAP adopts the low-rank representation model for each individual observation and fuses them together by seeking sparsity consistent low-rank coefficients. The MLAP objective is the following where @math , @math and @math are observation data, the fitting error and coefficient matrices for the @math th observation respectively, @math is the number of observations, the @math norm is defined as @math , @math and @math is the vectorisation operator such that @math .