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Frequent subgraph mining, i.e., the identification of relevant patterns in graph databases, is a well-known data mining problem with high practical relevance, since next to summarizing the data, the resulting patterns can also be used to define powerful domain-specific similarity functions for prediction. In recent years, significant progress has been made towards subgraph mining algorithms that scale to complex graphs by focusing on tree patterns and probabilistically allowing a small amount of incompleteness in the result. Nonetheless, the complexity of the pattern matching component used for deciding subtree isomorphism on arbitrary graphs has significantly limited the scalability of existing approaches. In this paper, we adapt sampling techniques from mathematical combinatorics to the problem of probabilistic subtree mining in arbitrary databases of many small to medium-size graphs or a single large graph. By restricting on tree patterns, we provide an algorithm that approximately counts or decides subtree isomorphism for arbitrary transaction graphs in sub-linear time with one-sided error. Our empirical evaluation on a range of benchmark graph datasets shows that the novel algorithm substantially outperforms state-of-the-art approaches both in the task of approximate counting of embeddings in single large graphs and in probabilistic frequent subtree mining in large databases of small to medium sized graphs.

Many applications process some form of tree-structured or recursively-nested data, such as parsing XML or JSON web content as well as various data mining tasks. Typical CPU processing solutions are hindered by branch misprediction penalties while attempting to reconstruct nested structures and also by irregular memory access patterns. Recent work has demonstrated improved performance for many data processing applications through memory-centric automata processing engines. Unfortunately, these architectures do not support a computational model rich enough for tasks such as XML parsing. In this paper, we present ASPEN, a general-purpose, scalable, and reconfigurable memory-centric architecture for processing of tree-like data. We take inspiration from previous automata processing architectures, but support the richer deterministic pushdown automata computational model. We propose a custom datapath capable of performing the state matching, stack manipulation, and transition routing operations of pushdown automata, all efficiently stored and computed in memory arrays. Further, we present compilation algorithms for transforming large classes of existing grammars to pushdown automata executable on ASPEN, and demonstrate their effectiveness on four different languages: Cool (object oriented programming), DOT (graph visualization), JSON, and XML. Finally, we present an empirical evaluation of two application scenarios for ASPEN: XML parsing, and frequent subtree mining. The proposed architecture achieves an average 704.5 ns per KB parsing XML compared to 9983 ns per KB in a state-of-the-art XML parser across 23 benchmarks. We also demonstrate a 37.2x and 6x better end-to-end speedup over CPU and GPU implementations of subtree mining.

Frequent subtree mining is a major research topic in knowledge discovery from tree-structured data, whose importance is witnessed by the pervasiveness of such data in several domains. In this paper, we present a novel approach to discover all the frequent ordered subtrees in a tree-structured database. A key aspect is that the structural aspects of the input tree instances are extracted to generate a transactional format that enables the application of standard itemset mining techniques. In this way, the expensive process of subtree enumeration is avoided, while subtrees can be reconstructed in a post-processing stage. As a result, more structurally complex tree data can be handled and much lower support thresholds can be used. In addition to discovering traditional subtrees, this is the first approach to frequent subtree mining that can discover position-constrained subtrees. Each node in the position-constrained subtree is annotated with its exact occurrence and level of embedding in the original database tree. Also, disconnected subtree associations can be represented via virtual connecting nodes. Experiments conducted on synthetic and real-world datasets confirm the expected advantages of our approach over competing methods in terms of efficiency, mining capabilities, and informativeness of the extracted patterns.

The problem of mining collections of trees to identify common patterns, called frequent subtrees (FSTs), arises often when trying to interpret the results of phylogenetic analysis. FST mining generalizes the well-known maximum agreement subtree problem. Here we present EvoMiner, a new algorithm for mining frequent subtrees in collections of phylogenetic trees. EvoMiner is an Apriori-like levelwise method, which uses a novel phylogeny-specific constant-time candidate generation scheme, an efficient fingerprinting-based technique for downward closure, and a lowest-common-ancestor-based support counting step that requires neither costly subtree operations nor database traversal. Our algorithm achieves speedups of up to 100 times or more over Phylominer, the current state-of-the-art algorithm for mining phylogenetic trees. EvoMiner can also work in depth-first enumeration mode to use less memory at the expense of speed. We demonstrate the utility of FST mining as a way to extract meaningful phylogenetic information from collections of trees when compared to maximum agreement subtrees and majority-rule trees--two commonly used approaches in phylogenetic analysis for extracting consensus information from a collection of trees over a common leaf set.

The increasing need for representing information through more complex structures where semantics and relationships among data objects can be more easily expressed has resulted in many semi-structured data sources. Structure comparison among semi-structured data objects can often reveal valuable information, and hence tree mining has gained a considerable amount of interest in areas such as XML mining, Bioinformatics, Web mining etc. We are primarily concerned with the task of mining frequent ordered induced and embedded subtrees from a database of rooted ordered labeled trees. Our previous contributions consist of the efficient Tree Model Guided (TMG) candidate enumeration approach for which we developed a mathematical model that provides an estimate of the worst case complexity for embedded subtree mining. This potentially reveals computationally impractical situations where one would be forced to constrain the mining process in some way so that at least some patterns can be discovered. This motivated our strategy of tackling the complexity of mining embedded subtrees by introducing the Level of Embedding constraint. Thus, when it is too costly to mine all frequent embedded subtrees, one can decrease the level of embedding constraint gradually down to 1, from which all the obtained frequent subtrees are induced subtrees. In this paper we develop alternative implementations and propose two algorithms MB3-R and iMB3-R, which achieve better efficiency in terms of time and space. Furthermore, we develop a mathematical model for estimating the worst case complexity for induced subtree mining. It is accompanied with a theoretical analysis of induced-embedded subtree relationships in terms of complexity for frequent subtree mining. Using synthetic and real world data we practically demonstrate the space and time efficiency of our new approach and provide some comparisons to the two well know algorithms for mining induced and embedded subtrees.

Large amount of online information is or can be represented using semi-structured documents, such as XML. The information contained in an XML document can be effectively represented using a rooted ordered labeled tree. This has made the frequent pattern mining problem recast as the frequent subtree mining problem, which is a pre-requisite for association rule mining form tree-structured documents. Driven by different application needs a number of algorithms have been developed for mining of different subtree types under different support definitions. In this paper we present an algorithm for mining unordered embedded subtrees. It is an extension of our general tree model guided (TMG) candidate generation framework and the proposed U3 algorithm considers all support definitions, namely, transaction-based, occurrence-match and hybrid support. A number of experiments are presented on synthetic and real world data sets. The results demonstrate the flexibility of our general TMG framework as well as its efficiency when compared to the existing state-of-the-art approach.

Social-media websites, such as newspapers, blogs, and forums, are the main places of generation and exchange of user-generated comments. These comments are viable sources for opinion mining, descriptive annotations and information extraction. User-generated comments are formatted using a HTML template, they are therefore entwined with the other information in the HTML document. Their unsupervised extraction is thus a taxing issue -- even greater when considering the extraction of nested answers by different users. This paper presents a novel technique (CommentsMiner) for unsupervised users comments extraction. Our approach uses both the theoretical framework of frequent subtree mining and data extraction techniques. We demonstrate that the comment mining task can be modelled as a constrained closed induced subtree mining problem followed by a learning-to-rank problem. Our experimental evaluations show that CommentsMiner solves the plain comments and nested comments extraction problems for 84% of a representative and accessible dataset, while outperforming existing baselines techniques.

Tree mining has recently attracted a lot of interest in areas such as Bioinformatics, XML mining, Web mining, etc. We are mainly concerned with mining frequent induced and embedded subtrees. While more interesting patterns can be obtained when mining embedded subtrees, unfortunately mining such embedding relationships can be very costly. In this paper, we propose an efficient approach to tackle the complexity of mining embedded subtrees by utilizing a novel Embedding List representation, Tree Model Guided enumeration, and introducing the Level of Embedding constraint. Thus, when it is too costly to mine all frequent embedded subtrees, one can decrease the level of embedding constraint gradually up to 1, from which all the obtained frequent subtrees are induced subtrees. Our experiments with both synthetic and real datasets against two known algorithms for mining induced and embedded subtrees, FREQT and TreeMiner, demonstrate the effectiveness and the efficiency of the technique.

Tree structures are used extensively in domains such as computational biology, pattern recognition, XML databases, computer networks, and so on. In this paper, we first present two canonical forms for labelled rooted unordered trees–the breadth-first canonical form (BFCF) and the depth-first canonical form (DFCF). Then the canonical forms are applied to the frequent subtree mining problem. Based on the BFCF, we develop a vertical mining algorithm, RootedTreeMiner, to discover all frequently occurring subtrees in a database of labelled rooted unordered trees. The RootedTreeMiner algorithm uses an enumeration tree to enumerate all (frequent) labelled rooted unordered subtrees. Next, we extend the definition of the DFCF to labelled free trees and present an Apriori-like algorithm, FreeTreeMiner, to discover all frequently occurring subtrees in a database of labelled free trees. Finally, we study the performance and the scalability of our algorithms through extensive experiments based on both synthetic data and datasets from real applications.

Mining frequent trees is very useful in domains like bioinformatics, Web mining, mining semistructured data, etc. We formulate the problem of mining (embedded) subtrees in a forest of rooted, labeled, and ordered trees. We present TREEMINER, a novel algorithm to discover all frequent subtrees in a forest, using a new data structure called scope-list. We contrast TREEMINER with a pattern matching tree mining algorithm (PATTERNMATCHER), and we also compare it with TREEMINERD, which counts only distinct occurrences of a pattern. We conduct detailed experiments to test the performance and scalability of these methods. We also use tree mining to analyze RNA structure and phylogenetics data sets from bioinformatics domain.

Tree structures are used extensively in domains such as computational biology, pattern recognition, XML databases, computer networks, and so on. One important problem in mining databases of trees is to find frequently occurring subtrees. Because of the combinatorial explosion, the number of frequent subtrees usually grows exponentially with the size of frequent subtrees and, therefore, mining all frequent subtrees becomes infeasible for large tree sizes. We present CMTreeMiner, a computationally efficient algorithm that discovers only closed and maximal frequent subtrees in a database of labeled rooted trees, where the rooted trees can be either ordered or unordered. The algorithm mines both closed and maximal frequent subtrees by traversing an enumeration tree that systematically enumerates all frequent subtrees. Several techniques are proposed to prune the branches of the enumeration tree that do not correspond to closed or maximal frequent subtrees. Heuristic techniques are used to arrange the order of computation so that relatively expensive computation is avoided as much as possible. We study the performance of our algorithm through extensive experiments, using both synthetic data and data sets from real applications. The experimental results show that our algorithm is very efficient in reducing the search space and quickly discovers all closed and maximal frequent subtrees.

With the semi-structured data rapidly growing, it is crucial to obtain valuable information for different applications. So many data mining methods are proposed and the frequent sub trees mining is an important and typical method. The current mining methods demand substantial computational time and space, and return a huge number of patterns, but some important sub trees are often missed and some patterns are uninteresting to users. In this paper we proposed two novel algorithms, namely FSMDC and FSMIC, for mining frequent embedded sub trees from rooted labeled ordered trees database. In these proposed algorithms, the distance and interest constraint are introduced respectively to achieve expected mining results. The experiments show that the two newly developed algorithms are efficient, scalable and more consistent with purpose of users.

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.

Credit risk assessment has been one of the most appealing topics in banking and finance studies, attracting both scholars’ and practitioners’ attention for some time. Following the success of the Grameen Bank, works on credit risk, in particular for Small Medium Enterprises (SMEs), have become essential. The distinctive character of SMEs requires a method that takes into account quantitative and qualitative information for loan granting decision purposes. In this chapter, we first provide a survey of existing credit risk assessment methods, which shows a current gap in the existing research in regards to taking qualitative information into account during the data mining process. To address this shortcoming, we propose a framework that utilizes an XML-based template to capture both qualitative and quantitative information in this domain. By representing this information in a domain-oriented way, the potential knowledge that can be discovered for evidence-based decision support will be maximized. An XML document can be effectively represented as a rooted ordered labelled tree and a number of tree mining methods exist that enable the efficient discovery of associations among tree-structured data objects, taking both the content and structure into account. The guidelines for correct and effective application of such methods are provided in order to gain detailed insight into the information governing the decision making process. We have obtained a number of textual reports from the banks regarding the information collected from SMEs during the credit application/evaluation process. These are used as the basis for generating a synthetic XML database that partially reflects real-world scenarios. A tree mining method is applied to this data to demonstrate the potential of the proposed method for credit risk assessment.

Many data mining and simulation based algorithms have been applied in the process mining field; nevertheless they mainly focus on the process discovery and conformance checking tasks. Even though the event logs are increasingly represented in semi-structured format using XML-based templates, commonly used XML mining techniques have not been explored. In this paper, we investigate the application of tree mining techniques and propose a general framework, within which a wider range of structure aware data mining techniques can be applied. Decision tree learning and frequent pattern mining are used as a case in point in the experiments on publicly available real dataset. The results indicate the promising properties of the proposed framework in adding to the available set of tools for process log analysis by enabling (i) direct data mining of tree-structured process logs (ii) extraction of informative knowledge patterns and (iii) frequent pattern mining at lower minimum support thresholds.

Mining frequent sub tree from databases of labeled trees is a new research field that has many practical applications in areas such as computer networks, Web mining, bioinformatics, XML document mining, etc. These applications share a requirement for the more expressive power of labeled trees to capture the complex relations among data entities. In this paper an efficient algorithm is introduced for mining frequent, ordered, embedded sub tree in tree-like databases. Using a new data structure called scope-list, which is a canonical representation of tree node, the algorithm first generates all candidate trees, then enumerates embedded, ordered trees, finally joins scope-list to compute frequency of embedded ordered trees. Experiments show the performance of the algorithm is about 15% better than other similar mining methods and has good scale-up properties.

In this paper, we present a closed labeled tree mining algorithm, FBMiner, based on the add-remove principle of closed sets which is newly introduced. Also, we propose a time-decay module to solve stream data mining which gives more attention on the latest data. Compared to the traditional mining algorithms in data stream, FBMiner performs well even that the data is of high complexity. The experiment shows that FBMiner is efficient in data streams mining by reducing consuming dramatically.

The first task of statistical computational linguistics, or any other type of datadriven processing of language, is the extraction of counts and distributions of phenomena. This is much more difficult for the type of complex structured data found in treebanks and in corpora with sophisticated annotation than for tokenized texts. Recent developments in data mining, particularly in the extraction of frequent subtrees from treebanks, offer some solutions. We have applied a modified version of the TreeMiner algorithm to a small treebank and present some promising results. ispartof: pages:84-92 ispartof: Proceedings of the 2009 Workshop on Graph-based Methods for Natural Language Processing (Textgraph-4) pages:84-92 ispartof: Textgraph location:Singapore date:7 Aug - 7 Aug 2009 status: published

In this paper, we systematically explore the problem of frequent subtree mining and present a novel pruning strategy, F2SC (Frequent 2-Subtree Checking), which can be used in all Apriori-like subtree mining algorithms. With a little more memory overhead of keeping frequent 2-subtrees list, F2SC can prunes the invalid candidate which contains infrequent 2-subtree by checking the frequent 2-subtrees list and decreases the total cost of frequency counting effectively. At the same time, we optimize TREEMINER [7] and present the improved algorithm TMp, which uses F2SC to prune invalid candidate subtree patterns. A set of comprehensive performance experiments demonstrates the efficiency of proposed pruning strategy by compare TMp with TREEMINER.

One crucial issue in genetic programming (GP) is how to acquire promising building blocks efficiently. In this paper, we propose a GP method (called GPTM, GP with Tree Mining) which protects the subtrees repeatedly appearing in superior individuals. Currently GPTM utilizes a FREQT-like efficient data mining method to find such subtrees. GPTM is evaluated by three benchmark problems, and the results indicate that GPTM is comparable to or better than POLE, one of the most advanced probabilistic model building GP methods, and finds the optimal individual earlier than the standard GP and POLE.

Frequent subtree mining is an important problem in the area of association rule mining from semi-structured or tree structured documents, often found in many commercial, web and scientific domains. This paper presents the u3Razor algorithm, for mining unordered embedded subtrees where the distance of nodes relative to the root of the subtree needs to be considered. Mining distance-constrained unordered embedded subtrees will have important applications in web information systems, conceptual model analysis and more sophisticated knowledge matching. An encoding strategy is presented to efficiently enumerate candidate unordered embedded subtrees taking the distance of nodes relative to the root of the subtree into account. Both synthetic and real-world datasets were used for experimental evaluation and discussion.

Frequent subtree mining has found many useful applications in areas where the domain knowledge is presented in a tree structured form, such as bioinformatics, web mining, scientific knowledge management etc. It involves the extraction of a set of frequent subtrees from a tree structured database, with respect to the user specified minimum support. Up to date, the commonly used support definitions are occurrence match and transaction based support. There are some application areas where using either of these support definitions would not provide the desired information automatically, but instead further querying on the extracted patterns needs to take place. This has motivated us to develop a hybrid support definition that constrains the kind of patterns to be extracted and provides additional information not provided by previous support definitions. This would simplify some of the reasoning process which commonly takes place in certain applications. In this paper we demonstrate the need for the hybrid support definition by presenting some applications of tree mining where traditional support definitions would fall short in providing the desired information. We have extended our previous tree mining algorithms to mine frequent subtrees using the hybrid support definition. Using real-world and synthetic data sets we demonstrate the effectiveness of the method, and further implications for reasoning with the extracted patterns.

Semi-structured data sources are increasingly in use today because of their capability of representing information through more complex structures where semantics and relationships of data objects are more easily expressed. Extraction of frequent sub-structures from such data has found important applications in areas such as Bioinformatics, XML mining, Web mining, scientific data management etc. This paper is concerned with the task of mining frequent unordered induced subtrees from a database of rooted ordered labeled subtrees. Our previous work in the area of frequent subtree mining is characterized by the efficient tree model guided (TMG) candidate enumeration, where candidate subtrees conform to the data's underlying tree structure. We apply the same approach to the unordered case, motivated by the fact that in many applications of frequent subtree mining the order among siblings is not considered important. The proposed UNI3 algorithm considers both transaction based and occurrence match support. Synthetic and real world data are used to evaluate the time performance of our approach in comparison to the well known algorithms developed for the same problem

Mining frequent induced subtree patterns is very useful in domains such as XML databases, web log analyzing. However, because of the combinatorial explosion, mining all frequent subtree patterns becomes infeasible for a large and dense tree database. And too many frequent subtree patterns also confuse users. Usually only a small set of the mining results can arouse users? interests. In this paper, we propose a problem to discover frequent induced subtree patterns that are super trees of a given pattern tree specified by users, i.e. frequent induced subtree patterns with subtree-constraint. Most existing frequent subtree mining algorithms are based on right-most extension, which does not work well in the new problem. So free extension is presented to replace right-most extension in this paper. To avoid the duplicate pattern problem caused by free extension, we develop an efficient method that ensures no duplicate patterns in mining process or results. Then Subtree- Constraint Frequent Subtree Patterns Mining Algorithm, i.e.SCFS algorithm, is given. The experiment results also show that our algorithm achieves good performance.

In this paper we consider the ?Prions? database that describes protein instances stored for Human Prion Proteins. The Prions database can be viewed as a database of rooted ordered labeled subtrees. Mining frequent substructures from tree databases is an important task and it has gained a considerable amount of interest in areas such as XML mining, Bioinformatics, Web mining etc. This has given rise to the development of many tree mining algorithms which can aid in structural comparisons, association rule discovery and in general mining of tree structured knowledge representations. Previously we have developed the MB3 tree mining algorithm, which given a minimum support threshold, efficiently discovers all frequent embedded subtrees from a database of rooted ordered labeled subtrees. In this work we apply the algorithm to the Prions database in order to extract the frequently occurring patterns, which in this case are of induced subtree type. Obtaining the set of frequent induced subtrees from the Prions database can potentially reveal some useful knowledge. This aspect will be demonstrated by providing an analysis of the extracted frequent subtrees with respect to discovering interesting protein information. Furthermore, the minimum support threshold can be used as the controlling factor for answering specific queries posed on the Prions dataset. This approach is shown to be a viable technique for mining protein data.

Frequent subtree mining has become increasingly important in recent years. In this paper, we present AMIOT algorithm to discover all frequent ordered subtrees in a tree-structured database. In order to avoid the generation of infrequent candidate trees, we propose the techniques such as right-and-left tree join and serial tree extension. Proposed methods enumerate only the candidate trees with high probability of being frequent without any duplication. The experiments on synthetic dataset and XML database show that AMIOT reduces redundant candidate trees and outperforms FREQT algorithm by up to five times in execution time.

Recent research in data mining has progressed from mining frequent itemsets to more general and structured patterns like trees and graphs. In this paper, we address the problem of frequent subtree mining that has proven to be viable in a wide range of applications such as bioinformatics, XML processing, computational linguistics, and web usage mining. We propose novel algorithms to mine frequent subtrees from a database of rooted trees. We evaluate the use of two popular sequential encodings of trees to systematically generate and evaluate the candidate patterns. The proposed approach is very generic and can be used to mine embedded or induced subtrees that can be labeled, unlabeled, ordered, unordered, or edge-labeled. Our algorithms are highly cache-conscious in nature because of the compact and simple array-based data structures we use. Typically, L1 and L2 hit rates above 99% are observed. Experimental evaluation showed that our algorithms can achieve up to several orders of magnitude speedup on real datasets when compared to state-of-the-art tree mining algorithms.

A new type of tree mining is defined, which uncovers maximal frequent induced subtrees from a database of unordered labeled trees. A novel algorithm, PathJoin, is proposed. The algorithm uses a compact data structure, FST-Forest, which compresses the trees and still keeps the original tree structure. PathJoin generates candidate subtrees by joining the frequent paths in FST-Forest. Such candidate subtree generation is localized and thus substantially reduces the number of candidate subtrees. Experiments with synthetic data sets show that the algorithm is effective and efficient.

Tree structures are used extensively in domains such as computational biology, pattern recognition, computer networks, and so on. We present an indexing technique for free trees and apply this indexing technique to the problem of mining frequent subtrees. We first define a novel representation, the canonical form, for rooted trees and extend the definition to free trees. We also introduce another concept, the canonical string, as a simpler representation for free trees in their canonical forms. We then apply our tree indexing technique to the frequent subtree mining problem and present FreeTreeMiner, a computationally efficient algorithm that discovers all frequently occurring subtrees in a database of free trees. We study the performance and the scalability of our algorithms through extensive experiments based on both synthetic data and datasets from two real applications: a dataset of chemical compounds and a dataset of Internet multicast trees.

Mining frequent tree patterns is an important research problems with broad applications in bioinformatics, digital library, e-commerce, and so on. Previous studies highly suggested that pattern-growth methods are efficient in frequent pattern mining. In this paper, we systematically develop the pattern growth methods for mining frequent tree patterns. Two algorithms, Chopper and XSpanner, are devised. An extensive performance study shows that the two newly developed algorithms outperform TreeMinerV [13], one of the fastest methods proposed before, in mining large databases. Furthermore, algorithm XSpanner is substantially faster than Chopper in many cases.

We investigate new approaches for frequent graph-based pattern mining in graph datasets and propose a novel algorithm called gSpan (graph-based substructure pattern mining), which discovers frequent substructures without candidate generation. gSpan builds a new lexicographic order among graphs, and maps each graph to a unique minimum DFS code as its canonical label. Based on this lexicographic order gSpan adopts the depth-first search strategy to mine frequent connected subgraphs efficiently. Our performance study shows that gSpan substantially outperforms previous algorithms, sometimes by an order of magnitude.

In this paper we consider the problem of searching frequent trees from a collection of tree-structured data modeling XML data. The TreeFinder algorithm aims at finding trees, such that their exact or perturbed copies are frequent in a collection of labelled trees. To cope with complexity issues, TreeFinder is correct but not complete: it finds a subset of actually frequent trees. The default of completeness is experimentally investigated on artificial medium size datasets; it is shown that TreeFinder reaches completeness or falls short for a range of experimental settings.

We are given a large database of customer transactions, where each transaction consists of customer-id, transaction time, and the items bought in the transaction. We introduce the problem of mining sequential patterns over such databases. We present three algorithms to solve this problem, and empirically evaluate their performance using synthetic data. Two of the proposed algorithms, AprioriSome and AprioriAll, have comparable performance, albeit AprioriSome performs a little better when the minimum number of customers that must support a sequential pattern is low. Scale-up experiments show that both AprioriSome and AprioriAll scale linearly with the number of customer transactions. They also have excellent scale-up properties with respect to the number of transactions per customer and the number of items in a transaction. >

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.

Mining frequent trees is very useful in domains like bioinformatics, web mining, mining semistructured data, and so on. We formulate the problem of mining (embedded) subtrees in a forest of rooted, labeled, and ordered trees. We present TREEMINER, a novel algorithm to discover all frequent subtrees in a forest, using a new data structure called scope-list. We contrast TREEMINER with a pattern matching tree mining algorithm (PATTERNMATCHER). We conduct detailed experiments to test the performance and scalability of these methods. We find that TREEMINER outperforms the pattern matching approach by a factor of 4 to 20, and has good scaleup properties. We also present an application of tree mining to analyze real web logs for usage patterns.

In this paper, we consider the problem of discovering interesting substructures from a large collection of semi-structured data in the framework of optimized pattern discovery. We model semi-structured data and patterns with labeled ordered trees, and present an efficient algorithm that discovers the best labeled ordered trees that optimize a given statistical measure, such as the information entropy and the classification accuracy, in a collection of semi-structured data. We give theoretical analyses of the computational complexity of the algorithm for patterns with bounded and unbounded size. Experiments show that the algorithm performs well and discovered interesting patterns on real datasets.