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.

该论文提出了一种基于贝叶斯无限混合模型的转换方法，该方法在不受函数或转换形式限制的情况下可以同时对数据集进行聚类和对齐，并通过使用狄利克雷过程先验来以数据驱动的方式确定聚类的最优数量，并且可适用于多种类型和转换函数的数据，该方法通过在合成数据和各种图像数据集上的实验取得了积极的结果。