Branch and bound is an effective technique for solving constraint optimization problems (COP’s). However, its search space expands very rapidly as the domain sizes of the problem variables grow. In this paper, we present an algorithm that clusters the values of a variable’s domain into sets. Branch and bound can then branch on these sets of values rather than on individual values, thereby reducing the branching factor of its search space. The aim of our clustering algorithm is to construct a collection of sets such that branching on these sets will still allow effective bounding. In conjunction with the reduced branching factor, the size of the explored search space is thus significantly reduced. We test our method and show empirically that it can yield significant performance gains over existing stateof- the-art techniques.

City-wide urban infrastructures are increasingly reliant on network technology to improve and ex-pand their services. As a side effect of this digitali-zation, large amounts of data can be sensed and analyzed to uncover patterns of human behavior. In this paper, we focus on the digital footprints from one type of emerging urban infrastructure: shared bicycling systems. We provide a spatiotemporal analysis of 13 weeks of bicycle station usage from Barcelona's shared bicycling system, called Bicing. We apply clustering techniques to identify shared behaviors across stations and show how these behaviors relate to location, neighborhood, and time of day. We then compare experimental results from four predictive models of near-term station usage. Finally, we analyze the impact of factors such as time of day and station activity in the prediction capabilities of the algorithms.

Automatic recognition of human activities is among the key capabilities of many intelligent systems with vision/perception. Most existing approaches to this problem require sophisticated feature extraction before classification can be performed. This paper presents a novel approach for human action recognition using only simple low-level visual features: motion captured from direct frame differencing. A codebook of key poses is first created from the training data through unsupervised clustering. Videos of actions are then coded as sequences of super-frames, defined as the key poses augmented with discriminative attributes. A weighted-sequence distance is proposed for comparing two super-frame sequences, which is further wrapped as a kernel embedded in a SVM classifier for the final classification. Compared with conventional methods, our approach provides a flexible non-parametric sequential structure with a corresponding distance measure for human action representation and classification without requiring complex feature extraction. The effectiveness of our approach is demonstrated with the widely-used KTH human activity dataset, for which the proposed method outperforms the existing state-of-the-art.

Many real-life datasets, such as those produced by gene expression studies, exhibit complex substructures at various levels of granularity and thus do not have unique well-defined numbers of clusters. In such cases, it is important to be able to trace the evolution of the individual clusters as the number of dimensions of the clustering is varied. While the dendrograms produced by bottom-up clustering methods such as hierarchical clustering are very useful for this purpose, the approach is known to produce unreliable clusters due to its instability w.r.t. resampling. Moreover, hierarchical clustering does not apply to overlapping (bi)clusters, such as those obtained in gene expression studies. On the other hand, the instability w.r.t. the initialization of top-down methods, such as k-means, prevents the comparison between clusters obtained at different dimensionalities. In this paper, we present a method for constructing generalized dendrograms for overlapping biclusters, which depict the evolution of the biclusters as their number is varied. An essential ingredient is a stable biclustering method based on positive tensor factorization of a number of nonnegative matrix factorization runs. We apply our approach to a large colon cancer dataset, which shows several distinct subclasses whose dimensional evolution must be carefully analyzed to enable a more meaningful biological interpretation and sub-classification.

However, most dimension reduction approaches are driven by objective functions that may not or only We will provide more detail on our solution to this problem partially suit the end users requirements. In this later but it is important to note the problem of focus in this work, we show how to incorporate general-purpose paper is different to spectral clustering (dimension reduction) domain expertise encoded as a graph into dimension in two keys ways. Firstly, we are projecting the entire space reduction in way that lends itself to an elegant D occupies not just the points in G or D. Secondly, we do generalized eigenvalue problem. We call not formulate the problem as some form of min-cut and then our approach Graph-Driven Constrained Dimension solve a relaxed version of the problem. Reduction via Linear Projection (GCDR-LP) Our work aims to find a reduced dimension space based on and show that it has several desirable properties.

Nonnegative Matrix Factorization (NMF) has been widely used in machine learning and data mining. It aims to find two nonnegative matrices whose product can well approximate the nonnegative data matrix, which naturally lead to parts-based representation. In this paper, we present a local learning regularized nonnegative matrix factorization (LLNMF) for clustering. It imposes an additional constraint on NMF that the cluster label of each point can be predicted by the points in its neighborhood. This constraint encodes both the discriminative information and the geometric structure, and is good at clustering data on manifold. An iterative multiplicative updating algorithm is proposed to optimize the objective, and its convergence is guaranteed theoretically. Experiments on many benchmark data sets demonstrate that the proposed method outperforms NMF as well as many state of the art clustering methods.

Cluster ensembles generate a large number of different clustering solutions and combine them into a more robust and accurate consensus clustering. On forming the ensembles, the literature has suggested that higher diversity among ensemble members produces higher performance gain. In contrast, some studies also indicated that medium diversity leads to the best performing ensembles. Such contradicting observations suggest that different data, with varying characteristics, may require different treatments. We empirically investigate this issue by examining the behavior of cluster ensembles on benchmark data sets. This leads to a novel framework that selects ensemble members for each data set based on its own characteristics. Our framework first generates a diverse set of solutions and combines them into a consensus partition P*. Based on the diversity between the ensemble members and P*, a subset of ensemble members is selected and combined to obtain the final output. We evaluate the proposed method on benchmark data sets and the results show that the proposed method can significantly improve the clustering performance, often by a substantial margin. In some cases, we were able to produce final solutions that significantly outperform even the best ensemble members.

Clustering aggregation has emerged as an important extension of the classical clustering problem. It refers to the situation in which a number of different (input) clusterings have been obtained for a particular data set and it is desired to aggregate those clustering results to get a better clustering solution. In this paper, we propose a unified framework to solve the clustering aggregation problem, where the aggregated clustering result is obtained by minimizing the (weighted) sum of the Bregman divergence between it and all the input clusterings. Moreover, under our algorithm framework, we also propose a novel cluster aggregation problem where some must-link and cannot-link constraints are given in addition to the input clusterings. Finally the experimental results on some real world data sets are presented to show the effectiveness of our method.

Clustering, classification, and regression, are three major research topics in machine learning. So far, much work has been conducted in solving multiple instance classification and multiple instance regression problems, where supervised training patterns are given as bags and each bag consists of some instances. But the research on unsupervised multiple instance clustering is still limited . This paper formulates a novel Maximum Margin Multiple Instance Clustering problem for the multiple instance clustering task. To avoid solving a non-convex  optimization problem directly, M 3 IC is further relaxed, which enables an efficient optimization solution with a combination of Constrained Concave-Convex Procedure CCCP) and the Cutting Plane method. Furthermore, this paper analyzes some important properties of the proposed method and the relationship between the proposed method and some other related ones. An extensive set of empirical results demonstrate the advantages of the proposed method against existing research for both effectiveness and efficiency.

In this paper, we propose a new spectral clustering method, referred to as Spectral Embedded Clustering (SEC), to minimize the normalized cut criterion in spectral clustering as well as control the mismatch between the cluster assignment matrix and the low dimensional embedded representation of the data. SEC is based on the observation that the cluster assignment matrix of high dimensional data can be represented by a low dimensional linear mapping of data. We also discover the connection between SEC and other clustering methods, such as spectral clustering, Clustering with local and global regularization, K-means and Discriminative K-means. The experiments on many real-world data sets show that SEC significantly outperforms the existing spectral clustering methods as well as K-means clustering related methods.