<p>The goal of multi-view clustering is to partition unlabeled objects into disjoint clusters or groups using consistent and complementary information provided by the different features of the same object. Most existing methods perform this clustering task sequentially: Computation of the individual or consistent graph matrices, spectral embedding, and clustering. In this work, we present an approach that can overcome some of the limitations of previous multiview clustering methods. We introduce a single objective function whose minimization can jointly determine the consistent graph matrix for all views, the unified spectral data representation, the soft cluster indices, and the view weights. We present a constraint term that relates the cluster indices to the convolution of the consistent spectral data representations over the consistent graph. The method we present has two interesting features that are not simultaneously present in recent work. First, the cluster indices can be estimated directly without the need for an additional clustering step, which depends heavily on initialization. Second, the soft cluster indices are directly linked to the kernel representation of the features of the views. Moreover, our proposed method automatically determines the weights of each view, thus requiring fewer hyperparameters. A series of experiments have been conducted on real datasets. These demonstrate the efficiency of the proposed method, which compares favorably to many multi-view clustering methods.</p>