The support-confidence framework is the most common measure used in itemset mining algorithms, for its antimonotonicity that effectively simplifies the search lattice. This computational convenience brings both quality and statistical flaws to the results as observed by many previous studies. In this paper, we introduce a novel algorithm that produces itemsets with ranked statistical merits under sophisticated test statistics such as chi-square, risk ratio, odds ratio, etc. Our algorithm is based on the concept of equivalence classes. An equivalence class is a set of frequent itemsets that always occur together in the same set of transactions. Therefore, itemsets within an equivalence class all share the same level of statistical significance regardless of the variety of test statistics. As an equivalence class can be uniquely determined and concisely represented by a closed pattern and a set of generators, we just mine closed patterns and generators, taking a simultaneous depth-first search scheme. This parallel approach has not been exploited by any prior work. We evaluate our algorithm on two aspects. In general, we compare to LCM and FPclose which are the best algorithms tailored for mining only closed patterns. In particular, we compare to epMiner which is the most recent algorithm for mining a type of relative risk patterns, known as minimal emerging patterns. Experimental results show that our algorithm is faster than all of them, sometimes even multiple orders of magnitude faster. These statistically ranked patterns and the efficiency have a high potential for reallife applications, especially in biomedical and financial fields where classical test statistics are of dominant interest.

Large amounts of remotely sensed data calls for data mining techniques to fully utilize their rich information content. In this paper, we study new means of discovery and summarization of knowledge contained in the spatial patterns of remote sensing datasets. Several geospatial feature variables are fused together, and the vector of their values at each spatial cell is considered as a transaction to be used in association analysis. The concept of emerging patterns is applied to ascertain the variables that exert dominant influence on the distribution of a selected class variable. A new value-iteration method is introduced to optimally split the spatial domain of the selected variable into two classes. This division is used to calculate the set of patterns that are emerging with respect to the two classes; these patterns are the controlling factors—they are responsible for the spatial distribution of the class variable. A method for a concise summarization of controlling factors is introduced using a similarity measure that is custom-made for the type of patterns stemmed from remote sensing measurements. Using such a similarity measure, controlling factors are clustered providing brief description of different manners, in which the class variable is constrained by the explanatory variables. We evaluate our method in a real-world application pertaining to the density of vegetation within the continental United States. Examination of patterns related to the high vegetation cover provides a summary of data dependencies that helps to develop a better empirical model of the vegetation growth.

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. FPtrees) 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.

Contrast- ``To compare or appraise in respect to differences’ ’ (Merriam Webster Dictionary) Contrast data mining- The mining of patterns and models contrasting two or more classes/conditions.

Contrast data mining is a key tool for finding differences between sets of objects, or classes, and contrast patterns are a popular method for discrimination between two classes. However, such patterns can be limited in two primary ways: i) They do not readily allow second order differentiation-i.e. discovering contrasts of contrasts, ii) Mining contrast patterns often results in an overwhelming volume of output for the user. To address these limitations, this paper proposes a method which can identify contrast behaviour across both classes and also groups of classes. Furthermore, to increase interpretability for the user, it presents a new technique for finding the attributes which represent the key underlying factors behind the contrast behaviour. The associated mining task is computationally challenging and we describe an efficient algorithm to handle it, based on binary decision diagrams. Experimental results demonstrate that our technique can efficiently identify and explain contrast behaviour which would be difficult or impossible to isolate using standard techniques.

(Abstract) Frequent itemset mining is one of the fundamental techniques for data mining and knowledge discovery. In the last decade, a number of efficient algorithms for frequent itemset mining have been presented, but most of them focused on just enumerating the itemsets which satisfy the given conditions, and it was a different matter how to store and index the mining result for efficient data analysis. In this paper, we propose a fast algorithm for generating very large-scale all/closed/maximal frequent itemsets using Zero-suppressed BDDs (ZBDDs), a compact graph-based data structure. Our method, “LCM over ZBDDs, ” is based on one of the most efficient state-of-the-art algorithms proposed before, and not only enumerating/listing the itemsets but also generating a compact output data structure on the main memory. The result can efficiently be post-processed by using algebraic ZBDD operations. The original LCM is known as an output linear time algorithm, but our new method requires a sub-linear time to the number of frequent patterns when the ZBDD-based data compression works well. Our method may greatly accelerate the data mining process and will lead a new style of on-memory processing for knowledge discovery problems. 1

(Abstract) Frequent itemset mining is one of the fundamental techniques for data mining and knowledge discovery. Recently, Minato et al. proposed a fast algorithm “LCM over ZDDs ” for generating very large-scale frequent itemsets using Zerosuppressed BDDs (ZDDs), a compact graph-based data structure. Their method is based on LCM algorithm, one of the most efficient state-of-the-art techniques for itemset mining, and directly generates compact output data structures on the main memory, to be efficiently post-processed by using ZDD-based algebraic operations. In this paper, we propose a novel method of finding distinctive frequent itemsets from time segmented (e.g. daily, weekly, monthly) sequential transaction databases. We define “frequency pattern chart” using regular expressions for specifying distinctive frequency patterns in time segmented databases. Our method efficiently extracts all itemsets satisfying a given frequency pattern chart using LCM over ZDDs algorithm and ZDD-based symbolic processing of finite automata. Experimental results show that our method is applicable to very large-scale problems, for example, we can find a small number of distinctive itemsets from a huge number (more than 1044) of frequent itemsets in a few seconds. Time segmented databases often appear in many real-life problems, so our new method will have a significant impact to various practical applications. 1

Abstract. The use of patterns in predictive models is a topic that has received a lot of attention in recent years. Pattern mining can help to obtain models for structured domains, such as graphs and sequences, and has been proposed as a means to obtain more accurate and more interpretable models. Despite the large amount of publications devoted to this topic, we believe however that an overview of what has been accomplished in this area is missing. This paper presents our perspective on this evolving area. We identify the principles of pattern mining that are important when mining patterns for models and provide an overview of pattern-based classification methods. We categorize these methods along the following dimensions: (1) whether they post-process a pre-computed set of patterns or iteratively execute pattern mining algorithms; (2) whether they select patterns model-independently or whether the pattern selection is guided by a model. We summarize the results that have been obtained for each of these methods. 1

binary decision diagram based approach for mining frequent subsequences

Discriminative patterns can provide valuable insights into datasets with class labels, that may not be available from the individual features or the predictive models built using them. Most existing approaches work efficiently for sparse or low-dimensional datasets. However, for dense and highdimensional datasets, they have to use high thresholds to produce the complete results within limited time, and thus, may miss interesting low-support patterns. In this paper, we address the necessity of trading off the completeness of discriminative pattern discovery with the efficient discovery of lowsupport discriminative patterns from such datasets. We propose a family of anti-monotonic measures named SupMaxK that organize the set of discriminative patterns into nested layers of subsets, which are progressively more complete in their coverage, but require increasingly more computation. In particular, the member of SupMaxK with K = 2, named SupMaxPair, is suitable for dense and high-dimensional datasets. Experiments on both synthetic datasets and a cancer gene expression dataset demonstrate that there are low-support patterns that can be discovered using SupMaxPair but not by existing approaches. Furthermore, we show that the low-support discriminative patterns that are only discovered