This paper discusses the topic of dimensionality reduction for k-means clustering. We prove that any set of n points in d dimensions (rows in a matrix A ∈ R) can be projected into t = Ω(k/ε) dimensions, for any ε ∈ (0, 1/3), in O(nd⌈ε−2k/ log(d)⌉) time, such that with constant probability the optimal k-partition of the point set is preserved within a factor of 2 + ε. The projection is done by p...

We study a random graph model called the “stochastic block model” in statistics and the “planted partition model” in theoretical computer science. In its simplest form, this is a random graph with two equal-sized classes of vertices, with a within-class edge probability of q and a between-class edge probability of q′. A striking conjecture of Decelle, Krzkala, Moore and Zdeborová [9], based on ...

Abstract We consider a hedonic coalition formation game in which chooses for each partition of the player set probability with it forms and thereby destroys current partition. These probabilities are commonly known so that farsighted players know at every what future partitions, hence payoffs, will be reached probability. Thus, can make rational decisions about moves they support. show if coali...

We consider the computability of entropy and information in classical Hamiltonian systems. We define the information part and total information capacity part of entropy in classical Hamiltonian systems using relative information under a computable discrete partition. Using a recursively enumerable nonrecursive set it is shown that even though the initial probability distribution, entropy, Hamil...