Research Of Latent Subspace Clustering Algorithm Based On Improved Dictionary Learning

As a tool of data analysis, clustering analysis has been widely used in pattern recognition, machine learning, document retrieval, data mining and so on. It is the analysis process that aggregates the abstract data objects to form multiple clusters. With the popularity of the network and the development of the computer graphics technology, a large number of image data and video data become available. In addition, since the people's requirements on image and video resolution are getting higher and higher, more and more high-dimensional data, often up to hundreds of TB are being generated. Most of the traditional clustering algorithms are designed for low-dimensional data, so it is difficult to deal with high-dimensional data efficiently.Subspace clustering algorithm, which is an extension of the traditional clustering algorithm, is an effective way to deal with high-dimensional data clustering. In this thesis, the main research objective is to improve the latent subspace clustering algorithm based on sparse representation to enhance its clustering performance. The main contents are as follows:1) This thesis gives an introduction about the basic principles of the sparse representation model and dictionary learning model in detail, and explains the steps, advantages and disadvantages of some classic algorithm of the sparse representation field and dictionary learning field. These algorithms includes the MP, OMP, MOD and KSVD algorithm. Then this thesis introduces some background knowledge of the subspace clustering algorithm and the spectral clustering algorithm. It also deduces the steps of spectral clustering algorithm in detail, which indeed provides the foundation for improving algorithm later.2) This thesis also gives an elaboration on a subspace clustering algorithm based on spectral clustering, sparse representation, as well as the dictionary learning, which are called latent subspace clustering algorithm(LSC), and it also introduces the main idea and the related derivation3) The training dictionary of the latent subspace clustering algorithm lacks stability and discrimination. In order to circumvent this shortcoming, this thesis proposes an improved latent subspace clustering algorithm based on the discriminant dictionary called ILSC. The algorithm improves the dictionary learning model by using the label information of a small number of training samples in the dictionary learning phase. In addition to the original reconstruction error term, a sparse coding error term and classification error term are also added to construct the discriminative dictionary. Therefore the sparse representation of the signals is more accurate, and the accuracy of the clustering algorithm is improved a lot.4) In order to enhance the discrimination of the dictionary, two new error terms are added into the objective function of the ILSC algorithm, which increases the time of the dictionary learning phase. To address this issue, an improved algorithm based on incremental dictionary training algorithm is proposed, which is called I2 LSC. This algorithm uses the idea of incremental algorithm, which reads a small part of the training data each time and updates the dictionary and the corresponding error term incrementally. The I2 LSC algorithm reduces the time cost in dictionary learning stage greatly, and guarantees the discrimination of the dictionary at the same time.