We present a general framework for graph clustering and bi-clustering where we are given a general observation (called a label) between each pair of nodes. This framework allows a rich encoding of various types of pairwise interactions between nodes. We propose a new tractable and robust approach to this problem based on convex optimization and maximum likelihood estimators. We analyze our algo...

Subspace clustering is a useful technique for many computer vision applications in which the intrinsic dimension of high-dimensional data is often smaller than the ambient dimension. Spectral clustering, as one of the main approaches to subspace clustering, often takes on a sparse representation or a low-rank representation to learn a block diagonal self-representation matrix for subspace gener...

When building a multivariate statistical process control model, it is commonly assumed that there is only one operational mode in the baseline data. However, multiple operational modes may exist due, for example, to several suppliers of raw materials or seasonal changes. It is important to know the number of modes in the data in order to construct an effective process control system. Each opera...

The non-negative matrix factorization (NMF) model with an additional orthogonality constraint on one of the factor matrices, called orthogonal NMF (ONMF), has been found a promising clustering and can outperform classical K-means. However, solving ONMF is challenging optimization problem because coupling non-negativity constraints introduces mixed combinatorial aspect into due to determination ...

The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice. While these relaxations can be solved globally optimally, they are often too loose and thus lead to results far away from the optimum. In this paper we show t...

We present a new algebraic algorithmic scheme to solve convex integer maximization problems of the following form, where c is a convex function on R and w1x, . . . , wdx are linear forms on R, max {c(w1x, . . . , wdx) : Ax = b, x ∈ N} . This method works for arbitrary input data A, b, d, w1, . . . , wd, c. Moreover, for fixed d and several important classes of programs in variable dimension, we...