Feature matching is used to match features in the model image to their correspondences in the test image. Hypergraph matching makes use of the relationship among multiple features to improve matching accuracy, and existing algorithms usually achieve this aim by maximizing the matching score between features. In this paper we transform hypergraph matching of features to hypergraph clustering of candidate matches, which is then solved in the scenario of a multi-player clustering game. Noticing that the number of matches generated by this algorithm is usually small, we discuss the reason and present a density based group expansion method to increase the number of matches. Furthermore, we enforce the one-to-one constraint to maintain a high matching accuracy. Experiments on three real datasets show that our algorithm is able to generate a large number of matches efficiently without degrading the matching accuracy evidently.

Feature matching is a fundamental problem in computer vision. Compared with graph matching, hypergraph matching is able to encode more invariance between correspondences. Different from the majority of existing hypergraph matching algorithms, a game-theoretic algorithm has been developed by transforming hypergraph matching to hypergraph clustering, which is then solved within the framework of a non-cooperative multi-player clustering game. This algorithm obtains the final matches as a cluster of consistent candidate matches and has high accuracy and robustness to outliers in comparison with other competitors. However, in further works we find that this algorithm tends to generate a small number of matches, and the increase of number of matches can only be obtained at the cost of a huge computation load. Our investigation of the algorithm shows that it has a large requirement of internal similarity in a cluster, and therefore generates small clusters of high density. This motivates us to expand the cluster so that more candidate matches are accepted as final matches. For this purpose, we define the density of vertices in a hypergraph and expand the cluster based on relative density relationship among the vertices. In matching experiments with both synthetic and real datasets, our algorithm is shown to generate the same number of or more matches with much less running time in comparison with the original algorithm. Meanwhile, it preserves the advantage of high accuracy and robustness to outliers in comparison with some competitors.

Clustering is able to find out implicit data distribution and is especially useful in data driven machine learning. Density based clustering has an attractive property of detecting clusters of arbitrary structures. The density peak algorithm makes use of two assumptions to detect cluster centers and then groups the other data. This approach is simple to implement and shown to be promising in many experiments. However, we find its clustering results are dependent on density kernel types and kernel parameters, and density difference across clusters also influences the results significantly. In this paper, we make a detailed study of the density peak algorithm and attribute the problems to the local density criterion in detecting cluster centers. We then use density normalization to relieve the influence of the problems, and present a density kernel to further improve clustering results. We conduct experiments with different types of datasets to demonstrate the performance of our approach.

Feature matching is aimed to establish the correspondences between features of two sets. Aside from the well-known graph matching, hyper-graph matching is receiving increasing interests due to its ability to encode more invariance information. Existing hyper-graph matching algorithms are usually based on the maximization of matching score between correspondences. In this paper we treat the candidate matches as pure strategies and formulate the hyper-graph matching problem as a non-cooperative multi-player clustering game. Specifically, we calculate the higher-order similarity as the payoff of players in selecting the corresponding triplet of pure strategies, and find that the subset of consistent matches can be extracted by optimizing a polynomial function with a higher-order replicator dynamics over the standard simplex. With the Baum-Eagon inequality, we arrive at the equilibrium of the game and obtain a subset of consistent matches as the final matching result. Our approach is especially useful in dealing with the case that some features in the model image have no correspondences in the test image. In addition, with our approach each match is assigned a weight which reflects the relationship with other matches and can be used to enforce the one-to-one constraint. Experiments on both synthetic datasets and real images demonstrate the effectiveness of our approach.

The density peak based clustering algorithm is a recently proposed density based clustering approach. This algorithm treats the data corresponding to local density peaks as cluster centers and groups non-center data based on the density relationship among neighboring data. While being simple, this algorithm is shown to be effective and computationally efficient. In the density peak based algorithm, the data with the largest local density are selected as cluster centers. On one hand, the real cluster centers may not have the largest local density in clusters. On the other hand, this practice may discriminate against the clusters of small density. In this paper we propose to measure the centerness of data and treat the centerness peaks as cluster centers. The centerness of one data is evaluated by the distribution of nearest neighbors in the neighborhood, and it measures to which degree one data is surrounded by its nearest neighbors. We present a histogram based method to calculate the centerness, and show that the centerness measure solves the problem resulted from density difference among clusters in the density peak based algorithm. In addition, the cluster centers identified by centerness peaks are more consistent with human observation. Experiments on various datasets and comparisons with other algorithms illustrate the effectiveness of our algorithm.

In image classification, feature combination is often used to combine the merits of multiple complementary features and improve the classification accuracy compared with one single feature. Existing feature combination algorithms, e.g., multiple kernel learning, usually determine the weights of features based on the optimization with respect to some classifier-dependent objective function. These algorithms are often computationally expensive, and in some cases are found to perform no better than simple baselines. In this paper, we solve the feature combination problem from a totally different perspective. Our algorithm is based on the simple idea of combining only base kernels suitable to be combined. Since the very aim of feature combination is to obtain the highest possible classification accuracy, we measure the combination suitableness of two base kernels by the maximum possible cross-validation accuracy of their combined kernel. By regarding the pairwise suitableness as the kernel adjacency, we obtain a weighted graph of all base kernels and find that the base kernels suitable to be combined correspond to a cluster in the graph. We then use the dominant sets algorithm to find the cluster and determine the weights of base kernels automatically. In this way, we transform the kernel combination problem into a clustering one. Our algorithm can be implemented in parallel easily and the running time can be adjusted based on available memory to a large extent. In experiments on several data sets, our algorithm generates comparable classification accuracy with the state of the art.

The existing clustering algorithms are usually dependent on one or more input parameters, which are not easy to determine in many cases. In this paper, DSets-histeq is presented as a parameter-independent framework for data clustering. By histogram equalization transformation of pairwise data similarity matrices, the dominant sets algorithm is used to generate parameter-independent initial clusters, which are typically relatively large subsets of real clusters. This enables one to expand the initial clusters to the final ones with a cluster-growing algorithm and determine the involved parameters adaptively by making use of the information in the initial clusters. A simple yet effective method is proposed to utilize the information captured in the initial clusters. Experiments on various datasets and comparison with state-of-the-art clustering algorithms are used to illustrate the potential of the proposed framework.

The clustering algorithm by fast search and find of density peaks is shown to be a promising clustering approach. However, this algorithm involves manual selection of cluster centers, which is not convenient in practical applications. In this paper we discuss the correlation between density peaks and cluster centers. As a result, we present a new local density estimation method to highlight the uniqueness of cluster centers by making use of the farthest ones in nearest neighbors of data. Furthermore, we propose to use density normalization to deal with the density difference among clusters. Given the number of clusters, our algorithm is able to accomplish the clustering process without human intervention and improve the clustering results. In experiments on several datasets, our algorithm is shown to outperform the original one with both cutoff and Gaussian kernels evidently.

In this paper, a data-driven approach of spherical kernel total projection to latent structures (ST-KPLS) is proposed to monitor the industrial process and detect the faults in the process. Considering that T-KPLS cannot deal with the outliers occurring in the process and outliers can be taken out effectively by using spherical method, a new method called ST-KPLS is obtained by importing the idea of spherical method into T-KPLS. First of all, we elaborate the key idea of spherical method and describe the whole procedures. Then, the implement of ST-KPLS algorithm is illustrated in details. After that, we select proper data variables and apply the benchmark simulation model no. 1 (BSM1) to collect a large amount of training and testing data needed to be monitored in the process. Finally, we utilize ST-KPLS to achieve the off-line modeling and the on-line process monitoring and properly select outliers that are used to the simulation of ST-KPLS. The results of ST-KPLS are compared with those of T-KPLS to illustrate the effectiveness of the proposed approach.

This work aims to study the fault classification problem in complicated industrial processes. Two modified multi-classification methods of Support Vector Machine (SVM), i.e., Principal Component Analysis based Support Vector Machine (PCA-SVM) as well as Kernel Principal Component Analysis based Support Vector Machine (KPCA-SVM), are respectively proposed to classify multi-fault for the underlying process. The continuous stirred tank heater (CSTH) benchmark is adopted in simulation to validate the effectiveness of the proposed approaches. Simulation results indicate that compared with the original PCA-SVM, KPCA-SVM generates a higher classification rate for the underlying process at the cost of larger computation loads.

As a graph-based clustering approach, dominant sets clustering determines the number of clusters automatically and possesses some other nice properties. By applying histogram equalization transformation to the similarity matrix before clustering, we are able to accomplish the dominant sets clustering process without any user-specified parameters. However, this transformation usually leads to over-segmented clustering results. In this paper, we analyze the correlation between histogram equalization transformation and the over-segmentation tendency, and attribute the over-segmentation to the over-strict global density constraint imposed by the dominant set definition. Therefore we propose to relax the global density constraint to a local one, which is then used in dominant set extension. We test our algorithm in experiments of data clustering and image segmentation, and validate its effectiveness in comparison with the original dominant sets algorithm and other algorithms.

Clustering image pixels is an important image segmentation technique. While a large amount of clustering algorithms have been published and some of them generate impressive clustering results, their performance often depends heavily on user-specified parameters. This may be a problem in the practical tasks of data clustering and image segmentation. In order to remove the dependence of clustering results on user-specified parameters, we investigate the characteristics of existing clustering algorithms and present a parameter-free algorithm based on the DSets (dominant sets) and DBSCAN (Density-Based Spatial Clustering of Applications with Noise) algorithms. First, we apply histogram equalization to the pairwise similarity matrix of input data and make DSets clustering results independent of user-specified parameters. Then, we extend the clusters from DSets with DBSCAN, where the input parameters are determined based on the clusters from DSets automatically. By merging the merits of DSets and DBSCAN, our algorithm is able to generate the clusters of arbitrary shapes without any parameter input. In both the data clustering and image segmentation experiments, our parameter-free algorithm performs better than or comparably with other algorithms with careful parameter tuning.

In object classification, feature combination can usually be used to combine the strength of multiple complementary features and produce better classification results than any single one. While multiple kernel learning (MKL) is a popular approach to feature combination in object classification, it does not always perform well in practical applications. On one hand, the optimization process in MKL usually involves a huge consumption of computation and memory space. On the other hand, in some cases, MKL is found to perform no better than the baseline combination methods. This observation motivates us to investigate the underlying mechanism of feature combination with average combination and weighted average combination. As a result, we empirically find that in average combination, it is better to use a sample of the most powerful features instead of all, whereas in one type of weighted average combination, the best classification accuracy comes from a nearly sparse combination. We integrate these observations into the k-nearest neighbors (kNNs) framework, based on which we further discuss some issues related to sparse solution and MKL. Finally, by making use of the kNN framework, we present a new weighted average combination method, which is shown to perform better than MKL in both accuracy and efficiency in experiments. We believe that the work in this paper is helpful in exploring the mechanism underlying feature combination.

Based on a graph‐theoretic concept of a cluster, dominant sets clustering has been shown to be an attractive clustering algorithm with many useful properties. In this study, the authors conduct a comprehensive study of related issues in dominant sets clustering, in an endeavour to explore the potential of this algorithm and obtain the best clustering results. Specifically, they empirically investigate how similarity parameters, similarity measures and game dynamics influence the dominant sets clustering results. From experiments on eight datasets, they conclude that distance‐based similarity measures perform evidently better than cosine and histogram intersection similarity measures potentially, and they need to find the best‐performing similarity parameter to make use of this advantage. They then study the effect of similarity parameter on dominant sets clustering results and induce the range of the best‐performing similarity parameters. Furthermore, they find that the recently proposed infection and immunisation dynamics performs better than the replicator dynamics in most cases while being much more efficient than the latter. These observations are helpful in applying dominant sets clustering to practical problems, and also indicate directions for further improvement of this algorithm.

Dominant sets clustering is a promising clustering approach based on a graph-theoretic concept of a cluster. With the pairwise similarity matrix of data as input, dominant sets clustering determines the number of clusters by itself and possesses some other nice properties. However, the original dominant sets clustering algorithm is sensitive to similarity measures, and appropriate parameters are required to generate satisfactory clustering results. In order to solve this problem, we firstly use histogram equalization to transform the similarity matrix and remove the sensitiveness to similarity parameters. In the second step we extend the clusters by merging dominant sets clustering and DBSCAN. Our algorithm requires no user-defined parameters, and is able to generate clusters of arbitrary shapes and determine the number of clusters automatically. In experiments of data clustering and image segmentation our algorithm performs evidently better than the original dominant sets clustering, and also comparably to other state-of-the-art clustering algorithms.

Clustering is an important unsupervised learning approach and widely used in pattern recognition, data mining and image processing, etc. Different from existing clustering algorithms based on partitioning within data, dominant sets clustering extracts clusters in a sequential fashion. Based on graph-theoretic concept of a cluster, dominant sets clustering can be accomplished with a game dynamics efficiently while being able to determine the number of clusters automatically. However, we have observed that the definition of dominant set over weights the importance of high intra-cluster similarity. Consequently, dominant sets clustering is found to be sensitive to similarity parameters and show the tendency to generate over-segmented clustering results. In order to solve these problems, in this paper we present a cluster extension algorithm by making use of the relationship of intra-cluster and inter-cluster similarity. In experiments on eight datasets, our algorithm performs evidently better than the original dominant sets algorithm, and comparably to other state-of-the-art clustering algorithms.

Clustering image pixels is an important technique in image segmentation. While normalized cuts is popularly used in image segmentation, dominant set clustering is another promising method and shown to outperform normalized cuts in some experiments. However, dominant set clustering suffers from the problems of sensitiveness to distance measures and over-segmentation tendency. In this paper we present DSET++ to enhance the original dominant set clustering and solve the two problems. Firstly, we use the histogram equalization in image enhancement to transform the similarity matrix and eliminate the sensitiveness to distance measures. In the second step we extend the dominant set based on density information to overcome the tendency of over-segmentation. Preliminary experiments on data clustering tasks validate the effectiveness of DSET++ clustering.

Although there is no shortage of clustering algorithms, existing algorithms are often afflicted by problems of one kind or another. Dominant sets clustering is a graph‐theoretic approach to clustering and exhibits significant potential in various applications. However, the authors' work indicates that this approach suffers from two major problems, namely over‐segmentation tendency and sensitiveness to distance measures. In order to overcome these two problems, the authors present a density‐based enhancement to dominant sets clustering where a cluster merging step is used to fuse adjacent clusters close enough from the original dominant sets clustering. Experiments on various datasets validate the effectiveness of the proposed method.

Classifier combination can be used to combine multiple classification decisions to improve object classification performance, and weighted average is a popular method for this purpose. In this paper we propose to use a graph-theoretic clustering method to define the weights for SVM classifier decisions. Specifically, we use the dominant set clustering to evaluate the difficulty of a kernel matrix for a SVM classifier. This degree of difficulty is found to be related to the SVM classification performance and thus used to define the weight of this classifier. Though simple and intuitive, the method is shown to be as powerful as more sophisticated methods in extensive experiments with several datasets of diverse object types.