Dominant Sets Algorithm Research Articles

On the definition of shape parts: a dominant sets approach

In the present paper, a novel graph-based approach to the shape decomposition problem is addressed. The shape is appropriately transformed into a visibility graph enriched with local neighborhood information. A two-step diffusion process is then applied to the visibility graph that efficiently enhances the information provided, thus leading to a more robust and meaningful graph construction. Inspired by the notion of a clique as a strict cluster definition, the dominant sets algorithm is invoked, slightly modified to comport with the specific problem of defining shape parts. The cluster cohesiveness and a node participation vector are two important outputs of the proposed graph partitioning method. Opposed to most of the existing techniques, the final number of the clusters is determined automatically, by estimating the cluster cohesiveness on a random network generation process. Experimental results on several shape databases show the effectiveness of our framework for graph-based shape decomposition.

Enhanced Dominant Sets Clustering by Cluster Expansion

While a vast amount of clustering algorithms of different types are available in the literature, the majority of existing algorithms depend on carefully tuned parameters to obtain satisfactory results. In this paper, we reduce the dependence on parameters on the basis of the dominant sets algorithm. The dominant sets algorithm is a parameter-independent clustering approach, which uses the pairwise data similarity matrix as input. If the data for clustering are in the form of feature vectors, it is necessary to measure the data similarity and build the similarity matrix. With the commonly used Gaussian kernel, the involved parameter is found to exert a significant influence on the clustering results. We study in depth why and how the dominant sets clustering results are influenced by the parameter and attribute the influence to the dominant set definition, which imposes a somewhat too strict constraint on internal similarity. A two-step clustering algorithm is then proposed to solve this problem. First, we transform the similarity matrix by histogram equalization before clustering, and this is shown to eliminate the influence of similarity parameter effectively. In the second step, we expand the clusters to maximize the ratio of internal similarity with respect to external similarity. Our algorithm is designed to achieve the balance between high internal similarity and low external similarity, thereby relieving the dependence on the similarity parameter. In experiments on ten publicly available data sets, our algorithm is shown to perform well in comparison with several other algorithms which benefit from carefully tuned parameters.

Density Based Cluster Growing via Dominant Sets

Although there are a lot of clustering algorithms available in the literature, existing algorithms are usually afflicted by practical problems of one form or another, including parameter dependence and the inability to generate clusters of arbitrary shapes. In this paper we aim to solve these two problems by merging the merits of dominant sets and density based clustering algorithms. We firstly apply histogram equalization to eliminate the parameter dependence problem of the dominant sets algorithm. Noticing that the obtained clusters are usually smaller than the real ones, a density threshold based cluster growing step is then used to improve the clustering results, where the involved parameters are determined based on the initial clusters. This is followed by the second cluster growing step which makes use of the density relationship between neighboring data. Data clustering experiments and comparison with other algorithms validate the effectiveness of the proposed algorithm.

A Parameter-Independent Clustering Framework

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.

Parameter independent clustering based on dominant sets and cluster merging

Clustering is an important unsupervised learning approach with wide application in data mining, pattern recognition and intelligent information processing. However, existing clustering algorithms usually involve one or more user-specified parameters as input and their clustering results depend heavily on these parameters. In order to solve this problem, we present a parameter independent clustering algorithm based on the dominant sets algorithm and cluster merging. In the first step histogram equalization transformation is applied to solve the parameter dependence problem of the dominant sets algorithm. We provide the theoretic foundation of this method and discuss the implementation details. The clustering result is then refined with a cluster merging method, which is based on a new clustering quality evaluation criterion. We use extensive experiments on several datasets to validate each step and the whole procedures of our algorithm. It is shown that our parameter independent algorithm performs comparably to some existing clustering algorithms which benefit from user-specified parameters.

Feature Combination via Clustering.

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.

A Data-Driven Clustering Approach for Fault Diagnosis

Clustering is an important approach in fault diagnosis. The dominant sets algorithm is a graph-based clustering algorithm, which defines the dominant set as a concept of a cluster. In this paper, we make an in-depth investigation of the dominant sets algorithm. As a result, we find that this algorithm is dependent on the similarity parameter in constructing the pairwise similarity matrix, and has the tendency to generate spherical clusters only. Based on the merits and drawbacks of this algorithm, we apply the histogram equalization transformation to the similarity matrices for the purpose of removing the influence of similarity parameters, and then use a density-based cluster expansion process to improve the clustering results. In experimental validation of the proposed algorithm, we use two criterions to evaluate the clustering results in order to arrive at convincing conclusions. Data clustering experiments on ten data sets and fault detection experiments on the Tennessee Eastman process demonstrate the effectiveness of the proposed algorithm.

Cluster merging based on a decision threshold

Data clustering is an important unsupervised learning technique and has wide application in various fields including pattern recognition, data mining, image analysis and bioinformatics. A vast amount of clustering algorithms have been proposed in the past decades. However, existing algorithms still face many problems in practical applications. One typical problem is the parameter dependence, which means that user-specified parameters are required as input and the clustering results are influenced by these parameters. Another problem is that many algorithms are not able to generate clusters of non-spherical shapes. In this paper, a cluster merging method is proposed to solve the above-mentioned problems based on a decision threshold and the dominant sets algorithm. Firstly, the influence of similarity parameter on dominant sets clustering results is studied, and it is found that the obtained clusters become larger with the increase in similarity parameter. We analyze the reason behind this behavior and propose to generate small initial clusters in the first step and then merge the initial clusters to improve the clustering results. Specifically, we select a similarity parameter which generates small but not too small clusters. Then, we calculate pairwise merging decisions among the initial clusters and obtain a merging decision threshold. Based on this threshold, we merge the small clusters and obtain the final clustering results. Experiments on several datasets are used to validate the effectiveness of the proposed algorithm.

Towards parameter-independent data clustering and image segmentation

While there are a large amount of clustering algorithms proposed in the literature, the clustering results of existing algorithms usually depend on user-specified parameters heavily, and it is usually difficult to determine the optimal parameters. With the pairwise data similarity matrix as the input, dominant sets clustering has been shown to be an effective data clustering and image segmentation approach, partly due to its ability to find out the underlying data structure and determine the number of clusters automatically. However, we find that the original dominant sets algorithm is sensitive to the similarity measures used in building the similarity matrix. This means that parameter tuning is required to generate satisfactory clustering results, and dominant sets clustering results are also parameter dependent. In order to remove the dependence on the user-specified parameter, we study how the similarity measures influence the dominant sets clustering results. As a result, we propose to transform similarity matrices by histogram equalization before clustering. While this transformation is shown to remove the sensitiveness to similarity measures effectively, it also results in over-segmentation. Therefore in the next step we present a cluster extension method to overcome the over-segmentation effect and generate more reasonable clustering results. We test the enhanced clustering algorithm in both data clustering and image segmentation experiments, and comparisons with the state-of-the-art algorithms validate the effectiveness of our algorithm.

Automated multi-subject fiber clustering of mouse brain using dominant sets.

Mapping of structural and functional connectivity may provide deeper understanding of brain function and disfunction. Diffusion Magnetic Resonance Imaging (DMRI) is a powerful technique to non-invasively delineate white matter (WM) tracts and to obtain a three-dimensional description of the structural architecture of the brain. However, DMRI tractography methods produce highly multi-dimensional datasets whose interpretation requires advanced analytical tools. Indeed, manual identification of specific neuroanatomical tracts based on prior anatomical knowledge is time-consuming and prone to operator-induced bias. Here we propose an automatic multi-subject fiber clustering method that enables retrieval of group-wise WM fiber bundles. In order to account for variance across subjects, we developed a multi-subject approach based on a method known as Dominant Sets algorithm, via an intra- and cross-subject clustering. The intra-subject step allows us to reduce the complexity of the raw tractography data, thus obtaining homogeneous neuroanatomically-plausible bundles in each diffusion space. The cross-subject step, characterized by a proper space-invariant metric in the original diffusion space, enables the identification of the same WM bundles across multiple subjects without any prior neuroanatomical knowledge. Quantitative analysis was conducted comparing our algorithm with spectral clustering and affinity propagation methods on synthetic dataset. We also performed qualitative analysis on mouse brain tractography retrieving significant WM structures. The approach serves the final goal of detecting WM bundles at a population level, thus paving the way to the study of the WM organization across groups.