In graph-based clustering, a relevant affinity matrix is crucial for good results. Double stochasticity of the has been shown to be an important condition, both in theory and practice. this paper, we emphasize idempotency as another key condition. fact, theorem from Sinkhorn, R. (1968) allows us exhibit bijective relationship between set doubly stochastic idempotent matrices order n (modulo per...

We study a semismooth Newton-type method for the nearest doubly stochastic matrix problem where nonsingularity of Jacobian can fail. The optimality conditions this are formulated as system strongly functions. show that does not hold system. By exploiting structure, we construct modified two step Newton guarantees nonsingular at each iteration, and converges to quadratically. Funding: This work ...

In this paper we use the Gray code representation of the genetic code C=00, U=10, G=11 and A=01 (C pairs with G, A pairs with U) to generate a sequence of genetic code-based matrices. In connection with these code-based matrices, we use the Hamming distance to generate a sequence of numerical matrices. We then further investigate the properties of the numerical matrices and show that they are d...

Cluster analysis by nonnegative low-rank approximations has experienced a remarkable progress in the past decade. However, the majority of such approximation approaches are still restricted to nonnegative matrix factorization (NMF) and suffer from the following two drawbacks: 1) they are unable to produce balanced partitions for large-scale manifold data which are common in real-world clusterin...

Moderated greedy search is based on the idea that it is helpful for greedy search algorithms to make non-optimal choices “once in a while.” This notion can be made precise by using the majorizationtheoretic approach to greedy algorithms. Majorization is the study of pre-orderings induced by doubly stochastic matrices. A majorization operator when applied to a distribution makes it “less unequal...

A stronger version of the van der Waerden permanent conjecture asserts that if J„ denotes the n X n matrix all of whose entries are \/n and A is any fixed matrix on the boundary of the set ofnxn doubly stochastic matrices, then per(A/4 + (1 — \)Jn) as a function of X is nondecreasing in the interval [0, 1]. In this paper, we elucidate the relation of this assertion to some other conjectures kno...

We study online combinatorial decision problems, where one must make sequential decisions in some combinatorial space without knowing in advance the cost of decisions on each trial; the goal is to minimize the total regret over some sequence of trials relative to the best fixed decision in hindsight. Such problems have been studied mostly in settings where decisions are represented by Boolean v...

Many modern clustering methods employ a non-convex objective function and use iterative optimization algorithms to find local minima. Thus initialization of the algorithms is very important. Conventionally the starting guess of the iterations is randomly chosen; however, such a simple initialization often leads to poor clusterings. Here we propose a new method to improve cluster analysis by com...