Learning a Metric Space for Neighbourhood Topology Estimation: Application to Manifold Learning

Karim Abou- Moustafa, Dale Schuurmans, Frank Ferrie
; Proceedings of the 5th Asian Conference on Machine Learning, PMLR 29:341-356, 2013.

Abstract

Manifold learning algorithms rely on a neighbourhood graph to provide an estimate of the data’s local topology. Unfortunately, current methods for estimating local topology assume local Euclidean geometry and locally uniform data density, which often leads to poor data embeddings. We address these shortcomings by proposing a framework that combines local learning with parametric density estimation for local topology estimation. Given a data set \mathcalD ⊂\mathcalX, we first estimate a new metric space (\mathbbX,d_\mathbbX) that characterizes the varying sample density of \mathcalX in \mathbbX, then use (\mathbbX,d_\mathbbX) as a new (pilot) input space for the graph construction step of the manifold learning process. The proposed framework results in significantly improved embeddings, which we demonstrated objectively by assessing clustering accuracy.

Cite this Paper


BibTeX
@InProceedings{pmlr-v29-Moustafa13, title = {Learning a Metric Space for Neighbourhood Topology Estimation: Application to Manifold Learning}, author = {Karim Abou- Moustafa and Dale Schuurmans and Frank Ferrie}, booktitle = {Proceedings of the 5th Asian Conference on Machine Learning}, pages = {341--356}, year = {2013}, editor = {Cheng Soon Ong and Tu Bao Ho}, volume = {29}, series = {Proceedings of Machine Learning Research}, address = {Australian National University, Canberra, Australia}, month = {13--15 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v29/Moustafa13.pdf}, url = {http://proceedings.mlr.press/v29/Moustafa13.html}, abstract = {Manifold learning algorithms rely on a neighbourhood graph to provide an estimate of the data’s local topology. Unfortunately, current methods for estimating local topology assume local Euclidean geometry and locally uniform data density, which often leads to poor data embeddings. We address these shortcomings by proposing a framework that combines local learning with parametric density estimation for local topology estimation. Given a data set \mathcalD ⊂\mathcalX, we first estimate a new metric space (\mathbbX,d_\mathbbX) that characterizes the varying sample density of \mathcalX in \mathbbX, then use (\mathbbX,d_\mathbbX) as a new (pilot) input space for the graph construction step of the manifold learning process. The proposed framework results in significantly improved embeddings, which we demonstrated objectively by assessing clustering accuracy.} }
Endnote
%0 Conference Paper %T Learning a Metric Space for Neighbourhood Topology Estimation: Application to Manifold Learning %A Karim Abou- Moustafa %A Dale Schuurmans %A Frank Ferrie %B Proceedings of the 5th Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Cheng Soon Ong %E Tu Bao Ho %F pmlr-v29-Moustafa13 %I PMLR %J Proceedings of Machine Learning Research %P 341--356 %U http://proceedings.mlr.press %V 29 %W PMLR %X Manifold learning algorithms rely on a neighbourhood graph to provide an estimate of the data’s local topology. Unfortunately, current methods for estimating local topology assume local Euclidean geometry and locally uniform data density, which often leads to poor data embeddings. We address these shortcomings by proposing a framework that combines local learning with parametric density estimation for local topology estimation. Given a data set \mathcalD ⊂\mathcalX, we first estimate a new metric space (\mathbbX,d_\mathbbX) that characterizes the varying sample density of \mathcalX in \mathbbX, then use (\mathbbX,d_\mathbbX) as a new (pilot) input space for the graph construction step of the manifold learning process. The proposed framework results in significantly improved embeddings, which we demonstrated objectively by assessing clustering accuracy.
RIS
TY - CPAPER TI - Learning a Metric Space for Neighbourhood Topology Estimation: Application to Manifold Learning AU - Karim Abou- Moustafa AU - Dale Schuurmans AU - Frank Ferrie BT - Proceedings of the 5th Asian Conference on Machine Learning PY - 2013/10/21 DA - 2013/10/21 ED - Cheng Soon Ong ED - Tu Bao Ho ID - pmlr-v29-Moustafa13 PB - PMLR SP - 341 DP - PMLR EP - 356 L1 - http://proceedings.mlr.press/v29/Moustafa13.pdf UR - http://proceedings.mlr.press/v29/Moustafa13.html AB - Manifold learning algorithms rely on a neighbourhood graph to provide an estimate of the data’s local topology. Unfortunately, current methods for estimating local topology assume local Euclidean geometry and locally uniform data density, which often leads to poor data embeddings. We address these shortcomings by proposing a framework that combines local learning with parametric density estimation for local topology estimation. Given a data set \mathcalD ⊂\mathcalX, we first estimate a new metric space (\mathbbX,d_\mathbbX) that characterizes the varying sample density of \mathcalX in \mathbbX, then use (\mathbbX,d_\mathbbX) as a new (pilot) input space for the graph construction step of the manifold learning process. The proposed framework results in significantly improved embeddings, which we demonstrated objectively by assessing clustering accuracy. ER -
APA
Moustafa, K.A., Schuurmans, D. & Ferrie, F.. (2013). Learning a Metric Space for Neighbourhood Topology Estimation: Application to Manifold Learning. Proceedings of the 5th Asian Conference on Machine Learning, in PMLR 29:341-356

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