Clustering Analysis Study Based On Kernel Function

Data mining is an important subject of information field. Data mining technique is widely used in many industries now. Clustering is one of the core technique of data mining. K-means clustering, which is widely used in presently clustering algorithms, is a concise and practical algorithm, but it didn't optimize the features of the data samples and so the result of the clustering is not satisfying if the boundaries of the samples is nonlinear or the samples doesn't subject to Gaussian distribution. The kernel method improves the optimization of the example features and transforms the nonlinear learning problems to linear learning problems by mapping the samples from input space to feature space. By introducing the kernel methods the clustering algorithm can obtain better performance.Aiming on absence of robust performance of presently kernel clustering based on hard partition and limitation of defining the fuzzy parameter in fuzzy clustering algorithm, this thesis presents a new clustering algorithm—kernel k-aggregate clustering algorithm in virtue of aggregate function approximating maximum function, which is both soft clustering and avoidance of choosing fuzzy parameter. Next, focus on amount of categorical valued and mixed valued data in practical use and the limitation of k-prototypes and fuzzy k-prototypes clustering dealing with categorical valued and mixed valued data, this thesis extends the algorithm to categorical valued and mixed valued data by combining categorical value attributes decomposing method with kernel k-aggregate clustering algorithm so as to make the algorithm more widely applicable.At the beginning, this thesis introduces some background information about clustering and relative theory about kernel function. Secondly, the thesis presents presenting kernel k-aggregate clustering algorithm based on explaining the limitation of existing clustering and proves the effectiveness by data experiment using Matlab. The author suggests this algorithm is more stable, robust and accurate in clustering. At last, the author apply the algorithm to segmentation of a certain hairdressing health center and the clustering analysis provides them implication and evidence of different marketing strategies for different segmental markets.