Spectral Clustering Analysis And Application Under The High Dimensional Circumstance

Clustering algorithm is a method that can be used to segregate an object to be several clusters. We can also extract useful information from clustering. For example, the clustering algorithm can help us research the similarity among individuals who belong to each cluster. In addition, we can also discover the dissimilarity between each cluster from clustering. In recent years, since spectral clustering can be manipulated by simple linear algebra, it is very popular. This paper is focus on the spectral clustering and its application under the high dimensional circumstance.First of all, spectral clustering and the idea used in spectral clustering are demonstrated. Then, the karate club data is used to illustrate the validity of spectral clustering. By using simulation through R software, the spectral clustering is compare with k-means method. From the simulation, the advantage and disadvantage of spectral clustering are pointed out. The similarity function parameter which plays a key point in spectral clustering is also discovered.In addition, this paper provides a clustering algorithm that can be used under the high dimensional circumstance. Firstly, the dimensional reduction is applied in the original data. In this paper, the random projection is used for dimensional reduction. Then, the spectral clustering is utilized in the reduced data. By taking disadvantage provided by random projection into considered, this paper proposes an algorithm which averages similarity matrixes that are produced by multiple random projections to overcome this difficult. At last, this algorithm is proved by Monte Carlo simulation. It is also compared with k-means method and subspace clustering method.