Nonlinear Dimensionality Reduction with Local Spline Embedding

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Authors Shiming Xiang, Feiping Nie, Changshui Zhang and Chunxia Zhang
Journal/Conference Name IEEE Transactions on Knowledge and Data Engineering(TKDE)
Paper Category
Paper Abstract This paper presents a new algorithm for Non-Linear Dimensionality Reduction (NLDR). Our algorithm is developed under the conceptual framework of compatible mapping. Each such mapping is a compound of a tangent space projection and a group of splines. Tangent space projection is estimated at each data point on the manifold, through which the data point itself and its neighbors are represented in tangent space with local coordinates. Splines are then constructed to guarantee that each of the local coordinates can be mapped to its own single global coordinate with respect to the underlying manifold. Thus the compatibility between local alignments is ensured. In such a work setting, we develop an optimization framework based on reconstruction error analysis, which can yield a global optimum. The proposed algorithm is also extended to embed out-of-samples via spline interpolation. Experiments on toy data sets and real-world data sets illustrate the validity of our method.
Date of publication 2009
Code Programming Language MATLAB
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