We study data structures for providing ε-approximations of convex functions whose slopes are bounded from above and below by n and −n, respectively. The structures we describe have size O((1/ε) log n) and can answer queries in O(log(1/ε) + log log n) time. We also give an informationtheoretic lower-bound, that shows it is impossible to obtain structures of size O(1/ε) for approximating this cla...

Clustering has been widely used in different fields of science, technology, social science, etc. Naturally, clusters are in arbitrary (non-convex) shapes in a dataset. One important class of clustering is distance based method. However, distance based clustering methods usually find clusters of convex shapes. Classical single-link is a distance based clustering method, which can find arbitrary ...

In this paper, we study the problem of learning from weakly labeled data, where labels of the training examples are incomplete. This includes, for example, (i) semi-supervised learning where labels are partially known; (ii) multi-instance learning where labels are implicitly known; and (iii) clustering where labels are completely unknown. Unlike supervised learning, learning with weak labels in...

Spectral clustering is a flexible clustering technique that finds data clusters in the spectral embedding space of the data. It doesn’t assume convexity of the shape of clusters, and is able to find non-linear cluster boundaries. Constrained spectral clustering aims at incorporating user-defined pairwise constraints in to spectral clustering. Typically, there are two kinds of pairwise constrain...

The large volume principle proposed by Vladimir Vapnik, which advocates that hypotheses lying in an equivalence class with a larger volume are more preferable, is a useful alternative to the large margin principle. In this paper, we introduce a new discriminative clustering model based on the large volume principle called maximum volume clustering (MVC), and then propose two approximation schem...

identifying clusters or clustering is an important aspect of data analysis. it is the task of grouping a set of objects in such a way those objects in the same group/cluster are more similar in some sense or another. it is a main task of exploratory data mining, and a common technique for statistical data analysis this paper proposed an improved version of k-means algorithm, namely persistent k...

Various techniques exist to solve the non-convex optimization problem of clustering. Recent developments have employed a deterministic annealing approach to solving this problem. In this letter a new approximation clustering algorithm, incorporating a gradient descent technique with deterministic annealing, is described. Results are presented for this new method, and its performance is compared...

one of the most important issues in urban planning is developing sustainable public transportation. the basic condition for this purpose is analyzing current condition especially based on data. data mining is a set of new techniques that are beyond statistical data analyzing. clustering techniques is a subset of it that one of it’s techniques used for analyzing passengers’ trip. the result of t...

This paper presents a statistical approach to collaborative filtering and investigates the use of latent class models for predicting individual choices and preferences based on observed preference behavior. Two models are discussed and compared: the aspect model, a probabilistic latent space model which models individual preferences as a convex combination of preference factors, and the two-sid...