Clustering Algorithm Research Base On Constructing Hyper-planes

As a kind of unsupervised method,the clustering algorithms reveal the data's intrinsic pattern by grouping data points based on their similarity.Because it always handles the datasets without pre-existing labels,only some basic information like the distance and density of points can be adopted for determining the clusters'information like the data centers for each cluster^[1,29,30],the numbers of clusters^[32],or the affinity matrix.Based on them,different objective functions are constructed to find the best results^[38-40].Here,we present a clustering method based on constructing hyper-planes.Its basis lies in an assumption that one group can be divided into sub groups of which points lie in a locally linear manifold.Therefore we can find the appropriate hyper-planes to distinguish points in different sub groups.Then we combine these hyper-planes to find the correct clusters.We applied the algorithm to the concentric circle,crescent and Swiss roll synthetic data sets,and the algorithm derived the correct results.To further evaluate the clustering performance of the algorithm,we applied the algorithm to some benchmark datasets:ORL(Olivetti Research Laboratory)face dataset,Yale face dataset and MNIST(Mixed National Institute of Standards and Technology database)dataset.ARI(Adjusted Rand Index)and NMI(Normalized Mutual Information)were used to evaluate the clustering results.Experiments indicate that our algorithm has two main advantages as follows.One is that the algorithm depends only on the marginal space between the points in different clusters.Therefore it can be approached on more general manifolds.The other advantage is that our algorithm can find the outliers.This enables our algorithm to cluster well in noisy datasets.