Research On Hyperplane Prototype Clustering Algorithm And Its Generalization In Neural Networks

As one of the basic tools digging internal structure from data, clustering analysis is also an important branch of unsupervised pattern classification in statistical pattern recognition. The common clustering algorithms can be divided into five types, i.e. partitioning methods, hierarchical methods, density-based methods, grid-based methods and model-based methods. And the main research object in this paper, i.e. the k-Plane Clustering (kPC) algorithm, belongs to the partitioning methods. It generalized the traditional k-means algorithm from the point of view of prototype selection. In detail, the kPC algorithm substituted hyperplanes for points used in k-means algorithm to be the prototypes and got these hyperplanes by minimizing the sum of the squared distances between each point and its closest hyperplane.In this paper, we propose a novel Fuzzy c-Plane Clustering (FcPC) algorithm by introducing the concept of fuzzy partitioning into the kPC algorithm. Similar to kPC, FcPC also uses hyperplanes to represent clustering centers. Further more, it considers the fuzzy membership between points and central hyperplanes and establishes a fuzzy objective function, which will be minimized to get the prototype hyperplanes. Therefore, FcPC represents the fuzzy membership between points and cluster center planes much more clearly compared with kPC. The experimental results have proved FcPC's clustering validity. To further extend kPC's usage, we generalize Gaussian radial-basis function to the so-called Plane-Gaussian function by combining the information got from kPC algorithm. Consequently, with such a Plane-Gaussian function as the activation function of the hidden layer, we develop a novel neural network named Plane-Gaussian (PG) network. PG network combines MLP's structure and RBF's fast learning method so that it can be viewed as a new class of the networks lying between MLP and RBF networks. The experimental results show that the proposed PG network has comparable classification performance to both MLP and RBF networks, and is particularly suitable for classifying the datasets with subspace characteristics. As a whole, we can get following conclusion: no matter in clustering or classification, the most effective models are the ones combined with prior knowledge.