Iterative Embedding with Robust Correction using Feedback of Error Observed

Praneeth Vepakomma, Ahmed Elgammal
; Proceedings of The 4th Workshop on Machine Learning for Interactive Systems at ICML 2015, PMLR 43:36-40, 2015.

Abstract

Nonlinear dimensionality reduction techniques of today are highly sensitive to outliers. Almost all of them are spectral methods and differ from each other over their treatment of the notion of neighborhood similarities computed amongst the high-dimensional input data points. These techniques aim to preserve the notion of this similarity structure in the low-dimensional output. The presence of unwanted outliers in the data directly influences the preservation of these neighborhood similarities amongst the majority of the non-outlier data, as these points ocuring in majority need to simultaneously satisfy their neighborhood similarities they form with the outliers while also satisfying the similarity structure they form with the non-outlier data. This issue disrupts the intrinsic structure of the manifold on which the majority of the non-outlier data lies when preserved via a homeomorphism on a low-dimensional manifold. In this paper we come up with an iterative algorithm that analytically solves for a non-linear embedding with mono- tonic improvements after each iteration. As an application of this iterative manifold learning algorithm, we come up with a framework that decomposes the pair-wise error observed between all pairs of points and update the neighborhood similarity matrix dynamically to downplay the effect of the outliers, over the majority of the non-outlier data being embedded into a lower dimension.

Cite this Paper


BibTeX
@InProceedings{pmlr-v43-vepakomma15, title = {Iterative Embedding with Robust Correction using Feedback of Error Observed}, author = {Praneeth Vepakomma and Ahmed Elgammal}, booktitle = {Proceedings of The 4th Workshop on Machine Learning for Interactive Systems at ICML 2015}, pages = {36--40}, year = {2015}, editor = {Heriberto Cuayáhuitl and Nina Dethlefs and Lutz Frommberger and Martijn Van Otterlo and Olivier Pietquin}, volume = {43}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {11 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v43/vepakomma15.pdf}, url = {http://proceedings.mlr.press/v43/vepakomma15.html}, abstract = {Nonlinear dimensionality reduction techniques of today are highly sensitive to outliers. Almost all of them are spectral methods and differ from each other over their treatment of the notion of neighborhood similarities computed amongst the high-dimensional input data points. These techniques aim to preserve the notion of this similarity structure in the low-dimensional output. The presence of unwanted outliers in the data directly influences the preservation of these neighborhood similarities amongst the majority of the non-outlier data, as these points ocuring in majority need to simultaneously satisfy their neighborhood similarities they form with the outliers while also satisfying the similarity structure they form with the non-outlier data. This issue disrupts the intrinsic structure of the manifold on which the majority of the non-outlier data lies when preserved via a homeomorphism on a low-dimensional manifold. In this paper we come up with an iterative algorithm that analytically solves for a non-linear embedding with mono- tonic improvements after each iteration. As an application of this iterative manifold learning algorithm, we come up with a framework that decomposes the pair-wise error observed between all pairs of points and update the neighborhood similarity matrix dynamically to downplay the effect of the outliers, over the majority of the non-outlier data being embedded into a lower dimension.} }
Endnote
%0 Conference Paper %T Iterative Embedding with Robust Correction using Feedback of Error Observed %A Praneeth Vepakomma %A Ahmed Elgammal %B Proceedings of The 4th Workshop on Machine Learning for Interactive Systems at ICML 2015 %C Proceedings of Machine Learning Research %D 2015 %E Heriberto Cuayáhuitl %E Nina Dethlefs %E Lutz Frommberger %E Martijn Van Otterlo %E Olivier Pietquin %F pmlr-v43-vepakomma15 %I PMLR %J Proceedings of Machine Learning Research %P 36--40 %U http://proceedings.mlr.press %V 43 %W PMLR %X Nonlinear dimensionality reduction techniques of today are highly sensitive to outliers. Almost all of them are spectral methods and differ from each other over their treatment of the notion of neighborhood similarities computed amongst the high-dimensional input data points. These techniques aim to preserve the notion of this similarity structure in the low-dimensional output. The presence of unwanted outliers in the data directly influences the preservation of these neighborhood similarities amongst the majority of the non-outlier data, as these points ocuring in majority need to simultaneously satisfy their neighborhood similarities they form with the outliers while also satisfying the similarity structure they form with the non-outlier data. This issue disrupts the intrinsic structure of the manifold on which the majority of the non-outlier data lies when preserved via a homeomorphism on a low-dimensional manifold. In this paper we come up with an iterative algorithm that analytically solves for a non-linear embedding with mono- tonic improvements after each iteration. As an application of this iterative manifold learning algorithm, we come up with a framework that decomposes the pair-wise error observed between all pairs of points and update the neighborhood similarity matrix dynamically to downplay the effect of the outliers, over the majority of the non-outlier data being embedded into a lower dimension.
RIS
TY - CPAPER TI - Iterative Embedding with Robust Correction using Feedback of Error Observed AU - Praneeth Vepakomma AU - Ahmed Elgammal BT - Proceedings of The 4th Workshop on Machine Learning for Interactive Systems at ICML 2015 PY - 2015/06/18 DA - 2015/06/18 ED - Heriberto Cuayáhuitl ED - Nina Dethlefs ED - Lutz Frommberger ED - Martijn Van Otterlo ED - Olivier Pietquin ID - pmlr-v43-vepakomma15 PB - PMLR SP - 36 DP - PMLR EP - 40 L1 - http://proceedings.mlr.press/v43/vepakomma15.pdf UR - http://proceedings.mlr.press/v43/vepakomma15.html AB - Nonlinear dimensionality reduction techniques of today are highly sensitive to outliers. Almost all of them are spectral methods and differ from each other over their treatment of the notion of neighborhood similarities computed amongst the high-dimensional input data points. These techniques aim to preserve the notion of this similarity structure in the low-dimensional output. The presence of unwanted outliers in the data directly influences the preservation of these neighborhood similarities amongst the majority of the non-outlier data, as these points ocuring in majority need to simultaneously satisfy their neighborhood similarities they form with the outliers while also satisfying the similarity structure they form with the non-outlier data. This issue disrupts the intrinsic structure of the manifold on which the majority of the non-outlier data lies when preserved via a homeomorphism on a low-dimensional manifold. In this paper we come up with an iterative algorithm that analytically solves for a non-linear embedding with mono- tonic improvements after each iteration. As an application of this iterative manifold learning algorithm, we come up with a framework that decomposes the pair-wise error observed between all pairs of points and update the neighborhood similarity matrix dynamically to downplay the effect of the outliers, over the majority of the non-outlier data being embedded into a lower dimension. ER -
APA
Vepakomma, P. & Elgammal, A.. (2015). Iterative Embedding with Robust Correction using Feedback of Error Observed. Proceedings of The 4th Workshop on Machine Learning for Interactive Systems at ICML 2015, in PMLR 43:36-40

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