Dimensionality reduction on Riemannian manifolds is challenging due to the complex nonlinear data structures. While probabilistic principal geodesic analysis~(PPGA) has been proposed to generalize conventional principal component analysis (PCA) onto manifolds, its effectiveness is limited to data with a single modality. In this paper, we present a novel Gaussian latent variable model that provides a unique way to integrate multiple PGA models into a maximum-likelihood framework. This leads to a well-defined mixture model of probabilistic principal geodesic analysis (MPPGA) on sub-populations, where parameters of the principal subspaces are automatically estimated by employing an Expectation Maximization algorithm. We further develop a mixture Bayesian PGA (MBPGA) model that automatically reduces data dimensionality by suppressing irrelevant principal geodesics. We demonstrate the advantages of our model in the contexts of clustering and statistical shape analysis, using synthetic sphere data, real corpus callosum, and mandible data from human brain magnetic resonance~(MR) and CT images.

Machine Learning is all the rage as companies try to make sense of the mountains of data they are collecting. Data is everywhere and proliferating at unprecedented speed. But, more data is not always better. In fact, large amounts of data can not only considerably slow down the system execution but can sometimes even produce worse performances in Data Analytics applications. We have found, through years of formal and informal testing, that data dimensionality reduction -- or the process of reducing the number of attributes under consideration when running analytics -- is useful not only for speeding up algorithm execution but also for improving overall model performance. This doesn't mean minimizing the volume of data being analyzed per se but rather being smarter about how data sets are constructed.

Click to learn more about author Rosaria Silipo. Machine Learning is all the rage as companies try to make sense of the mountains of data they are collecting. Data is everywhere and proliferating at unprecedented speed. But, more data is not always better. In fact, large amounts of data can not only considerably slow down the system execution but can sometimes even produce worse performances in Data Analytics applications.

The recent explosion of data set size, in number of records and attributes, has triggered the development of a number of big data platforms as well as parallel data analytics algorithms. At the same time though, it has pushed for usage of data dimensionality reduction procedures. Indeed, more is not always better. Large amounts of data might sometimes produce worse performances in data analytics applications. One of my most recent projects happened to be about churn prediction and to use the 2009 KDD Challenge large data set.