In this report we propose a methodology to automatically classify products and cluster similar products together. This enhances user interaction and performance metrics for e-commerce (product shopping) websites, with applications in product search, site navigation, product comparison, etc. For this project, a variant of the multinomial Naive Bayes algorithm was used for classification. We pres...

Aim of the paper is to propose a segmentation technique based on the Bagged Clustering (BC) method. In the partitioning step of the BC method, B bootstrap samples with replacement are generated by drawing from the original sample. The Fuzzy C–Medoids Clustering (FCMdC) method is run on each bootstrap sample, obtaining (B×C) medoids and the membership degrees of each unit to the different cluste...

This paper presents a general framework for adapting any generative (model-based) clustering algorithm to provide balanced solutions, i.e., clusters of comparable sizes. Partitional, model-based clustering algorithms are viewed as an iterative two-step optimization process—iterative model re-estimation and sample re-assignment. Instead of a maximum-likelihood (ML) assignment, a balanceconstrain...

We construct a new harmonic family: dielectric flow solutions with maximal supersymmetry in eleven-dimensional supergravity. These solutions are asymptotically AdS4 ×S7, while in the infra-red the M2 branes are dielectrically polarized into M5 branes. These solutions are holographically dual to vacua of the mass deformed theory on M2 branes. They also provide an interesting insight on the super...

As mentioned before, the success of CASE relies on two noteworthy properties: the Sure Screening (SS) property and the Separable After Screening (SAS) property. In this section, we discuss the two properties in detail, and illustrate how these properties enable us to decompose the original regression problem to many small-size regression problems which can be fit separately. We then use these p...

I describe a modification to Shanks’ baby-step giant-step algorithm for computing the order n of an element g of a group G, assuming n is finite. My method has the advantage of being able to compute n quickly, which Shanks’ method fails to do when the order of G is infinite, unknown, or much larger than n. I describe the algorithm in detail. I also present the results of implementations of my a...