Constrained sequential pattern mining aims at identifying frequent patterns on a sequential database of items while observing constraints defined over the item attributes. We introduce novel techniques for constraint-based sequential pattern mining that rely on a multi-valued decision diagram representation of the database. Specifically, our representation can accommodate multiple item attributes and various constraint types, including a number of non-monotone constraints. To evaluate the applicability of our approach, we develop an MDD-based prefix-projection algorithm and compare its performance against a typical generate-and-check variant, as well as a state-of-the-art constraint-based sequential pattern mining algorithm. Results show that our approach is competitive with or superior to these other methods in terms of scalability and efficiency.
Graphical representations of a database have been shown to be effective in item-set mining @cite_30 @cite_23 @cite_13 and SPM @cite_25 . Previous works have also applied binary decision diagrams as a database modeling tool @cite_29 @cite_11 @cite_7 @cite_3 , which are effective when the sequences of the database are similar, but typically do not scale otherwise. We show that our MDD representation retains its size regardless of the similarity between sequences, and provides a more concise representation in the context of SPM.
@cite_30 @cite_7 @cite_29 @cite_3 @cite_23 @cite_13 @cite_25 @cite_11
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An investigation was made of the analogous graph structure for representing and manipulating discrete variable problems. The authors define the multi-valued decision diagram (MDD), analyze its properties (in particular prove a strong canonical form) and provide algorithms for combining and manipulating MDDs. They give a method for mapping an MDD into an equivalent BDD (binary decision diagram) which allows them to provide a highly efficient implementation using the previously developed BDD packages. A direct implementation of the MDD structure has also been carried out, but this initial implementation has not yet been tuned to the same extent as the BDDs to allow a reasonable comparison to be made. The authors have used the mapping to BDDs to provide an initial understanding of the limits on the sizes of real problems that can be executed. The results are encouraging. > Recent sequential pattern mining methods have used the minimum description length (MDL) principle to define an encoding scheme which describes an algorithm for mining the most compressing patterns in a database. We present a novel subsequence interleaving model based on a probabilistic model of the sequence database, which allows us to search for the most compressing set of patterns without designing a specific encoding scheme. Our proposed algorithm is able to efficiently mine the most relevant sequential patterns and rank them using an associated measure of interestingness. The efficient inference in our model is a direct result of our use of a structural expectation-maximization framework, in which the expectation-step takes the form of a submodular optimization problem subject to a coverage constraint. We show on both synthetic and real world datasets that our model mines a set of sequential patterns with low spuriousness and redundancy, high interpretability and usefulness in real-world applications. Furthermore, we demonstrate that the quality of the patterns from our approach is comparable to, if not better than, existing state of the art sequential pattern mining algorithms. Investigations into probabilistic graphical models for decision making have predominantly centered on influence diagrams (IDs) and decision circuits (DCs) for representation and computation of decision rules that maximize expected utility. Since IDs are typically handcrafted and DCs are compiled from IDs, in this paper we propose an approach to learn the structure and parameters of decision-making problems directly from data. We present a new representation called sum-product-max network (SPMN) that generalizes a sum-product network (SPN) to the class of decision-making problems and whose solution, analogous to DCs, scales linearly in the size of the network. We show that SPMNs may be reduced to DCs linearly and present a first method for learning SPMNs from data. This approach is significant because it facilitates a novel paradigm of tractable decision making driven by data. We present a novel approach to itemset mining whereby the set of all itemsets are compiled into a compact form, closely related to binary decision diagrams. While there were previous attempts to utilize decision diagrams for storing the set of frequent itemsets this is the first approach that does not rely on backtrack search to generate such a set. Our empirical evaluation demonstrates that our approach is complementary to current approaches. Discovering contrasts between collections of data is an important task in data mining. In this paper, we introduce a new type of contrast pattern, called a minimal distinguishing subsequence (MDS). An MDS is a minimal subsequence that occurs frequently in one class of sequences and infrequently in sequences of another class. It is a natural way of representing strong and succinct contrast information between two sequential datasets and can be useful in applications such as protein comparison, document comparison and building sequential classification models. Mining MDS patterns is a challenging task and is significantly different from mining contrasts between relational transactional data. One particularly important type of constraint that can be integrated into the mining process is the maximum gap constraint. We present an efficient algorithm called ConSGapMiner, to mine all MDSs according to a maximum gap constraint. It employs highly efficient bitset and Boolean operations, for powerful gap based pruning within a prefix growth framework. A performance evaluation with both sparse and dense datasets, demonstrates the scalability of ConSGapMiner and shows its ability to mine patterns from high dimensional datasets at low supports. Sequential pattern mining is an important problem in data mining. State of the art techniques for mining sequential patterns, such as frequent subsequences, are often based on the pattern-growth approach, which recursively projects conditional databases. Explicitly creating database projections is thought to be a major computational bottleneck, but we will show in this paper that it can be beneficial when the appropriate data structure is used. Our technique uses a canonical directed acyclic graph as the sequence database representation, which can be represented as a binary decision diagram (BDD). In this paper, we introduce a new type of BDD, namely a sequence BDD (SeqBDD), and show how it can be used for efficiently mining frequent subsequences. A novel feature of the SeqBDD is its ability to share results between similar intermediate computations and avoid redundant computation. We perform an experimental study to compare the SeqBDD technique with existing pattern growth techniques, that are based on other data structures such as prefix trees. Our results show that a SeqBDD can be half as large as a prefix tree, especially when many similar sequences exist. In terms of mining time, it can be substantially more efficient when the support is low, the number of patterns is large, or the input sequences are long and highly similar. Learning rich visual representations often require training on datasets of millions of manually annotated examples. This substantially limits the scalability of learning effective representations as labeled data is expensive or scarce. In this paper, we address the problem of unsupervised visual representation learning from a large, unlabeled collection of images. By representing each image as a node and each nearest-neighbor matching pair as an edge, our key idea is to leverage graph-based analysis to discover positive and negative image pairs (i.e., pairs belonging to the same and different visual categories). Specifically, we propose to use a cycle consistency criterion for mining positive pairs and geodesic distance in the graph for hard negative mining. We show that the mined positive and negative image pairs can provide accurate supervisory signals for learning effective representations using Convolutional Neural Networks (CNNs). We demonstrate the effectiveness of the proposed unsupervised constraint mining method in two settings: (1) unsupervised feature learning and (2) semi-supervised learning. For unsupervised feature learning, we obtain competitive performance with several state-of-the-art approaches on the PASCAL VOC 2007 dataset. For semi-supervised learning, we show boosted performance by incorporating the mined constraints on three image classification datasets. Symbolic model checking with Binary Decision Diagrams (BDDs) has been successfully used in the last decade for formally verifying finite state systems such as sequential circuits and protocols. Since its introduction in the beginning of the 90's, it has been integrated in the quality assurance process of several major hardware companies. The main bottleneck of this method is that BDDs may grow exponentially, and hence the amount of available memory re- stricts the size of circuits that can be verified efficiently. In this article we survey a technique called Bounded Model Checking (BMC), which uses a propositional SAT solver rather than BDD manipulation techniques. Since its introduction in 1999, BMC has been well received by the industry. It can find many logical er- rors in complex systems that can not be handled by competing techniques, and is therefore widely perceived as a complementary technique to BDD-based model checking. This observation is supported by several independent comparisons that have been published in the last few years.