DocumentCode :
180041
Title :
Multiple kernel interpolation for inverting non-linear dimensionality reduction and dimension estimation
Author :
Thiagarajan, J.J. ; Bremer, Peer-Timo ; Ramamurthy, K.N.
fYear :
2014
fDate :
4-9 May 2014
Firstpage :
6751
Lastpage :
6755
Abstract :
The problem of stably inverting a non-linear dimensionality reduction map has applications in data visualization and machine learning, besides being of theoretical interest. In this paper, we propose a meshfree interpolation method for obtaining such inverse maps using a non-negative linear combination of multiple interpolants. We show that the proposed scheme can improve upon the approximation power of its individual constituent kernels, and discuss the conditions under which its parameters can be uniquely estimated. We also provide an approach for estimating the intrinsic dimensionality (ID) of manifolds using the proposed inverse map. Experiments using multiple kernel interpolation for reconstruction of novel test data and ID estimation show an improved or similar performance compared to existing techniques.
Keywords :
approximation theory; data reduction; data visualisation; interpolation; inverse problems; learning (artificial intelligence); approximation power improvement; data visualization; dimension estimation inversion; intrinsic dimensionality estimation; machine learning; meshfree interpolation method; multiple kernel interpolation; nonlinear dimensionality reduction map inversion; novel test data reconstruction; Estimation; Interpolation; Kernel; Manifolds; Noise; Polynomials; intrinsic dimension estimation; inverse map; kernel interpolation; manifold learning;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Acoustics, Speech and Signal Processing (ICASSP), 2014 IEEE International Conference on
Conference_Location :
Florence
Type :
conf
DOI :
10.1109/ICASSP.2014.6854907
Filename :
6854907
Link To Document :
بازگشت