Overlapping and Robust Edge-Colored Clustering in Hypergraphs

A recent trend in data mining has explored (hyper)graph clustering algorithms for data with categorical relationship types. Such algorithms have applications in the analysis of social, co-authorship, and protein interaction networks, to name a few. Many such applications naturally have some overlap between clusters, a nuance which is missing from current combinatorial models. Additionally, existing models lack a mechanism for handling noise in datasets. We address these concerns by generalizing Edge-Colored Clustering, a recent framework for categorical clustering of hypergraphs. Our generalizations allow for a budgeted number of either (a) overlapping cluster assignments or (b) node deletions. For each new model we present a greedy algorithm which approximately minimizes an edge mistake objective, as well as bicriteria approximations where the second approximation factor is on the budget. Additionally, we address the parameterized complexity of each problem, providing FPT algorithms and hardness results

Fast and Guaranteed Tensor Decomposition via Sketching

Tensor CANDECOMP/PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We build on the idea of count sketches, but introduce many novel ideas which are unique to tensors. We develop novel methods for randomized computation of tensor contractions via FFTs, without explicitly forming the tensors. Such tensor contractions are encountered in decomposition methods such as tensor power iterations and alternating least squares. We also design novel colliding hashes for symmetric tensors to further save time in computing the sketches. We then combine these sketching ideas with existing whitening and tensor power iterative techniques to obtain the fastest algorithm on both sparse and dense tensors. The quality of approximation under our method does not depend on properties such as sparsity, uniformity of elements, etc. We apply the method for topic modeling and obtain competitive results.Comment: 29 pages. Appeared in Proceedings of Advances in Neural Information Processing Systems (NIPS), held at Montreal, Canada in 201

Fair and Representative Subset Selection from Data Streams

We study the problem of extracting a small subset of representative items from a large data stream. In many data mining and machine learning applications such as social network analysis and recommender systems, this problem can be formulated as maximizing a monotone submodular function subject to a cardinality constraint k. In this work, we consider the setting where data items in the stream belong to one of several disjoint groups and investigate the optimization problem with an additional fairness constraint that limits selection to a given number of items from each group. We then propose efficient algorithms for the fairness-aware variant of the streaming submodular maximization problem. In particular, we first give a (1/2-ε)-approximation algorithm that requires O((1/ε) log(k/ε)) passes over the stream for any constant ε>0. Moreover, we give a single-pass streaming algorithm that has the same approximation ratio of (1/2-ε) when unlimited buffer sizes and post-processing time are permitted, and discuss how to adapt it to more practical settings where the buffer sizes are bounded. Finally, we demonstrate the efficiency and effectiveness of our proposed algorithms on two real-world applications, namely maximum coverage on large graphs and personalized recommendation.Peer reviewe

Mining High Utility Patterns Over Data Streams

Mining useful patterns from sequential data is a challenging topic in data mining. An important task for mining sequential data is sequential pattern mining, which discovers sequences of itemsets that frequently appear in a sequence database. In sequential pattern mining, the selection of sequences is generally based on the frequency/support framework. However, most of the patterns returned by sequential pattern mining may not be informative enough to business people and are not particularly related to a business objective. In view of this, high utility sequential pattern (HUSP) mining has emerged as a novel research topic in data mining recently. The main objective of HUSP mining is to extract valuable and useful sequential patterns from data by considering the utility of a pattern that captures a business objective (e.g., profit, users interest). In HUSP mining, the goal is to find sequences whose utility in the database is no less than a user-specified minimum utility threshold. Nowadays, many applications generate a huge volume of data in the form of data streams. A number of studies have been conducted on mining HUSPs, but they are mainly intended for non-streaming data and thus do not take data stream characteristics into consideration. Mining HUSP from such data poses many challenges. First, it is infeasible to keep all streaming data in the memory due to the high volume of data accumulated over time. Second, mining algorithms need to process the arriving data in real time with one scan of data. Third, depending on the minimum utility threshold value, the number of patterns returned by a HUSP mining algorithm can be large and overwhelms the user. In general, it is hard for the user to determine the value for the threshold. Thus, algorithms that can find the most valuable patterns (i.e., top-k high utility patterns) are more desirable. Mining the most valuable patterns is interesting in both static data and data streams. To address these research limitations and challenges, this dissertation proposes techniques and algorithms for mining high utility sequential patterns over data streams. We work on mining HUSPs over both a long portion of a data stream and a short period of time. We also work on how to efficiently identify the most significant high utility patterns (namely, the top-k high utility patterns) over data streams. In the first part, we explore a fundamental problem that is how the limited memory space can be well utilized to produce high quality HUSPs over the entire data stream. An approximation algorithm, called MAHUSP, is designed which employs memory adaptive mechanisms to use a bounded portion of memory, to efficiently discover HUSPs over the entire data streams. The second part of the dissertation presents a new sliding window-based algorithm to discover recent high utility sequential patterns over data streams. A novel data structure named HUSP-Tree is proposed to maintain the essential information for mining recenT HUSPs. An efficient and single-pass algorithm named HUSP-Stream is proposed to generate recent HUSPs from HUSP-Tree. The third part addresses the problem of top-k high utility pattern mining over data streams. Two novel methods, named T-HUDS and T-HUSP, for finding top-k high utility patterns over a data stream are proposed. T-HUDS discovers top-k high utility itemsets and T-HUSP discovers top-k high utility sequential patterns over a data stream. T-HUDS is based on a compressed tree structure, called HUDS-Tree, that can be used to efficiently find potential top-k high utility itemsets over data streams. T-HUSP incrementally maintains the content of top-k HUSPs in a data stream in a summary data structure, named TKList, and discovers top-k HUSPs efficiently. All of the algorithms are evaluated using both synthetic and real datasets. The performances, including the running time, memory consumption, precision, recall and Fmeasure, are compared. In order to show the effectiveness and efficiency of the proposed methods in reallife applications, the fourth part of this dissertation presents applications of one of the proposed methods (i.e., MAHUSP) to extract meaningful patterns from a real web clickstream dataset and a real biosequence dataset. The utility-based sequential patterns are compared with the patterns in the frequency/support framework. The results show that high utility sequential pattern mining provides meaningful patterns in real-life applications

Techniques for improving clustering and association rules mining from very large transactional databases

Clustering and association rules mining are two core data mining tasks that have been actively studied by data mining community for nearly two decades. Though many clustering and association rules mining algorithms have been developed, no algorithm is better than others on all aspects, such as accuracy, efficiency, scalability, adaptability and memory usage. While more efficient and effective algorithms need to be developed for handling the large-scale and complex stored datasets, emerging applications where data takes the form of streams pose new challenges for the data mining community. The existing techniques and algorithms for static stored databases cannot be applied to the data streams directly. They need to be extended or modified, or new methods need to be developed to process the data streams.In this thesis, algorithms have been developed for improving efficiency and accuracy of clustering and association rules mining on very large, high dimensional, high cardinality, sparse transactional databases and data streams.A new similarity measure suitable for clustering transactional data is defined and an incremental clustering algorithm, INCLUS, is proposed using this similarity measure. The algorithm only scans the database once and produces clusters based on the user’s expectations of similarities between transactions in a cluster, which is controlled by the user input parameters, a similarity threshold and a support threshold. Intensive testing has been performed to evaluate the effectiveness, efficiency, scalability and order insensitiveness of the algorithm.To extend INCLUS for transactional data streams, an equal-width time window model and an elastic time window model are proposed that allow mining of clustering changes in evolving data streams. The minimal width of the window is determined by the minimum clustering granularity for a particular application. Two algorithms, CluStream_EQ and CluStream_EL, based on the equal-width window model and the elastic window model respectively, are developed by incorporating these models into INCLUS. Each algorithm consists of an online micro-clustering component and an offline macro-clustering component. The online component writes summary statistics of a data stream to the disk, and the offline components uses those summaries and other user input to discover changes in a data stream. The effectiveness and scalability of the algorithms are evaluated by experiments.This thesis also looks into sampling techniques that can improve efficiency of mining association rules in a very large transactional database. The sample size is derived based on the binomial distribution and central limit theorem. The sample size used is smaller than that based on Chernoff Bounds, but still provides the same approximation guarantees. The accuracy of the proposed sampling approach is theoretically analyzed and its effectiveness is experimentally evaluated on both dense and sparse datasets.Applications of stratified sampling for association rules mining is also explored in this thesis. The database is first partitioned into strata based on the length of transactions, and simple random sampling is then performed on each stratum. The total sample size is determined by a formula derived in this thesis and the sample size for each stratum is proportionate to the size of the stratum. The accuracy of transaction size based stratified sampling is experimentally compared with that of random sampling.The thesis concludes with a summary of significant contributions and some pointers for further work