SMAC: Simultaneous Mapping and Clustering Using Spectral Decompositions

Chandrajit Bajaj, Tingran Gao, Zihang He, Qixing Huang, Zhenxiao Liang
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:324-333, 2018.

Abstract

We introduce a principled approach for simultaneous mapping and clustering (SMAC) for establishing consistent maps across heterogeneous object collections (e.g., 2D images or 3D shapes). Our approach takes as input a heterogeneous object collection and a set of maps computed between some pairs of objects, and outputs a homogeneous object clustering together with a new set of maps possessing optimal intra- and inter-cluster consistency. Our approach is based on the spectral decomposition of a data matrix storing all pairwise maps in its blocks. We additionally provide tight theoretical guarantees on the exactness of SMAC under established noise models. We also demonstrate the usefulness of the approach on synthetic and real datasets.

Cite this Paper


BibTeX
@InProceedings{pmlr-v80-bajaj18a, title = {{SMAC}: Simultaneous Mapping and Clustering Using Spectral Decompositions}, author = {Bajaj, Chandrajit and Gao, Tingran and He, Zihang and Huang, Qixing and Liang, Zhenxiao}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {324--333}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/bajaj18a/bajaj18a.pdf}, url = {http://proceedings.mlr.press/v80/bajaj18a.html}, abstract = {We introduce a principled approach for simultaneous mapping and clustering (SMAC) for establishing consistent maps across heterogeneous object collections (e.g., 2D images or 3D shapes). Our approach takes as input a heterogeneous object collection and a set of maps computed between some pairs of objects, and outputs a homogeneous object clustering together with a new set of maps possessing optimal intra- and inter-cluster consistency. Our approach is based on the spectral decomposition of a data matrix storing all pairwise maps in its blocks. We additionally provide tight theoretical guarantees on the exactness of SMAC under established noise models. We also demonstrate the usefulness of the approach on synthetic and real datasets.} }
Endnote
%0 Conference Paper %T SMAC: Simultaneous Mapping and Clustering Using Spectral Decompositions %A Chandrajit Bajaj %A Tingran Gao %A Zihang He %A Qixing Huang %A Zhenxiao Liang %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-bajaj18a %I PMLR %P 324--333 %U http://proceedings.mlr.press/v80/bajaj18a.html %V 80 %X We introduce a principled approach for simultaneous mapping and clustering (SMAC) for establishing consistent maps across heterogeneous object collections (e.g., 2D images or 3D shapes). Our approach takes as input a heterogeneous object collection and a set of maps computed between some pairs of objects, and outputs a homogeneous object clustering together with a new set of maps possessing optimal intra- and inter-cluster consistency. Our approach is based on the spectral decomposition of a data matrix storing all pairwise maps in its blocks. We additionally provide tight theoretical guarantees on the exactness of SMAC under established noise models. We also demonstrate the usefulness of the approach on synthetic and real datasets.
APA
Bajaj, C., Gao, T., He, Z., Huang, Q. & Liang, Z.. (2018). SMAC: Simultaneous Mapping and Clustering Using Spectral Decompositions. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:324-333 Available from http://proceedings.mlr.press/v80/bajaj18a.html.

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