When users search online for a business, the search engine may present them with a list of related business recommendations. We address the problem of constructing a useful and diverse list of such recommendations that would include an optimal combination of substitutes and complements. Substitutes are similar potential alternatives to the searched business, whereas complements are local businesses that can offer a more comprehensive and better rounded experience for a user visiting the searched locality. In our problem setting, each business belongs to a category in an ontology of business categories. Two businesses are defined as substitutes of one another if they belong to the same category, and as complements if they are otherwise relevant to each other.

Big data for security informatics requires an analysis of both actors and measurement instruments. By analogy with social and political network analyses, primary questions involve who is doing what and in concert with whom. We seek to examine these questions using cluster analysis, non-linear dimensionality reduction, and machine learning techniques. We apply them to available political science and international relations databases, as these are natural proxies for security informatics databases. In particular we develop an embedding/clustering algorithm that reveals those political themes driving UN voting patterns as well as IGO (Inter-Governmental Organization) memberships. Our algorithm could readily be applied to international conflict, urban crime, and military engagement databases.

Association field models have been used to explain human contour grouping performance and to explain the mean frequency of long-range horizontal connections across cortical columns in V1. However, association fields essentially depend on pairwise statistics of edges in natural scenes. We develop a spectral test of the sufficiency of pairwise statistics and show that there is significant higher-order structure. An analysis using a probabilistic spectral embedding reveals curvature-dependent components to the association field, and reveals a challenge for biological learning algorithms.