Length-decreasing Support Constraint Research Articles

A Weight-Based Approach: Frequent Graph Pattern Mining with Length-Decreasing Support Constraints Using Weighted Smallest Valid Extension

A Weight-Based Approach: Frequent Graph Pattern Mining with Length-Decreasing Support Constraints Using Weighted Smallest Valid Extension

The Smallest Valid Extension-Based Efficient, Rare Graph Pattern Mining, Considering Length-Decreasing Support Constraints and Symmetry Characteristics of Graphs

Frequent graph mining has been proposed to find interesting patterns (i.e., frequent sub-graphs) from databases composed of graph transaction data, which can effectively express complex and large data in the real world. In addition, various applications for graph mining have been suggested. Traditional graph pattern mining methods use a single minimum support threshold factor in order to check whether or not mined patterns are interesting. However, it is not a sufficient factor that can consider valuable characteristics of graphs such as graph sizes and features of graph elements. That is, previous methods cannot consider such important characteristics in their mining operations since they only use a fixed minimum support threshold in the mining process. For this reason, in this paper, we propose a novel graph mining algorithm that can consider various multiple, minimum support constraints according to the types of graph elements and changeable minimum support conditions, depending on lengths of graph patterns. In addition, the proposed algorithm performs in mining operations more efficiently because it can minimize duplicated operations and computational overheads by considering symmetry features of graphs. Experimental results provided in this paper demonstrate that the proposed algorithm outperforms previous mining approaches in terms of pattern generation, runtime and memory usage.

길이에 따라 감소하는 빈도수 제한조건을 고려한 가중화 그래프 패턴 마이닝 기법

대규모의 데이터베이스로부터 숨겨진 유용한 패턴 정보를 찾기 위해 빈발 패턴 마이닝이 제안된 이래로, 다양한 종류의 접근 방법들과 어플리케이션들이 연구되어 왔다. 특히, 빈발 그래프 패턴 마이닝은 계속해서 복잡해져 가는 최근의 데이터들을 효과적으로 다루기 위해 제안되었고, 이와 관련한 다양한 효율적인 알고리즘들이 연구되어 왔다. 그래프 데이터베이스로부터 얻을 수 있는 그래프 패턴들은 이를 구성하는 요소들에 따라 다른 중요도를 가지며 길이에 따라 다른 특성을 갖는다. 하지만, 전통적인 빈발 그래프 패턴 마이닝 접근 방법들은 이러한 문제들을 고려할 수 없다는 한계점을 지닌다. 즉, 기존의 방법들은 마이닝 과정에서 추출되는 그래프 패턴들의 길이에 상관없이 오직 하나의 최소 지지도 임계값만을 고려하고 이들의 가중치 요소들을 사용하지 않기 때문에, 실제적으로 쓸모없는 그래프 패턴들이 상당량 생성될 수 있다. 작은 수의 정점과 간선을 갖는 작은 그래프 패턴들은 이들에 대한 가중화 지지도 값이 상대적으로 높을 때 흥미로운 특성을 갖는 경향이 있는 반면, 많은 정점과 간선을 갖는 큰 그래프 패턴들은 비록 가중화 지지도 값이 상대적으로 낮을지라도 흥미로운 특성을 가질 수 있다. 이러한 이유로, 본 논문에서는 길이에 따라 감소하는 지지도 제한조건을 고려한 가중치 기반의 빈발 그래프 패턴 마이닝 알고리즘을 제안한다. 본 논문에서 제공되는 총체적인 실험 결과들은 제안되는 방법이 기존의 최신 그래프 마이닝 알고리즘과 비교하여 패턴 생성, 수행시간, 그리고 메모리 사용량 측면에서 더욱 뛰어난 성능을 보장함을 보인다. Since frequent pattern mining was proposed in order to search for hidden, useful pattern information from large-scale databases, various types of mining approaches and applications have been researched. Especially, frequent graph pattern mining was suggested to effectively deal with recent data that have been complicated continually, and a variety of efficient graph mining algorithms have been studied. Graph patterns obtained from graph databases have their own importance and characteristics different from one another according to the elements composing them and their lengths. However, traditional frequent graph pattern mining approaches have the limitations that do not consider such problems. That is, the existing methods consider only one minimum support threshold regardless of the lengths of graph patterns extracted from their mining operations and do not use any of the patterns' weight factors; therefore, a large number of actually useless graph patterns may be generated. Small graph patterns with a few vertices and edges tend to be interesting when their weighted supports are relatively high, while large ones with many elements can be useful even if their weighted supports are relatively low. For this reason, we propose a weight-based frequent graph pattern mining algorithm considering length-decreasing support constraints. Comprehensive experimental results provided in this paper show that the proposed method guarantees more outstanding performance compared to a state-of-the-art graph mining algorithm in terms of pattern generation, runtime, and memory usage.

DISCOVERING IMPORTANT SEQUENTIAL PATTERNS WITH LENGTH-DECREASING WEIGHTED SUPPORT CONSTRAINTS

Sequential pattern mining with constraints has been developed to improve the efficiency and effectiveness in mining process. Specifically, there are two interesting constraints for sequential pattern mining. First, some sequences are more important and others are less important. Weight constraints consider the importance of sequences and items within sequences. Second, patterns including only a few items are interesting if they have high support. Meanwhile, long patterns can be interesting although their supports are relatively small. Weight constraints and length-decreasing support constraints are two paradigms aimed at finding important sequential patterns and reducing uninteresting patterns. Although weight and length-decreasing support constraints are vital elements, it is hard to consider both constraints by using previous approaches. In this paper, we integrate weight and length-decreasing support constraints by pushing two constraints into the prefix projection growth method. For pruning techniques, we define the Weighted Smallest Valid Extension property and apply the property to our pruning methods for reducing search space. In performance test, we show that our algorithm mines important sequential patterns with length-decreasing support constraints.

An efficient mining of weighted frequent patterns with length decreasing support constraints

Frequent pattern mining has been extensively studied in the data mining field due to its broad applications in mining association rules, correlations, closed frequent patterns, graph patterns, constraint-based frequent patterns, sequential patterns, and many other data mining tasks. Two concerns exist for frequent pattern mining in the real world. First, each item has different importance so researchers have proposed weighted frequent pattern mining algorithms that reflect the importance of items. Second, previous mining algorithms use a constant support constraint irrespective of the length of discovered patterns. However, short patterns having only a fewer items tend to be interesting if they have high support, while long patterns can still be interesting although their supports are relatively low. Weight and length decreasing support constraints are important constraints, but no mining algorithms consider both constraints. In this paper, we propose weighted frequent pattern mining with length decreasing support constraints. Our main approach is to push weight constraints and length decreasing support constraints into the pattern growth algorithm. For pruning techniques, we propose the notion of the Weighted Smallest Valid Extension (WSVE) property with/without Minimum Weight (MinW). The WSVE property with/without MinW is applied to transaction pruning, node pruning and path pruning to eliminate weighted infrequent patterns earlier. Our approach generates more concise but important weighted frequent patterns with length decreasing support constraints by applying the WSVE property with/without MinW.

Finding Frequent Patterns Using Length-Decreasing Support Constraints

Finding prevalent patterns in large amount of data has been one of the major problems in the area of data mining. Particularly, the problem of finding frequent itemset or sequential patterns in very large databases has been studied extensively over the years, and a variety of algorithms have been developed for each problem. The key feature in most of these algorithms is that they use a constant support constraint to control the inherently exponential complexity of these two problems. In general, patterns that contain only a few items will tend to be interesting if they have a high support, whereas long patterns can still be interesting even if their support is relatively small. Ideally, we want to find all the frequent patterns whose support decreases as a function of their length without having to find many uninteresting infrequent short patterns. Developing such algorithms is particularly challenging because the downward closure property of the constant support constraint cannot be used to prune short infrequent patterns. In this paper we present two algorithms, LPMiner and SLPMiner. Given a length-decreasing support constraint, LPMiner finds all the frequent itemset patterns from an itemset database, and SLPMiner finds all the frequent sequential patterns from a sequential database. Each of these two algorithms combines a well-studied efficient algorithm for constant-support-based pattern discovery with three effective database pruning methods that dramatically reduce the runtime. Our experimental evaluations show that both LPMiner and SLPMiner, by effectively exploiting the length-decreasing support constraint, are up to two orders of magnitude faster, and their runtime increases gradually as the average length of the input patterns increases.