Abstract
With the rapid development of data collection, communication technology and
network technology, dimensionality of natural data becomes higher and higher, thus
how to represent data effectively so as to facilitate subsequent processing, such as
cluster analysis has become a hot research direction. This dissertation mainly studies
the data feature extraction methods based on manifold, mapping the original data to the
low structure space, and then facilitating the data clustering in the low dimensional
space. The main contents and contributions are as follows:
1. Inspired by LPP and PCA, the combined Local Similarity and Local Diversity
based on the manifold learning clustering algorithm (LSDPC) is proposed.
LSDPC defines adjacency graphs to characterize the geometry of data, which reflects
the similarity of data; and variability of data. And then, similarity scatter, diversity
scatter are calculated from the corresponding graphs respectively. At last, A feature
extraction criterion is raised by minimizing the scatter, which efficiently preserves the
locality, and simultaneously maximizing the variation of data. Compared with the
traditional clustering methods, LSDPC overcomes the influence of the data dimension
and get the effective represent high dimension data of the low dimensional, the
experiments show the effectiveness of the proposed algorithm.
2. Most existing semi-supervised clustering algorithm only are suitable for the
low dimensional data., a semi-supervised clustering based on the discirminant analysis
(LDESC) is proposed to deal with the high-dimensional data. The algorithm LDESC
defines two adjacency graphs, one adjacency graph and margin graph, one adjacency
graph, which includes similarity and variation of the data points belonging to the same
class. And then, adjacency scatter, diversity scatter are calculated from the
corresponding graphs respectively. At last, A feature extraction criterion is raised,
which can get the best projection directions. The experiments show the effectiveness of
the proposed algorithm.
Keywords : Clustering Manifold learning Semi-supervised clustering
Discirminant analysis
