Bilinear Random Projections for Locality-Sensitive Binary Codes

Locality-sensitive hashing (LSH) is a popular data-independent indexing method for approximate similarity search, where random projections followed by quantization hash the points from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. Most of high-dimensional visual descriptors for images exhibit a natural matrix structure. When visual descriptors are represented by high-dimensional feature vectors and long binary codes are assigned, a random projection matrix requires expensive complexities in both space and time. In this paper we analyze a bilinear random projection method where feature matrices are transformed to binary codes by two smaller random projection matrices. We base our theoretical analysis on extending Raginsky and Lazebnik's result where random Fourier features are composed with random binary quantizers to form locality sensitive binary codes. To this end, we answer the following two questions: (1) whether a bilinear random projection also yields similarity-preserving binary codes; (2) whether a bilinear random projection yields performance gain or loss, compared to a large linear projection. Regarding the first question, we present upper and lower bounds on the expected Hamming distance between binary codes produced by bilinear random projections. In regards to the second question, we analyze the upper and lower bounds on covariance between two bits of binary codes, showing that the correlation between two bits is small. Numerical experiments on MNIST and Flickr45K datasets confirm the validity of our method.Comment: 11 pages, 23 figures, CVPR-201

Three Essays on Interaction in Public Management

Public management is one of the most important subfields in public administration and plays a role in explaining the variations of government performance. Encouraging public administrators to get motivated through enhancing public service motivation (PSM) and collaborating with each other to accomplish their jobs and organizational objectives are key strategies to enhance the government’s accountability to the public under scarce resources. This dissertation attempts to address these concerns. First, it conducts a meta-analytical structural equation analysis with regard to the relationships among PSM, value congruence, individual work attitudes, and individual performance and finds that person-organization fit, job satisfaction, and organizational commitment have partial mediation effects on the relationship between PSM and individual performance. It contributes to the extant PSM literature in two ways: (1) it investigates the overall average effect size of each factor and (2) examines the possibility of mediating effects of key variables on the PSM-performance relationship to specify those relationships that has not yet been fully investigated. Drawing on the findings from the first essay, the second essay theoretically clarifies the relationship between PSM and performance by suggesting a framework in which social networks among members provide an explicit mechanism linking employees’ PSM with their performance and by proposing several empirically testable propositions. Conceptually, it shows that (1) the extent of the social relationships and interaction among group members and their positions within a network differ depending on the level of PSM; (2) individual employees with high PSM are more likely to complete their tasks via their central positions in a network of advice relations; and (3) group members with high PSM are more likely to complete group tasks via the density of a social network of advice relations. In the third essay, using a data set that is a mixed panel at the school- and district-level in the state of Kentucky across the school years from SY 2002-3 to SY 2008-9, it examines the impacts of intra-organizational collaborative behavior on organizational performance. More specifically, it investigates the linear and moderating effects of the collaborative interaction between superintendents and school principals as well as the impacts of characteristics of districts on school performance. The results from this essay provide evidence supporting the propositions. This dissertation concludes by discussing academic and practical implications and suggesting future research directions

Convex Optimization for Binary Classifier Aggregation in Multiclass Problems

Multiclass problems are often decomposed into multiple binary problems that are solved by individual binary classifiers whose results are integrated into a final answer. Various methods, including all-pairs (APs), one-versus-all (OVA), and error correcting output code (ECOC), have been studied, to decompose multiclass problems into binary problems. However, little study has been made to optimally aggregate binary problems to determine a final answer to the multiclass problem. In this paper we present a convex optimization method for an optimal aggregation of binary classifiers to estimate class membership probabilities in multiclass problems. We model the class membership probability as a softmax function which takes a conic combination of discrepancies induced by individual binary classifiers, as an input. With this model, we formulate the regularized maximum likelihood estimation as a convex optimization problem, which is solved by the primal-dual interior point method. Connections of our method to large margin classifiers are presented, showing that the large margin formulation can be considered as a limiting case of our convex formulation. Numerical experiments on synthetic and real-world data sets demonstrate that our method outperforms existing aggregation methods as well as direct methods, in terms of the classification accuracy and the quality of class membership probability estimates.Comment: Appeared in Proceedings of the 2014 SIAM International Conference on Data Mining (SDM 2014