Similarity Function Learning with Data Uncertainty

Similarity functions are at the core of many pattern recognition applications. Standard approaches use feature vectors extracted from a pair of images to compute their degree of similarity. Often feature vectors are noisy and a direct application of standard similarly learning methods may result in unsatisfactory performance. However, information on statistical properties of the feature extraction process may be available, such as the covariance matrix of the observation noise. In this paper, we present a method which exploits this information to improve the process of learning a similarity function. Our approach is composed of an unsupervised dimensionality reduction stage and the similarity function itself. Uncertainty is taken into account throughout the whole processing pipeline during both training and testing. Our method is based on probabilistic models of the data and we propose EM algorithms to estimate their parameters. In experiments we show that the use of uncertainty significantly outperform other standard similarity function learning methods on challenging tasks.