In many areas of machine learning, the characterization of the input data is given by a form of proximity measure between data points. Examples of such representations are pairwise differences, pairwise distances, and pairwise comparisons. In this work, we investigate different learning problems on data represented in terms of such pairwise proximities. More specifically, we consider three problems: masking (feature selection) for dimensionality reduction, extension of the dimensionality reduction for time series, and online collaborative filtering. For each of these problems, we start with a form of pairwise proximity which is relevant in the problem at hand. We evaluate the performance of the proposed algorithms in terms of both theoretical metrics and in practical applications such as eye gaze estimation and movie recommendations.