Discovering Unexpected Patterns in Temporal Data Using Temporal Logic

There has been much attention given recently to the task of finding interesting patterns in temporal databases. Since there are so many different approaches to the problem of discovering temporal patterns, we first present a characterization of different discovery tasks and then focus on one task of discovering interesting patterns of events in temporal sequences. Given an (infinite) temporal database or a sequence of events one can, in general, discover an infinite number of temporal patterns in this data. Therefore, it is important to specify some measure of interestingness for discovered patterns and then select only the patterns interesting according to this measure. We present a probabilistic measure of interestingness based on unexpectedness, whereby a pattern P is deemed interesting if the ratio of the actual number of occurrences of P exceeds the expected number of occurrences of P by some user defined threshold. We then make use of a subset of the propositional, linear temporal logic and present an efficient algorithm that discovers unexpected patterns in temporal data. Finally, we apply this algorithm to synthetic data, UNIX operating system calls, and Web logfiles and present the results of these experiments.Information Systems Working Papers Serie

String Searching with Ranking Constraints and Uncertainty

Strings play an important role in many areas of computer science. Searching pattern in a string or string collection is one of the most classic problems. Different variations of this problem such as document retrieval, ranked document retrieval, dictionary matching has been well studied. Enormous growth of internet, large genomic projects, sensor networks, digital libraries necessitates not just efficient algorithms and data structures for the general string indexing, but indexes for texts with fuzzy information and support for queries with different constraints. This dissertation addresses some of these problems and proposes indexing solutions. One such variation is document retrieval query for included and excluded/forbidden patterns, where the objective is to retrieve all the relevant documents that contains the included patterns and does not contain the excluded patterns. We continue the previous work done on this problem and propose more efficient solution. We conjecture that any significant improvement over these results is highly unlikely. We also consider the scenario when the query consists of more than two patterns. The forbidden pattern problem suffers from the drawback that linear space (in words) solutions are unlikely to yield a solution better than O(root(n/occ)) per document reporting time, where n is the total length of the documents and occ is the number of output documents. Continuing this path, we introduce a new variation, namely document retrieval with forbidden extension query, where the forbidden pattern is an extension of the included pattern.We also address the more general top-k version of the problem, which retrieves the top k documents, where the ranking is based on PageRank relevance metric. This problem finds motivation from search applications. It also holds theoretical interest as we show that the hardness of forbidden pattern problem is alleviated in this problem. We achieve linear space and optimal query time for this variation. We also propose succinct indexes for both these problems. Position restricted pattern matching considers the scenario where only part of the text is searched. We propose succinct index for this problem with efficient query time. An important application for this problem stems from searching in genomic sequences, where only part of the gene sequence is searched for interesting patterns. The problem of computing discriminating(resp. generic) words is to report all minimal(resp. maximal) extensions of a query pattern which are contained in at most(resp. at least) a given number of documents. These problems are motivated from applications in computational biology, text mining and automated text classification. We propose succinct indexes for these problems. Strings with uncertainty and fuzzy information play an important role in increasingly many applications. We propose a general framework for indexing uncertain strings such that a deterministic query string can be searched efficiently. String matching becomes a probabilistic event when a string contains uncertainty, i.e. each position of the string can have different probable characters with associated probability of occurrence for each character. Such uncertain strings are prevalent in various applications such as biological sequence data, event monitoring and automatic ECG annotations. We consider two basic problems of string searching, namely substring searching and string listing. We formulate these well known problems for uncertain strings paradigm and propose exact and approximate solution for them. We also discuss a constrained variation of orthogonal range searching. Given a set of points, the task of orthogonal range searching is to build a data structure such that all the points inside a orthogonal query region can be reported. We introduce a new variation, namely shared constraint range searching which naturally arises in constrained pattern matching applications. Shared constraint range searching is a special four sided range reporting query problem where two constraints has sharing among them, effectively reducing the number of independent constraints. For this problem, we propose a linear space index that can match the best known bound for three dimensional dominance reporting problem. We extend our data structure in the external memory model

Periodic Pattern Mining a Algorithms and Applications

Owing to a large number of applications periodic pattern mining has been extensively studied for over a decade Periodic pattern is a pattern that repeats itself with a specific period in a give sequence Periodic patterns can be mined from datasets like biological sequences continuous and discrete time series data spatiotemporal data and social networks Periodic patterns are classified based on different criteria Periodic patterns are categorized as frequent periodic patterns and statistically significant patterns based on the frequency of occurrence Frequent periodic patterns are in turn classified as perfect and imperfect periodic patterns full and partial periodic patterns synchronous and asynchronous periodic patterns dense periodic patterns approximate periodic patterns This paper presents a survey of the state of art research on periodic pattern mining algorithms and their application areas A discussion of merits and demerits of these algorithms was given The paper also presents a brief overview of algorithms that can be applied for specific types of datasets like spatiotemporal data and social network

Enhancing Text Compression Method Using Information Source Indexing

Text compression methods where the original texts are directly mapped into binary domain are attractive to compress English text files. This paper proposes an intermediate mapping scheme in which the original English text is transformed firstly to decimal domain and then to binary domain. Each two-decimal-digit value in the resulting intermediate decimal file represents the index to the location of each alphabet found in the original text. If the already indexed alphabet is seen again, it will be replaced by the previously given decimal-index number. The decimal file is converted into binary domain by assigning each decimal digit a 4-bit weighted code in according to its frequency of occurrence that is akin to BCD code. The assigned codes aim at generating an equivalent binary file with entropy as close as much to that of the original one. Thereafter, any conventional compression algorithm such as Lempel-Ziv algorithms can be applied to the generated binary file. The obtained compression ratios outperform those ones obtained when applying the same compression algorithm to the binary files generated either via direct mapping of the original text or via mapping the decimal file using Binary Coded Decimal (BCD) codes. Keywords: Lossless data compression; Source encoding, LZW coding, Hamming weights, Compression ratio