Research And Application Of Possibilistic Clustering Method

With the rapid progress of modern industry, the automation and intelligent level for themechanical equipment becomes more and more high. Machine learning and patternrecognition can provide powerful support for its development. The representation, acquisitionand processing of the knowledge and information is an important step in Machine learningand pattern recognition. As an unsupervised data processing method, cluster analysis hasbeen widely applied in mechanical automation and intelligence. Because of thenon-repeatability, uncertainty, influence by multi-factors and data contamination in the realenvironment of machinery industry, the conventional hard and fuzzy clustering methodencountered difficulties in practical application. As an improved method for the fuzzyclustering, possibilistic clustering method will have better performance and applicationprospect. This paper takes a research on the possibilistic clustering method and itsapplications, the main works are summarized as follows:1. Research on possibilistic clustering modelA new clustering algorithm called improved unsupervised possibilistic clustering (IUPC)algorithm is proposed by adding the constraint conditions on cluster centers in theunsupervised possibilistic clustering (UPC) model. Since IUPC limits the feasible regions ofdifferent clusters disjoint, it can solve the problem of generating coincident clusters of thepossibilistic clustering method. IUPC avoid the problem of trapping into the local minimumor the saddle point by introducing the global optimization method. In order to furtherreinforce the noise robustness of the model and decrease the influence of the data around theboundary, IUPC based multi-model support vector regression (MSVR) is proposed toestimate the state of charge (SOC) for battery of electric vehicles. The contrast experimentsshow higher precision than the conventional fuzzy cluster based method.2. The research on prototype representation and distance function in possibilisticclustering(1) A novel clustering algorithm called unsupervised possibilistic clustering based onimproved mahalanobis distance (UPC-IMD) is proposed in this paper. The distance functionof UPC-IMD is determined by the possibilistic Covariance matrix which is weighted by thepossibilistic partition. UPC-IMD is more robust to noise than UPC because the possibilisticmembership function makes noise points have little influence on the distance function. UPC-IMD can indicate ellipsoid data structure because of introducing the mahalanobisdistance function into the clustering model.(2) Unsupervised possibilistic clustering based on the kernelized distance (UKDPC) isproposed. In UKDPC, the dissimilarity measure between data point and prototype is definedby the kernel function. Contrast experimental results show that UKDPC further increase therobustness of the UPC.(3) To get more robust to different shapes of the data structures, the kernel method isintroduced into the UPC model and a new algorithm called unsupervised possibilisticclustering based on kernel method (UKPC) is proposed. In UKPC, the sample points aremapped into the feature space by the introduced kernel function, which makes it have theability of revealing the non-convex cluster structure because the input data are mappedimplicitly into a high-dimensional feature space where the nonlinear pattern now appearslinear. Contrast experimental results show the effectiveness of UKPC.3. Establishing framework of the multi-scale possibilistic clusteringScales are the essential attributes of all the nature phenomena and things. The model ofmulti-scale clustering can reveal the data structure from different scales, which conforms tothe actual need. This paper establishes two multi-scale possibilistic clustering scheme fromtwo different points of view.(1) Establishing the framework of the multi-scale possibilistic clustering (MPC) based onthe mean shift (MS). The initial cluster centers are obtained by MS first, and then thepossibilistic cluster algorithm is executed to search for the actual models (centers). In thiscase, the cluster number and partitions are both determined automatically, and the multi-scalepossibilistic partition is obtained by controlling the bandwidth of the kernel function in MS.Moreover, mesh generation technique is also introduced to accelerate the algorithm. Severalalgorithms can be derived from this MPC framework by combining with different possibilisticclustering algorithms. The derived MPC-PCM algorithm is introduced into the imagesegmentation, based on which a novel image segmentation method called dynamic weightedmulti-scale possibilistic clustering (DWMSP) is proposed. Unsupervised image segmentationis realized by analyzing the weighted image by multi-scale possibilistic clustering algorithm.Several contrast experiments with classic tested images show that it can preserve image detailand gray information better than conventional methods, determine the cluster numberautomatically, and has a high computational efficiency(2) Putting forward a multi-scale possibilistic clustering based on automatic merging(MPC-AM). MPC-AM can determine the cluster number and structure adaptively according to the data features, and can reveal the data structures from different scales by adjusting thevalues of the scale factor.4. Research on the cluster validityThe mostly used cluster validity indexes such as FS, XB and PCAES index are alldefined by the inter-class separability and intra-class compactness. These indexes considerfully the fuzzy membership function and the construction geometry structure. However, it alsohas some drawbacks. Based on analyzing the problems of these indexes, a new index calledMPO is proposed by modifying the CO index. MPO is defined only by the partition matrix,and avoids the monotonous tendency with the cluster number. MPO does not need to set theparameter of the intra-class compactness, and is robust to the noises and outliers. Anotherindex called VS is also proposed. In VS, the exponential type distance is adopted and thegeometrical structure is considered, which makes it robust to the cluster sizes. Theexperimental results show the effectiveness of the proposed indexes.5. Research of robust theory in clustering method and cluster validityThe robustness of kernel based clustering algorithms and cluster validity indexes areanalyzed by using the statistical theory. First, the connection between M-estimator and thesecases are constructively established, and then the property of the influence function fordifferent kernel functions is analyzed. Based on the above obtained conclusions, therobustness theory is established. These results provide the theory support for the selection ofthe clustering algorithms and cluster validity indexes in practical applications. In themeanwhile, the robustness of the previously proposed indexes of MPO and VS are alsoproved by the statistical theory.6. Application research of unsupervised possibilistic clustering algorithm in faultdiagnosis of rolling bearingAll the proposed algorithms in this paper are applied to fault diagnosis of rolling bearing,and based on the extensive experimental results, conclusion and analysis are given. In theearly stage, both time features and frequency features based on the empirical mode andwavelet packet decomposition are considering. Then the features are selected by theestablished separability measure. Finally the diagnosis data are automatically clustered by thepossibilistic clustering algorithm. The results show UKPC fails to detect the diagnosticpatterns, which implies the features of diagnosis signals do not have the characteristic ofnon-linear separability. MPC-AM itself can execute unsupervised fault diagnosis, and otheralgorithms can also execute unsupervised fault diagnosis by combining the cluster validity.UKDPC has a similar recognition rate with the conventional fuzzy clustering method, and IUPC has a slightly higher recognition rate, while UPC-IMD and MPC-AM have asignificantly higher than fuzzy clustering method. UPC-IMD has the highest recognition rateamong all the contrast fuzzy and possibilistic clustering method, which owes to its ability ofdetecting the cluster structure with different sizes and distributions. MPC-AM can predict thediagnosis classes and judge whether the data have the diagnosis. By decreasing the value ofthe scale factor, the algorithm can divide the diagnosis signal in more details. This methodsolves the problem that the conventional method can not judge the clustering tendency andhave a low computational efficiency in executing the unsupervised clustering. Consideringthat the fault of rolling bearing has the features of multi-scale, and on-line monitoring anddiagnosis can not predict the diagnosis classes and whether having the diagnosis, MPC-AM isfit for the unsupervised fault diagnosis task.