Unsupervised Joint Alignment and Clustering using Bayesian Nonparametrics

Marwan A. Mattar, Allen R. Hanson, Erik G. Learned-Miller
Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, PMLR R10:582-591, 2012.

Abstract

Joint alignment of a collection of functions is the process of independently transforming the functions so that they appear more similar to each other. Typically, such unsupervised alignment algorithms fail when presented with complex data sets arising from multiple modalities or make restrictive assumptions about the form of the functions or transformations, limiting their generality. We present a transformed Bayesian infinite mixture model that can simultaneously align and cluster a data set. Our model and associated learning scheme offer two key advantages: the optimal number of clusters is determined in a data-driven fashion through the use of a Dirichlet process prior, and it can accommodate any transformation function parameterized by a continuous parameter vector. As a result, it is applicable to a wide range of data types, and transformation functions. We present positive results on synthetic two-dimensional data, on a set of one-dimensional curves, and on various image data sets, showing large improvements over previous work. We discuss several variations of the model and conclude with directions for future work.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR10-mattar12a, title = {Unsupervised Joint Alignment and Clustering using {B}ayesian Nonparametrics}, author = {Mattar, Marwan A. and Hanson, Allen R. and Learned-Miller, Erik G.}, booktitle = {Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence}, pages = {582--591}, year = {2012}, editor = {de Freitas, Nando and Murphy, Kevin}, volume = {R10}, series = {Proceedings of Machine Learning Research}, month = {14--18 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r10/main/assets/mattar12a/mattar12a.pdf}, url = {https://proceedings.mlr.press/r10/mattar12a.html}, abstract = {Joint alignment of a collection of functions is the process of independently transforming the functions so that they appear more similar to each other. Typically, such unsupervised alignment algorithms fail when presented with complex data sets arising from multiple modalities or make restrictive assumptions about the form of the functions or transformations, limiting their generality. We present a transformed Bayesian infinite mixture model that can simultaneously align and cluster a data set. Our model and associated learning scheme offer two key advantages: the optimal number of clusters is determined in a data-driven fashion through the use of a Dirichlet process prior, and it can accommodate any transformation function parameterized by a continuous parameter vector. As a result, it is applicable to a wide range of data types, and transformation functions. We present positive results on synthetic two-dimensional data, on a set of one-dimensional curves, and on various image data sets, showing large improvements over previous work. We discuss several variations of the model and conclude with directions for future work.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Unsupervised Joint Alignment and Clustering using Bayesian Nonparametrics %A Marwan A. Mattar %A Allen R. Hanson %A Erik G. Learned-Miller %B Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2012 %E Nando de Freitas %E Kevin Murphy %F pmlr-vR10-mattar12a %I PMLR %P 582--591 %U https://proceedings.mlr.press/r10/mattar12a.html %V R10 %X Joint alignment of a collection of functions is the process of independently transforming the functions so that they appear more similar to each other. Typically, such unsupervised alignment algorithms fail when presented with complex data sets arising from multiple modalities or make restrictive assumptions about the form of the functions or transformations, limiting their generality. We present a transformed Bayesian infinite mixture model that can simultaneously align and cluster a data set. Our model and associated learning scheme offer two key advantages: the optimal number of clusters is determined in a data-driven fashion through the use of a Dirichlet process prior, and it can accommodate any transformation function parameterized by a continuous parameter vector. As a result, it is applicable to a wide range of data types, and transformation functions. We present positive results on synthetic two-dimensional data, on a set of one-dimensional curves, and on various image data sets, showing large improvements over previous work. We discuss several variations of the model and conclude with directions for future work. %Z Reissued by PMLR on 04 October 2026.
APA
Mattar, M.A., Hanson, A.R. & Learned-Miller, E.G.. (2012). Unsupervised Joint Alignment and Clustering using Bayesian Nonparametrics. Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R10:582-591 Available from https://proceedings.mlr.press/r10/mattar12a.html. Reissued by PMLR on 04 October 2026.

Related Material