Spectral Clustering Algorithm And Its Application Research

Cluster analysis is a statistical method for classification of the sample, but also a datamining method that can effectively achieve the detection data structures, machine learning hasbecome a hot topic in recent years in the international arena. Spectral clustering algorithm isan important research direction in the clustering algorithm, its theoretical foundation fromgraph theory that changes the clustering problem into a graph theory problem withoutdividing the weighted graph. Compared with the other existing clustering algorithm, spectralclustering algorithm can be implemented any clustering problem in any sample space, and canovercome the phenomenon that the appearance of local optimal solution, at last obtained theoptimal solution.Based on the systematic study of spectral clustering algorithm this paper improves thepart of the relevant algorithm. Specific content of the work are summarized below:1) This thesis introduces the basis of knowledge of clustering algorithms and spectralclustering algorithm, and analysis the technology research and application of spectralclustering, summed up several key issues involved in the field of spectral clustering andseveral research directions of spectral clustering algorithm.2) For the traditional spectral clustering of two key issues-how to define the similaritymatrix and determines the number of classes automatically, this article put forward thealgorithm that a kind of density sensitive adaptive spectral clustering algorithm based on thetwo concepts that density–sensitive distance and feature gap. The experiments of the newalgorithm is effective on artificial datasets and UCI datasets, while the algorithm compareswith the traditional algorithm SC in the classification accuracy, the comparison results showthe new algorithm has better clustering effect.3) For IPCM algorithm doesn’t have ideal clustering effect for different degrees ofsparse data set, and you need to initialize the number of clustering, this article put forward the algorithm that a kind of adaptive IPCM algorithm based on spectral clustering based on thetwo concepts that density–sensitive distance and feature gap. New algorithm use the densitysensitive distance instead of Euclidean distance and calculate the number of clusters by thefeature space accurately. The experiment proves the effectiveness of the improved algorithm,the algorithm can compensate for the lack of IPCM spectral clustering algorithm andweaknesses when each individual clusters that exist.4) This article improve the D-cut algorithm by using density sensitive similaritymeasure mentioned in place of the original Euclidean distance, and put forward a newalgorithm that a kind of image threshold segmentation based on density cut sensitivediscriminated method. The algorithm use gray-scale weight matrix (instead of pixel-levelimage-based weight matrix) to describe the relationship between the image pixels, thismethod is less complexity and need less storage space than other graph-based imagesegmentation method.