Constrained Laplacian Eigenmap for dimensionality reduction

Dimensionality reduction is a commonly used tool in machine learning, especially when dealing with high dimensional data. We consider semi-supervised graph based dimensionality reduction in this paper, and a novel dimensionality reduction algorithm called constrained Laplacian Eigenmap (CLE) is proposed. Suppose the data set contains r classes, and for each class we have some labeled points. CLE maps each data point into r different lines, and each map i tries to separate points belonging to class i from others by using label information. CLE constrains the solution space of Laplacian Eigenmap only to contain embedding results that are consistent with the labels. Then, each point is represented as a r-dimensional vector. Labeled points belonging to the same class are merged together, labeled points belonging to different classes are separated, and similar points are close to one another. We perform semi-supervised document clustering using CLE on two standard corpora. Experimental results show that CLE is very effective.