Abstract
This paper proposes an inner product Laplacian embedding algorithm based on semi-definite programming, named as IPLE algorithm. The new algorithm learns a geodesic distance-based kernel matrix by using semi-definite programming under the constraints of local contraction. The criterion function is to make the neighborhood points on manifold as close as possible while the geodesic distances between those distant points are preserved. The IPLE algorithm sufficiently integrates the advantages of LE, ISOMAP and MVU algorithms. The comparison experiments on two image datasets from COIL-20 images and USPS handwritten digit images are performed by applying LE, ISOMAP, MVU and the proposed IPLE. Experimental results show that the intrinsic low-dimensional coordinates obtained by our algorithm preserve more information according to the fraction of the dominant eigenvalues and can obtain the better comprehensive performance in clustering and manifold structure.
Highlights
In the current information age, a large quantity of data can be obtained
This paper proposes an inner product Laplacian embedding algorithm based on semi-definite programming, named as Inner Production Laplacian Embedding (IPLE) algorithm
We propose a new manifold learning algorithm which is named as Inner Production Laplacian Embedding (IPLE) based on the following four considerations: 1) the geodesic distances along the curve are more meaningful than Euclidean distances, 2) the geodesic distance-based kernel matrix should be guaranteed to be positive semi- definite, 3) the requirement of natural clustering is constrained in the intrinsic low-dimensional space, 4) the solving scheme of the semi-definite programming is applied to optimizing the objection function with positive semi-definite constraint condition
Summary
In the current information age, a large quantity of data can be obtained . The valuable information is submerged into large scale datasets. It is urgently necessary to find the intrinsic laws of the data sets and predict the future development trend. One of the central problems in machine learning, computer vision and pattern recognition, is to develop appropriate representations for complex data. Manifold learning assumes that these observed data lie on or close to intrinsic low-dimensional manifolds embedded in the high-dimensional Euclidean space. The main goal of manifold learning is to find intrinsic low-dimensional manifold structures of high-dimensional observed dataset. Several known manifold learning algorithms have been proposed, such as ISOmetric feature MAPping (ISOMAP) [1], Laplacian Eigenmaps (LE) [2], and Maximum Variance Unfolding (MVU) [3], etc
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