Mining patterns from multi-relational data is a problem attracting increasing interest within the data mining community. Traditional data mining approaches are typically developed for highly simplified types of data, such as an attribute-value table or a binary database, such that those methods are not directly applicable to multi-relational data. Nevertheless, multi-relational data is a more truthful and therefore often also a more powerful representation of reality. Mining patterns of a suitably expressive syntax directly from this representation, is thus a research problem of great importance. In this paper we introduce a novel approach to mining patterns in multi-relational data. We propose a new syntax for multi-relational patterns as complete connected subgraphs in a representation of the database as a K-partite graph. We show how this pattern syntax is generally applicable to multirelational data, while it reduces to well-known tiles [7] when the data is a simple binary or attribute-value table. We propose RMiner, an efficient algorithm to mine such patterns, and we introduce a method for quantifying their interestingness when contrasted with prior information of the data miner. Finally, we illustrate the usefulness of our approach by discussing results on real-world and synthetic databases.
Well known ideas and algorithms from frequent itemset mining can be used for MRDs unaltered if applied on the join of all tables. The syntax of this type of patterns is essentially that of itemsets, with items in this case being attribute values and transactions being the tuples of the join table @cite_14 @cite_9 @cite_7 . The characteristic of this pattern syntax is that a tuple always contains one attribute value per attribute and as a result it is impossible to have two values of the same attribute in the same pattern. An itemset of this type for instance would not be able to capture the fact that a director can be related to many films. This is something that an MCCS pattern naturally captures. However, itemsets on the join table can still capture co-occurrences of attribute values that belong to different attributes.
@cite_9 @cite_14 @cite_7
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Local pattern mining methods are fragmented along two dimensions: the pattern syntax, and the data types on which they are applicable. Pattern syntaxes considered in the literature include subgroups, n-sets, itemsets, and many more; common data types include binary, categorical, and real-valued. Recent research on pattern mining in relational databases has shown how the aforementioned pattern syntaxes can be unified in a single framework. However, a unified understanding of how to deal with various data types is lacking, certainly for more complexly structured types such as time of day (which is circular), geographical location, terms from a taxonomy, etc. In this paper, we introduce a generic approach for mining interesting local patterns in (relational) data involving such structured data types as attributes. Importantly, we show how this can be done in a generic manner, by modelling the structure within a set of attribute values as a partial order. We then derive a measure of subjective interestingness of such patterns using Information Theory, and propose an algorithm for effectively enumerating all patterns of this syntax. Through empirical evaluation, we found that (a) the new interestingness derivation is relevant and cannot be approximated using existing tools, (b) the new tool, P-N-RMiner, finds patterns that are substantially more informative, and (c) the new enumeration algorithm is considerably faster. Mining frequent patterns from a hidden dataset is an important task with 43 various real-life applications. In this research, we propose a solution to this problem that is based on Markov Chain Monte Carlo (MCMC) sampling of frequent patterns. Instead of returning all the frequent patterns, the proposed paradigm returns a small set of randomly selected patterns so that the clandestinity of the dataset can be maintained. Our solution also allows interactive sampling, so that the sampled patterns can fulfill the user's requirement effectively. We show experimental results from several real life datasets to validate the capability and usefulness of our solution; in particular, we show examples that by using our proposed solution, an eCommerce marketplace can allow pattern mining on user session data without disclosing the data to the public; such a mining paradigm helps the sellers of the marketplace, which eventually boost the marketplace's own revenue. One of the major problems in pattern mining is the explosion of the number of results. Tight constraints reveal only common knowledge, while loose constraints lead to an explosion in the number of returned patterns. This is caused by large groups of patterns essentially describing the same set of transactions. In this paper we approach this problem using the MDL principle: the best set of patterns is that set that compresses the database best. For this task we introduce the Krimp algorithm. Experimental evaluation shows that typically only hundreds of itemsets are returned; a dramatic reduction, up to seven orders of magnitude, in the number of frequent item sets. These selections, called code tables, are of high quality. This is shown with compression ratios, swap-randomisation, and the accuracies of the code table-based Krimp classifier, all obtained on a wide range of datasets. Further, we extensively evaluate the heuristic choices made in the design of the algorithm. As data mining techniques are being increasingly applied to non-traditional domains, existing approaches for finding frequent itemsets cannot be used as they cannot model the requirement of these domains. An alternate way of modeling the objects in these data sets is to use graphs. Within that model, the problem of finding frequent patterns becomes that of discovering subgraphs that occur frequently over the entire set of graphs.The authors present a computationally efficient algorithm for finding all frequent subgraphs in large graph databases. We evaluated the performance of the algorithm by experiments with synthetic datasets as well as a chemical compound dataset. The empirical results show that our algorithm scales linearly with the number of input transactions and it is able to discover frequent subgraphs from a set of graph transactions reasonably fast, even though we have to deal with computationally hard problems such as canonical labeling of graphs and subgraph isomorphism which are not necessary for traditional frequent itemset discovery. One of the biggest setbacks in traditional frequent pattern mining is that overwhelmingly many of the discovered patterns are redundant. A prototypical example of such redundancy is a freerider pattern where the pattern contains a true pattern and some additional noise events. A technique for filtering freerider patterns that has proved to be efficient in ranking itemsets is to use a partition model where a pattern is divided into two subpatterns and the observed support is compared to the expected support under the assumption that these two subpatterns occur independently. In this paper we develop a partition model for episodes, patterns discovered from sequential data. An episode is essentially a set of events, with possible restrictions on the order of events. Unlike with itemset mining, computing the expected support of an episode requires surprisingly sophisticated methods. In order to construct the model, we partition the episode into two subepisodes. We then model how likely the events in each subepisode occur close to each other. If this probability is high--which is often the case if the subepisode has a high support--then we can expect that when one event from a subepisode occurs, then the remaining events occur also close by. This approach increases the expected support of the episode, and if this increase explains the observed support, then we can deem the episode uninteresting. We demonstrate in our experiments that using the partition model can effectively and efficiently reduce the redundancy in episodes. Mining frequent patterns such as frequent itemsets is a core operation in many important data mining tasks, such as in association rule mining. Mining frequent itemsets in high-dimensional datasets is challenging, since the search space is exponential in the number of dimensions and the volume of patterns can be huge. Many of the state-of-the-art techniques rely upon the use of prefix trees (e.g. FP-trees) which allow nodes to be shared among common prefix paths. However, the scalability of such techniques may be limited when handling high dimensional datasets. The purpose of this paper is to analyse the behaviour of mining frequent itemsets when instead of a tree data structure, a canonical directed acyclic graph namely Zero Suppressed Binary Decision Diagram (ZBDD) is used. Due to its compactness and ability to promote node reuse, ZBDD has proven very effective in other areas of computer science, such as boolean SAT solvers. In this paper, we show how ZBDDs can be used to mine frequent itemsets (and their common varieties). We also introduce a weighted variant of ZBDD which allows a more efficient mining algorithm to be developed. We provide an experimental study concentrating on high dimensional biological datasets, and identify indicative situations where a ZBDD technology can be superior over the prefix tree based technique. Over the years, frequent itemset discovery algorithms have been used to find interesting patterns in various application areas. However, as data mining techniques are being increasingly applied to nontraditional domains, existing frequent pattern discovery approaches cannot be used. This is because the transaction framework that is assumed by these algorithms cannot be used to effectively model the data sets in these domains. An alternate way of modeling the objects in these data sets is to represent them using graphs. Within that model, one way of formulating the frequent pattern discovery problem is that of discovering subgraphs that occur frequently over the entire set of graphs. We present a computationally efficient algorithm, called FSG, for finding all frequent subgraphs in large graph data sets. We experimentally evaluate the performance of FSG using a variety of real and synthetic data sets. Our results show that despite the underlying complexity associated with frequent subgraph discovery, FSG is effective in finding all frequently occurring subgraphs in data sets containing more than 200,000 graph transactions and scales linearly with respect to the size of the data set. In many applications, such as data integration and big data analytics, one has to integrate data from multiple sources without detailed and accurate schema information. The state of the art focuses on matching attributes among sources based on the information derived from the data in those sources. However, a best join result according to a method's own pre-determined criteria may not fit a user's best interest. In this paper, we tackle the challenge from a novel angle and investigate how to join schemaless tables to meet a user preference the best. We identify a set of essential preferences that are useful in various scenarios, such as minimizing the number of tuples in outer join results and maximizing the entropy of the joining key's distribution. We also develop a systematic method to compute the best join predicate optimizing an objective function representing a user preference. We conduct extensive experiments on 4 large datasets and compare with 4 baselines from the state of the art of schema matching and attribute clustering. The experimental results clearly show that our algorithm outperforms the baselines significantly in accuracy in all the cases, and consumes comparable running time. In this paper, we propose a general framework for graph matching which is suitable for different problems of pattern recognition. The pattern representation we assume is at the same time highly structured, like for classic syntactic and structural approaches, and of subsymbolic nature with real-valued features, like for connectionist and statistic approaches. We show that random walk based models, inspired by Google's PageRank, give rise to a spectral theory that nicely enhances the graph topological features at node level. As a straightforward consequence, we derive a polynomial algorithm for the classic graph isomorphism problem, under the restriction of dealing with Markovian spectrally distinguishable graphs (MSD), a class of graphs that does not seem to be easily reducible to others proposed in the literature. The experimental results that we found on different test-beds of the TC-15 graph database show that the defined MSD class "almost always" covers the database, and that the proposed algorithm is significantly more efficient than top scoring VF algorithm on the same data. Most interestingly, the proposed approach is very well-suited for dealing with partial and approximate graph matching problems, derived for instance from image retrieval tasks. We consider the objects of the COIL-100 visual collection and provide a graph-based representation, whose node's labels contain appropriate visual features. We show that the adoption of classic bipartite graph matching algorithms offers a straightforward generalization of the algorithm given for graph isomorphism and, finally, we report very promising experimental results on the COIL-100 visual collection. The result size of a query that involves multiple attributes from the same relation depends on these attributes’joinr data distribution, i.e., the frequencies of all combinations of attribute values. To simplify the estimation of that size, most commercial systems make the artribute value independenceassumption and maintain statistics (typically histograms) on individual attributes only. In reality, this assumption is almost always wrong and the resulting estimations tend to be highly inaccurate. In this paper, we propose two main alternatives to effectively approximate (multi-dimensional) joint data distributions. (a) Using a multi-dimensional histogram, (b) Using the Singular Value Decomposition (SVD) technique from linear algebra. An extensive set of experiments demonstrates the advantages and disadvantages of the two approaches and the benefits of both compared to the independence assumption. Mining frequent patterns in transaction databases, time-series databases, and many other kinds of databases has been studied popularly in data mining research. Most of the previous studies adopt an Apriori-like candidate set generation-and-test approach. However, candidate set generation is still costly, especially when there exist a large number of patterns and or long patterns. In this study, we propose a novel frequent-pattern tree (FP-tree) structure, which is an extended prefix-tree structure for storing compressed, crucial information about frequent patterns, and develop an efficient FP-tree-based mining method, FP-growth, for mining the complete set of frequent patterns by pattern fragment growth. Efficiency of mining is achieved with three techniques: (1) a large database is compressed into a condensed, smaller data structure, FP-tree which avoids costly, repeated database scans, (2) our FP-tree-based mining adopts a pattern-fragment growth method to avoid the costly generation of a large number of candidate sets, and (3) a partitioning-based, divide-and-conquer method is used to decompose the mining task into a set of smaller tasks for mining confined patterns in conditional databases, which dramatically reduces the search space. Our performance study shows that the FP-growth method is efficient and scalable for mining both long and short frequent patterns, and is about an order of magnitude faster than the Apriori algorithm and also faster than some recently reported new frequent-pattern mining methods. Mining frequent patterns in transaction databases, time-series databases, and many other kinds of databases has been studied popularly in data mining research. Most of the previous studies adopt an Apriori-like candidate set generation-and-test approach. However, candidate set generation is still costly, especially when there exist prolific patterns and or long patterns. In this study, we propose a novel frequent pattern tree (FP-tree) structure, which is an extended prefix-tree structure for storing compressed, crucial information about frequent patterns, and develop an efficient FP-tree-based mining method, FP-growth, for mining the complete set of frequent patterns by pattern fragment growth. Efficiency of mining is achieved with three techniques: (1) a large database is compressed into a highly condensed, much smaller data structure, which avoids costly, repeated database scans, (2) our FP-tree-based mining adopts a pattern fragment growth method to avoid the costly generation of a large number of candidate sets, and (3) a partitioning-based, divide-and-conquer method is used to decompose the mining task into a set of smaller tasks for mining confined patterns in conditional databases, which dramatically reduces the search space. Our performance study shows that the FP-growth method is efficient and scalable for mining both long and short frequent patterns, and is about an order of magnitude faster than the Apriori algorithm and also faster than some recently reported new frequent pattern mining methods. Big data analytics often involves complex join queries over two or more tables. Such join processing is expensive in a distributed setting both because large amounts of data must be read from disk, and because of data shuffling across the network. Many techniques based on data partitioning have been proposed to reduce the amount of data that must be accessed, often focusing on finding the best partitioning scheme for a particular workload, rather than adapting to changes in the workload over time. In this paper, we present AdaptDB, an adaptive storage manager for analytical database workloads in a distributed setting. It works by partitioning datasets across a cluster and incrementally refining data partitioning as queries are run. AdaptDB introduces a novel hyper-join that avoids expensive data shuffling by identifying storage blocks of the joining tables that overlap on the join attribute, and only joining those blocks. Hyper-join performs well when each block in one table overlaps with few blocks in the other table, since that will minimize the number of blocks that have to be accessed. To minimize the number of overlapping blocks for common join queries, AdaptDB users smooth repartitioning to repartition small portions of the tables on join attributes as queries run. A prototype of AdaptDB running on top of Spark improves query performance by 2--3x on TPC-H as well as real-world dataset, versus a system that employs scans and shuffle-joins. This work proposes a process for efficiently searching over combinations of individual object 6D pose hypotheses in cluttered scenes, especially in cases involving occlusions and objects resting on each other. The initial set of candidate object poses is generated from state-of-the-art object detection and global point cloud registration techniques. The best-scored pose per object by using these techniques may not be accurate due to overlaps and occlusions. Nevertheless, experimental indications provided in this work show that object poses with lower ranks may be closer to the real poses than ones with high ranks according to registration techniques. This motivates a global optimization process for improving these poses by taking into account scene-level physical interactions between objects. It also implies that the Cartesian product of candidate poses for interacting objects must be searched so as to identify the best scene-level hypothesis. To perform the search efficiently, the candidate poses for each object are clustered so as to reduce their number but still keep a sufficient diversity. Then, searching over the combinations of candidate object poses is performed through a Monte Carlo Tree Search (MCTS) process that uses the similarity between the observed depth image of the scene and a rendering of the scene given the hypothesized pose as a score that guides the search procedure. MCTS handles in a principled way the tradeoff between fine-tuning the most promising poses and exploring new ones, by using the Upper Confidence Bound (UCB) technique. Experimental results indicate that this process is able to quickly identify in cluttered scenes physically-consistent object poses that are significantly closer to ground truth compared to poses found by point cloud registration methods. In this paper, we examine the issue of mining association rules among items in a large database of sales transactions. The mining of association rules can be mapped into the problem of discovering large itemsets where a large itemset is a group of items which appear in a sufficient number of transactions. The problem of discovering large itemsets can be solved by constructing a candidate set of itemsets first and then, identifying, within this candidate set, those itemsets that meet the large itemset requirement. Generally this is done iteratively for each large k-itemset in increasing order of k where a large k-itemset is a large itemset with k items. To determine large itemsets from a huge number of candidate large itemsets in early iterations is usually the dominating factor for the overall data mining performance. To address this issue, we propose an effective hash-based algorithm for the candidate set generation. Explicitly, the number of candidate 2-itemsets generated by the proposed algorithm is, in orders of magnitude, smaller than that by previous methods, thus resolving the performance bottleneck. Note that the generation of smaller candidate sets enables us to effectively trim the transaction database size at a much earlier stage of the iterations, thereby reducing the computational cost for later iterations significantly. Extensive simulation study is conducted to evaluate performance of the proposed algorithm. The application of frequent patterns in classification has demonstrated its power in recent studies. It often adopts a two-step approach: frequent pattern (or classification rule) mining followed by feature selection (or rule ranking). However, this two-step process could be computationally expensive, especially when the problem scale is large or the minimum support is low. It was observed that frequent pattern mining usually produces a huge number of "patterns" that could not only slow down the mining process but also make feature selection hard to complete. In this paper, we propose a direct discriminative pattern mining approach, DDPMine, to tackle the efficiency issue arising from the two-step approach. DDPMine performs a branch-and-bound search for directly mining discriminative patterns without generating the complete pattern set. Instead of selecting best patterns in a batch, we introduce a "feature-centered" mining approach that generates discriminative patterns sequentially on a progressively shrinking FP-tree by incrementally eliminating training instances. The instance elimination effectively reduces the problem size iteratively and expedites the mining process. Empirical results show that DDPMine achieves orders of magnitude speedup without any downgrade of classification accuracy. It outperforms the state-of-the-art associative classification methods in terms of both accuracy and efficiency. Sufficient training examples are the fundamental requirement for most of the learning tasks. However, collecting well-labelled training examples is costly. Inspired by Zero-shot Learning (ZSL) that can make use of visual attributes or natural language semantics as an intermediate level clue to associate low-level features with high-level classes, in a novel extension of this idea, we aim to synthesise training data for novel classes using only semantic attributes. Despite the simplicity of this idea, there are several challenges. First, how to prevent the synthesised data from over-fitting to training classes? Second, how to guarantee the synthesised data is discriminative for ZSL tasks? Third, we observe that only a few dimensions of the learnt features gain high variances whereas most of the remaining dimensions are not informative. Thus, the question is how to make the concentrated information diffuse to most of the dimensions of synthesised data. To address the above issues, we propose a novel embedding algorithm named Unseen Visual Data Synthesis (UVDS) that projects semantic features to the high-dimensional visual feature space. Two main techniques are introduced in our proposed algorithm. (1) We introduce a latent embedding space which aims to reconcile the structural difference between the visual and semantic spaces, meanwhile preserve the local structure. (2) We propose a novel Diffusion Regularisation (DR) that explicitly forces the variances to diffuse over most dimensions of the synthesised data. By an orthogonal rotation (more precisely, an orthogonal transformation), DR can remove the redundant correlated attributes and further alleviate the over-fitting problem. On four benchmark datasets, we demonstrate the benefit of using synthesised unseen data for zero-shot learning. Extensive experimental results suggest that our proposed approach significantly outperforms the state-of-the-art methods. Computing frequent itemsets is one of the most prominent problems in data mining. Recently, a new related problem, called FREQSAT, was introduced and studied: given some itemset–interval pairs, does there exist a database such that for every pair, the frequency of the itemset falls in the interval? In this paper, we extend this FREQSAT-problem by further constraining the database by giving other characteristics as part of the input as well. These characteristics are the maximal transaction length, the maximal number of transactions, and the maximal number of duplicates of a transaction. These extensions and all their combinations are studied in depth, and a hierarchy w.r.t. complexity is given. To make a complete picture, also the cases where the characteristics are constant; i.e., bounded and the bound being a fixed constant that is not a part of the input, are studied. This paper considers the problem of mining closed frequent itemsets over a data stream sliding window using limited memory space. We design a synopsis data structure to monitor transactions in the sliding window so that we can output the current closed frequent itemsets at any time. Due to time and memory constraints, the synopsis data structure cannot monitor all possible itemsets. However, monitoring only frequent itemsets will make it impossible to detect new itemsets when they become frequent. In this paper, we introduce a compact data structure, the closed enumeration tree (CET), to maintain a dynamically selected set of itemsets over a sliding window. The selected itemsets contain a boundary between closed frequent itemsets and the rest of the itemsets. Concept drifts in a data stream are reflected by boundary movements in the CET. In other words, a status change of any itemset (e.g., from non-frequent to frequent) must occur through the boundary. Because the boundary is relatively stable, the cost of mining closed frequent itemsets over a sliding window is dramatically reduced to that of mining transactions that can possibly cause boundary movements in the CET. Our experiments show that our algorithm performs much better than representative algorithms for the sate-of-the-art approaches. Data mining algorithms look for patterns in data. While most existing data mining approaches look for patterns in a single data table, multi-relational data mining (MRDM) approaches look for patterns that involve multiple tables (relations) from a relational database. In recent years, the most common types of patterns and approaches considered in data mining have been extended to the multi-relational case and MRDM now encompasses multi-relational (MR) association rule discovery, MR decision trees and MR distance-based methods, among others. MRDM approaches have been successfully applied to a number of problems in a variety of areas, most notably in the area of bioinformatics. This article provides a brief introduction to MRDM, while the remainder of this special issue treats in detail advanced research topics at the frontiers of MRDM.