I. Introduction
To extract knowledge from data, it is generally assumed that input data is drawn from a vector space with a well-defined p airwise p roximity m easure [ 3]. H owever, b ig data comes in a wide variety; and, in many cases (e.g., sequences, images, and text), the data objects are not given as feature vectors. Such data needs to be mapped to a meaningful feature space, where vector-space-based data mining algorithms can be employed. Many data mining and machine learning methods, such as support vector machines (SVM), kernel-PCA, and agglomerative clustering, do not explicitly require input data as feature vectors; instead, they only utilize the pairwise distance information [2]. Moreover, the choice of a distance or similarity measure is often arbitrary and does not necessarily capture the inherent similarity between objects.