Nonlinear Dimensionality Reduction with Local Spline Embedding

View Researcher II's Other Codes

Disclaimer: “The provided code links for this paper are external links. Science Nest has no responsibility for the accuracy, legality or content of these links. Also, by downloading this code(s), you agree to comply with the terms of use as set out by the author(s) of the code(s).”

Please contact us in case of a broken link from here

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

Copyright Researcher II 2022