An Incidence Geometry approach to Dictionary Learning

We study the Dictionary Learning (aka Sparse Coding) problem of obtaining a sparse representation of data points, by learning \emph{dictionary vectors} upon which the data points can be written as sparse linear combinations. We view this problem from a geometry perspective as the spanning set of a subspace arrangement, and focus on understanding the case when the underlying hypergraph of the subspace arrangement is specified. For this Fitted Dictionary Learning problem, we completely characterize the combinatorics of the associated subspace arrangements (i.e.\ their underlying hypergraphs). Specifically, a combinatorial rigidity-type theorem is proven for a type of geometric incidence system. The theorem characterizes the hypergraphs of subspace arrangements that generically yield (a) at least one dictionary (b) a locally unique dictionary (i.e.\ at most a finite number of isolated dictionaries) of the specified size. We are unaware of prior application of combinatorial rigidity techniques in the setting of Dictionary Learning, or even in machine learning. We also provide a systematic classification of problems related to Dictionary Learning together with various algorithms, their assumptions and performance

Quantifying Shannon's Work Function for Cryptanalytic Attacks

Attacks on cryptographic systems are limited by the available computational resources. A theoretical understanding of these resource limitations is needed to evaluate the security of cryptographic primitives and procedures. This study uses an Attacker versus Environment game formalism based on computability logic to quantify Shannon's work function and evaluate resource use in cryptanalysis. A simple cost function is defined which allows to quantify a wide range of theoretical and real computational resources. With this approach the use of custom hardware, e.g., FPGA boards, in cryptanalysis can be analyzed. Applied to real cryptanalytic problems, it raises, for instance, the expectation that the computer time needed to break some simple 90 bit strong cryptographic primitives might theoretically be less than two years.Comment: 19 page

Finding Patterns in a Knowledge Base using Keywords to Compose Table Answers

We aim to provide table answers to keyword queries against knowledge bases. For queries referring to multiple entities, like "Washington cities population" and "Mel Gibson movies", it is better to represent each relevant answer as a table which aggregates a set of entities or entity-joins within the same table scheme or pattern. In this paper, we study how to find highly relevant patterns in a knowledge base for user-given keyword queries to compose table answers. A knowledge base can be modeled as a directed graph called knowledge graph, where nodes represent entities in the knowledge base and edges represent the relationships among them. Each node/edge is labeled with type and text. A pattern is an aggregation of subtrees which contain all keywords in the texts and have the same structure and types on node/edges. We propose efficient algorithms to find patterns that are relevant to the query for a class of scoring functions. We show the hardness of the problem in theory, and propose path-based indexes that are affordable in memory. Two query-processing algorithms are proposed: one is fast in practice for small queries (with small patterns as answers) by utilizing the indexes; and the other one is better in theory, with running time linear in the sizes of indexes and answers, which can handle large queries better. We also conduct extensive experimental study to compare our approaches with a naive adaption of known techniques.Comment: VLDB 201

A Case Study of Using Online Communities and Virtual Environment in Massively Multiplayer Role Playing Games (MMORPGs) as a Learning and Teaching Tool for Second Language Learners

Massively Multiplayer Online Role Playing Games (MMORPGs) create large virtual communities. Online gaming shows potential not just for entertaining, but also in education. This research investigates the use of commercial MMORPGs to support second language teaching. MMORPGs offer virtual safe spaces in which students can communicate by using their target second language with global players. Using a mix of ethnography and action research, this study explores the students’ experiences of language learning and performing while playing MMORPGs. The results show that the use of MMORPGs can facilitate language development by offering fun, informal, individualised and secure virtual spaces for students to practise their language with native and other second language speakers