Existing methods on representation-based subspace clustering mainly treat all features of data as a whole to learn a single self-representation and get one clustering solution. Real data however are often complex and consist of multiple attributes or sub-features, such as a face image has expressions or genders. Each attribute is distinct and complementary on depicting the data. Failing to explore attributes and capture the complementary information among them may lead to an inaccurate representation. Moreover, a single clustering solution is rather limited to depict data, which can often be interpreted from different aspects and grouped into multiple clusters according to attributes. Therefore, we propose an innovative model called attributed subspace clustering (ASC). It simultaneously learns multiple self-representations on latent representations derived from original data. By utilizing Hilbert Schmidt Independence Criterion as a co-regularizing term, ASC enforces that each self-representation is independent and corresponds to a specific attribute. A more comprehensive self-representation is then established by adding these self-representations. Experiments on several benchmark image datasets have demonstrated the effectiveness of ASC not only in terms of clustering accuracy achieved by the integrated representation, but also the diverse interpretation of data, which is beyond what current approaches can offer.