Constraint-based Sequential Pattern Mining with Decision Diagrams

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.Comment: AAAI201

Reductions for Frequency-Based Data Mining Problems

Studying the computational complexity of problems is one of the - if not the - fundamental questions in computer science. Yet, surprisingly little is known about the computational complexity of many central problems in data mining. In this paper we study frequency-based problems and propose a new type of reduction that allows us to compare the complexities of the maximal frequent pattern mining problems in different domains (e.g. graphs or sequences). Our results extend those of Kimelfeld and Kolaitis [ACM TODS, 2014] to a broader range of data mining problems. Our results show that, by allowing constraints in the pattern space, the complexities of many maximal frequent pattern mining problems collapse. These problems include maximal frequent subgraphs in labelled graphs, maximal frequent itemsets, and maximal frequent subsequences with no repetitions. In addition to theoretical interest, our results might yield more efficient algorithms for the studied problems.Comment: This is an extended version of a paper of the same title to appear in the Proceedings of the 17th IEEE International Conference on Data Mining (ICDM'17

Direct mining of subjectively interesting relational patterns

Data is typically complex and relational. Therefore, the development of relational data mining methods is an increasingly active topic of research. Recent work has resulted in new formalisations of patterns in relational data and in a way to quantify their interestingness in a subjective manner, taking into account the data analyst's prior beliefs about the data. Yet, a scalable algorithm to find such most interesting patterns is lacking. We introduce a new algorithm based on two notions: (1) the use of Constraint Programming, which results in a notably shorter development time, faster runtimes, and more flexibility for extensions such as branch-and-bound search, and (2), the direct search for the most interesting patterns only, instead of exhaustive enumeration of patterns before ranking them. Through empirical evaluation, we find that our novel bounds yield speedups up to several orders of magnitude, especially on dense data with a simple schema. This makes it possible to mine the most subjectively-interesting relational patterns present in databases where this was previously impractical or impossible

The most persistent soft-clique in a set of sampled graphs

When searching for characteristic subpatterns in potentially noisy graph data, it appears self-evident that having multiple observations would be better than having just one. However, it turns out that the inconsistencies introduced when different graph instances have different edge sets pose a serious challenge. In this work we address this challenge for the problem of finding maximum weighted cliques. We introduce the concept of most persistent soft-clique. This is subset of vertices, that 1) is almost fully or at least densely connected, 2) occurs in all or almost all graph instances, and 3) has the maximum weight. We present a measure of clique-ness, that essentially counts the number of edge missing to make a subset of vertices into a clique. With this measure, we show that the problem of finding the most persistent soft-clique problem can be cast either as: a) a max-min two person game optimization problem, or b) a min-min soft margin optimization problem. Both formulations lead to the same solution when using a partial Lagrangian method to solve the optimization problems. By experiments on synthetic data and on real social network data, we show that the proposed method is able to reliably find soft cliques in graph data, even if that is distorted by random noise or unreliable observations

A Triclustering Approach for Time Evolving Graphs

This paper introduces a novel technique to track structures in time evolving graphs. The method is based on a parameter free approach for three-dimensional co-clustering of the source vertices, the target vertices and the time. All these features are simultaneously segmented in order to build time segments and clusters of vertices whose edge distributions are similar and evolve in the same way over the time segments. The main novelty of this approach lies in that the time segments are directly inferred from the evolution of the edge distribution between the vertices, thus not requiring the user to make an a priori discretization. Experiments conducted on a synthetic dataset illustrate the good behaviour of the technique, and a study of a real-life dataset shows the potential of the proposed approach for exploratory data analysis

Prefix-Projection Global Constraint for Sequential Pattern Mining

Sequential pattern mining under constraints is a challenging data mining task. Many efficient ad hoc methods have been developed for mining sequential patterns, but they are all suffering from a lack of genericity. Recent works have investigated Constraint Programming (CP) methods, but they are not still effective because of their encoding. In this paper, we propose a global constraint based on the projected databases principle which remedies to this drawback. Experiments show that our approach clearly outperforms CP approaches and competes well with ad hoc methods on large datasets

Flexible constrained sampling with guarantees for pattern mining

Pattern sampling has been proposed as a potential solution to the infamous pattern explosion. Instead of enumerating all patterns that satisfy the constraints, individual patterns are sampled proportional to a given quality measure. Several sampling algorithms have been proposed, but each of them has its limitations when it comes to 1) flexibility in terms of quality measures and constraints that can be used, and/or 2) guarantees with respect to sampling accuracy. We therefore present Flexics, the first flexible pattern sampler that supports a broad class of quality measures and constraints, while providing strong guarantees regarding sampling accuracy. To achieve this, we leverage the perspective on pattern mining as a constraint satisfaction problem and build upon the latest advances in sampling solutions in SAT as well as existing pattern mining algorithms. Furthermore, the proposed algorithm is applicable to a variety of pattern languages, which allows us to introduce and tackle the novel task of sampling sets of patterns. We introduce and empirically evaluate two variants of Flexics: 1) a generic variant that addresses the well-known itemset sampling task and the novel pattern set sampling task as well as a wide range of expressive constraints within these tasks, and 2) a specialized variant that exploits existing frequent itemset techniques to achieve substantial speed-ups. Experiments show that Flexics is both accurate and efficient, making it a useful tool for pattern-based data exploration.Comment: Accepted for publication in Data Mining & Knowledge Discovery journal (ECML/PKDD 2017 journal track

BIG DATA MINING FOR INTERESTING PATTERNS WITH MAP REDUCE TECHNIQUE

There are many algorithms available in data mining to search interesting patterns from transactional databases of precise data. Frequent pattern mining is a technique to find the frequently occurred items in data mining. Most of the techniques used to find all the interesting patterns from a collection of precise data, where items occurred in each transaction are certainly known to the system. As well as in many real-time applications, users are interested in a tiny portion of large frequent patterns. So the proposed user constrained mining approach, will help to find frequent patterns in which user is interested. This approach will efficiently find user interested frequent patterns by applying user constraints on the collections of uncertain data. The user can specify their own interest in the form of constraints and uses the Map Reduce model to find uncertain frequent pattern that satisfy the user-specified constraintsÂ

Discovering Knowledge from Local Patterns with Global Constraints

It is well known that local patterns are at the core of a lot of knowledge which may be discovered from data. Nevertheless, use of local patterns is limited by their huge number and computational costs. Several approaches (e.g., condensed representations, pattern set discovery) aim at grouping or synthesizing local patterns to provide a global view of the data. A global pattern is a pattern which is a set or a synthesis of local patterns coming from the data. In this paper, we propose the idea of global constraints to write queries addressing global patterns. A key point is the ability to bias the designing of global patterns according to the expectation of the user. For instance, a global pattern can be oriented towards the search of exceptions or a clustering. It requires to write queries taking into account such biases. Open issues are to design a generic framework to express powerful global constraints and solvers to mine them. We think that global constraints are a promising way to discover relevant global patterns