Lossy compression and clustering fundamentally involve a decision about which features are relevant and which are not. The information bottleneck method (IB) by Tishby, Pereira, and Bialek ( 1999 ) formalized this notion as an information-theoretic optimization problem and proposed an optimal trade-off between throwing away as many bits as possible and selectively keeping those that are most im...

We study bottleneck constrained network upgrading problems. We are given an edge weighted graph G = (V; E) where node v 2 V can be upgraded at a cost of c(v). This upgrade reduces the delay of each link emanating from v. The goal is to nd a minimum cost set of nodes to be upgraded so that the resulting network has a good performance. The performance is measured by the bottleneck weight of a con...

The bottleneck network flow problem (BNFP) is a generalization of several well-studied bottleneck problems such as the bottleneck transportation problem (BTP), bottleneck assignment problem (BAP), bottleneck path problem (BPP), and so on. In this paper we provide a review of important results on this topic and its various special cases. We observe that the BNFP can be solved as a sequence of O(...

The problem of optimally choosing message rates for users of a store-and-forward network is analyzed. Multiple users sharing the links of the network each attempt to adjust their message rates to achieve an ideal network operating point or an " ideal tradeoff point between high throughput and low delay. " Each user has a fixed path or virtual circuit. In this environment, a basic definition of ...

This paper addresses the issue of passenger waiting and being stored at a station platform, from which point they plan to board route services towards egress stations. Route services are operated using dedicated vehicles of limited capacity. Each route service has a specific set of downstream egress stations and is operated at given frequency using homogeneous vehicles of limited available capa...

We introduce a novel distributional clustering algorithm that explicitly maximizes the mutual information per cluster between the data and given categories. This algorithm can be considered as a bottom up hard version of the recently introduced “Information Bottleneck Method”. We relate the mutual information between clusters and categories to the Bayesian classification error, which provides a...

For a weighted directed multigraph, let fij be the total weight of spanning converging forests that have vertex i in a tree converging to j. We prove that fij fjk = fik fjj if and only if every directed path from i to k contains j (a graph bottleneck equality). Otherwise, fij fjk < fik fjj (a graph bottleneck inequality). In a companion paper [1] (P. Chebotarev, A new family of graph distances,...

The Information bottleneck method is an unsupervised non-parametric data organization technique. Given a joint distribution P (A;B), this method constructs a new variable T that extracts partitions, or clusters, over the values of A that are informative about B. In a recent paper, we introduced a general principled framework for multivariate extensions of the information bottleneck method that ...

Information bottleneck [IB] is a technique for extracting information in some ‘input’ random variable that is relevant for predicting some different ‘output’ random variable. IB works by encoding the input in a compressed ‘bottleneck variable’ from which the output can then be accurately decoded. IB can be difficult to compute in practice, and has been mainly developed for two limited cases: (1...

Knowledge engineering upholds a longstanding tradition that emphasises methodological issues associated with the acquisition and representation of knowledge in some (formal) language. This focus on methodology implies an ex ante approach: “think before you act”. The rapid increase of linked data poses new challenges for knowledge engineering, and the Semantic Web project as a whole. Although th...