Self-supervised learning (SSL) is an emerging paradigm that exploits supervisory signals generated from the data itself, and many recent studies have leveraged SSL to conduct graph anomaly detection. However, we empirically found that three important factors can substantially impact detection performance across datasets: (1) the specific SSL strategy employed; (2) the tuning of the strategy’s hyperparameters; and (3) the allocation of combination weights when using multiple strategies. Most SSL-based graph anomaly detection methods circumvent these issues by arbitrarily or selectively (i.e., guided by label information) choosing SSL strategies, hyperparameter settings, and combination weights. While an arbitrary choice may lead to subpar performance, using label information in an unsupervised setting is label information leakage and leads to severe overestimation of a method’s performance. Leakage has been criticized as 'one of the top ten data mining mistakes', yet many recent studies on SSL-based graph anomaly detection have been using label information to select hyperparameters. To mitigate this issue, we propose to use an internal evaluation strategy (with theoretical analysis) to select hyperparameters in SSL for unsupervised anomaly detection. We perform extensive experiments using 10 recent SSL-based graph anomaly detection algorithms on various benchmark datasets, demonstrating both the prior issues with hyperparameter selection and the effectiveness of our proposed strategy.

Discovering subgroups with the maximum average treatment effect is crucial for targeted decision making in domains such as precision medicine, public policy, and education. While most prior work is formulated in the potential‑outcome framework, the corresponding structural causal model (SCM) for this task has been largely overlooked. In practice, two approaches dominate. The first estimates pointwise conditional treatment effects and then fits a tree on those estimates, effectively turning subgroup estimation into the harder problem of accurate pointwise estimation. The second constructs decision trees or rule sets with ad‑hoc 'causal' heuristics, typically without rigorous justification for why a given heuristic may be used or whether such heuristics are necessary at all. We address these issues by studying the problem directly under the SCM framework. Under the assumption of a partition-based model, we show that optimal subgroup discovery reduces to recovering the data-generating models and hence a standard supervised learning problem (regression or classification). This allows us to adopt any partition-based methods to learn the subgroup from data. We instantiate the approach with CART, arguably one of the most widely used tree-based method, to learn the subgroup with maximum treatment effect. Finally, on a large collection of synthetic and semi‑synthetic datasets, we compare our method against a wide range of baselines and find that our approach, which avoids such causal heuristics, more accurately identifies subgroups with maximum treatment effect.

Abstract Event logs are widely used to record the status of high-tech systems, making log anomaly detection important for monitoring those systems. Most existing log anomaly detection methods take a log event count matrix or log event sequences as input, exploiting quantitative and/or sequential relationships between log events to detect anomalies. However, only considering quantitative or sequential relationships may result in low detection accuracy. To alleviate this problem, we propose a graph-based method for unsupervised log anomaly detection, dubbed Logs2Graphs , which first converts event logs into attributed, directed, and weighted graphs, and then leverages graph neural networks to perform graph-level anomaly detection. Specifically, we introduce One-Class Digraph Inception Convolutional Networks, abbreviated as OCDiGCN, a novel graph neural network model for detecting graph-level anomalies in a collection of attributed, directed, and weighted graphs. By integrating graph representation and anomaly detection, OCDiGCN learns a specialized representation that leads to high detection accuracy. Crucially, we furnish a concise set of nodes pivotal in OCDiGCN’s prediction as explanations for each detected anomaly, offering valuable insights for subsequent root cause analysis. Experiments on five benchmark datasets show that Logs2Graphs exhibits comparable or superior performance when compared to state-of-the-art log anomaly detection methods.

OBJECTIVE: Estimating readmission risk for intensive care unit (ICU) patients is critical for clinicians to optimize resource allocation and prevent premature discharges. Machine learning models currently applied to this task either lack interpretability or cannot identify patient subgroups with distinctive readmission risks and characteristics. We addressed this gap by introducing a cutting-edge rule-based model, namely truly unordered rule sets (TURS), to reveal heterogeneous readmission risks and subgroup-level patient characteristics. MATERIALS AND METHODS: We trained TURS on all ICU admissions from January 2011 to January 2020 at Leiden University Medical Center. For each subgroup, patient characteristics and the influence of feature variables on readmission risk were analyzed. RESULTS: TURS identified subgroups with heterogeneous feature distributions and feature importance, providing actionable insights for ICU discharge planning. Its predictive performance (area under the receiver operating characteristic curve [ROC-AUC] 70.5%) and model complexity (5 rules, average length 2) surpassed other rule-based models. DISCUSSION: Subgroup analysis highlighted the heterogeneity of patients. First, we compared the conditional probability distribution of each feature variable, conditioned on the fact that a patient was in a certain subgroup, with its unconditional distribution. We identified features deviating from the unconditional distribution, illustrating unique subgroup-specific implications. Furthermore, we demonstrated that features with the highest impact on the readmission risk were distinctive for each subgroup. CONCLUSION: The TURS model provided a concise summary of patient subgroups, aiding ICU discharge decisions and advancing knowledge discovery in the ICU.

We introduce Time-Conditioned Contraction Matching (TCCM), a novel method for semi-supervised anomaly detection in tabular data. TCCM is inspired by flow matching, a recent generative modeling framework that learns velocity fields between probability distributions and has shown strong performance compared to diffusion models and generative adversarial networks. Instead of directly applying flow matching as originally formulated, TCCM builds on its core idea—learning velocity fields between distributions—but simplifies the framework by predicting a time-conditioned contraction vector toward a fixed target (the origin) at each sampled time step. This design offers three key advantages: (1) a lightweight and scalable training objective that removes the need for solving ordinary differential equations during training and inference; (2) an efficient scoring strategy called one time-step deviation, which quantifies deviation from expected contraction behavior in a single forward pass, addressing the inference bottleneck of existing continuous-time models such as DTE (a diffusion-based model with leading anomaly detection accuracy but heavy inference cost); and (3) explainability and provable robustness, as the learned velocity field operates directly in input space, making the anomaly score inherently feature-wise attributable; moreover, the score function is Lipschitz-continuous with respect to the input, providing theoretical guarantees under small perturbations. Extensive experiments on the ADBench benchmark show that TCCM strikes a favorable balance between detection accuracy and inference cost, outperforming state-of-the-art methods—especially on high-dimensional and large-scale datasets. The source code is provided at https://github.com/ZhongLIFR/TCCM-NIPS.

Antibiotic resistance is one of the major global threats to human health and occurs when antibiotics lose their ability to combat bacterial infections. In this problem, a clinical decision support system could use phenotypes in order to alert clinicians of the emergence of patterns of antibiotic resistance in patients. Patient phenotyping is the task of finding a set of patient characteristics related to a specific medical problem such as the one described in this work. However, a single explanation of a medical phenomenon might be useless in the eyes of a clinical expert and be discarded. The discovery of multiple patient phenotypes for the same medical phenomenon would be useful in such cases. Therefore, in this work, we define the problem of mining diverse top-k phenotypes and propose the EDSLM algorithm, which is based on the Subgroup Discovery technique, the subgroup list model, and the Minimum Description Length principle. Our proposal provides clinicians with a method with which to obtain multiple and diverse phenotypes of a set of patients. We show a real use case of phenotyping in antimicrobial resistance using the well-known MIMIC-III dataset.

Abstract Self-supervised learning (SSL) is an emerging paradigm that exploits supervisory signals generated from the data itself, and many recent studies have leveraged SSL to conduct graph anomaly detection. However, we empirically found that three important factors can substantially impact detection performance across datasets: (1) the specific SSL strategy employed; (2) the tuning of the strategy’s hyperparameters; and (3) the allocation of combination weights when using multiple strategies. Most SSL-based graph anomaly detection methods circumvent these issues by arbitrarily or selectively (i.e., guided by label information) choosing SSL strategies, hyperparameter settings, and combination weights. While an arbitrary choice may lead to subpar performance, using label information in an unsupervised setting is label information leakage and leads to severe overestimation of a method’s performance. Leakage has been criticized as “one of the top ten data mining mistakes", yet many recent studies on SSL-based graph anomaly detection have been using label information to select hyperparameters. To mitigate this issue, we propose to use an internal evaluation strategy (with theoretical analysis) to select hyperparameters in SSL for unsupervised anomaly detection. We perform extensive experiments using 10 recent SSL-based graph anomaly detection algorithms on various benchmark datasets, demonstrating both the prior issues with hyperparameter selection and the effectiveness of our proposed strategy.

Conditional density estimation (CDE) goes beyond regression by modeling the full conditional distribution, providing a richer understanding of the data than just the conditional mean in regression. This makes CDE particularly useful in critical application domains. However, interpretable CDE methods are understudied. Current methods typically employ kernel-based approaches, using kernel functions directly for kernel density estimation or as basis functions in linear models. In contrast, despite their conceptual simplicity and visualization suitability, tree-based methods---which are arguably more comprehensible---have been largely overlooked for CDE tasks. Thus, we propose the Conditional Density Tree (CDTree), a fully non-parametric model consisting of a decision tree in which each leaf is formed by a histogram model. Specifically, we formalize the problem of learning a CDTree using the minimum description length (MDL) principle, which eliminates the need for tuning the hyperparameter for regularization. Next, we propose an iterative algorithm that, although greedily, searches the optimal histogram for every possible node split. Our experiments demonstrate that, in comparison to existing interpretable CDE methods, CDTrees are both more accurate (as measured by the log-loss) and more robust against irrelevant features. Further, our approach leads to smaller tree sizes than existing tree-based models, which benefits interpretability.

In the past two decades, most research on anomaly detection has focused on improving the accuracy of the detection, while largely ignoring the explainability of the corresponding methods and thus leaving the explanation of outcomes to practitioners. As anomaly detection algorithms are increasingly used in safety-critical domains, providing explanations for the high-stakes decisions made in those domains has become an ethical and regulatory requirement. Therefore, this work provides a comprehensive and structured survey on state-of-the-art explainable anomaly detection techniques. We propose a taxonomy based on the main aspects that characterise each explainable anomaly detection technique, aiming to help practitioners and researchers find the explainable anomaly detection method that best suits their needs.

Existing graph level anomaly detection methods are predominantly unsupervised due to high costs for obtaining labels, yielding sub-optimal detection accuracy when compared to supervised methods. Moreover, they heavily rely on the assumption that the training data exclusively consists of normal graphs. Hence, even the presence of a few anomalous graphs can lead to substantial performance degradation. To alleviate these problems, we propose across-domain graph level anomaly detection method, aiming to identify anomalous graphs from a set of unlabeled graphs (target domain) by using easily accessible normal graphs from a different but related domain (source domain). Our method consists of four components: a feature extractor that preserves semantic and topological information of individual graphs while incorporating the distance between different graphs; an adversarial domain classifier to make graph level representations domain-invariant; a one-class classifier to exploit label information in the source domain; and a class aligner to align classes from both domains based on pseudolabels. Experiments on seven benchmark datasets show that the proposed method largely outperforms state-of-the-art methods.

Abstract Traditional anomaly detection methods aim to identify objects that deviate from most other objects by treating all features equally. In contrast, contextual anomaly detection methods aim to detect objects that deviate from other objects within a context of similar objects by dividing the features into contextual features and behavioral features. In this paper, we develop connections between dependency-based traditional anomaly detection methods and contextual anomaly detection methods. Based on resulting insights, we propose a novel approach to inherently interpretable contextual anomaly detection that uses Quantile Regression Forests to model dependencies between features. Extensive experiments on various synthetic and real-world datasets demonstrate that our method outperforms state-of-the-art anomaly detection methods in identifying contextual anomalies in terms of accuracy and interpretability.

Abstract Unsupervised discretization is a crucial step in many knowledge discovery tasks. The state-of-the-art method for one-dimensional data infers locally adaptive histograms using the minimum description length (MDL) principle, but the multi-dimensional case is far less studied: current methods consider the dimensions one at a time (if not independently), which result in discretizations based on rectangular cells of adaptive size. Unfortunately, this approach is unable to adequately characterize dependencies among dimensions and/or results in discretizations consisting of more cells (or bins) than is desirable. To address this problem, we propose an expressive model class that allows for far more flexible partitions of two-dimensional data. We extend the state of the art for the one-dimensional case to obtain a model selection problem based on the normalized maximum likelihood, a form of refined MDL. As the flexibility of our model class comes at the cost of a vast search space, we introduce a heuristic algorithm, named PALM, whichpartitions each dimensionalternately and thenmerges neighboring regions, all using the MDL principle. Experiments on synthetic data show that PALM (1) accurately reveals ground truth partitions that are within the model class (i.e., the search space), given a large enough sample size; (2) approximates well a wide range of partitions outside the model class; (3) converges, in contrast to the state-of-the-art multivariate discretization method IPD. Finally, we apply our algorithm to three spatial datasets, and we demonstrate that, compared to kernel density estimation (KDE), our algorithm not only reveals more detailed density changes, but also fits unseen data better, as measured by the log-likelihood.

Abstract We introduce the problem ofrobust subgroup discovery, i.e., finding a set of interpretable descriptions of subsets that 1) stand out with respect to one or more target attributes, 2) are statistically robust, and 3) non-redundant. Many attempts have been made to mine eitherlocallyrobust subgroups or to tackle the pattern explosion, but we are the first to address both challenges at the same time from aglobalmodelling perspective. First, we formulate the broad model class of subgroup lists, i.e., ordered sets of subgroups, for univariate and multivariate targets that can consist of nominal or numeric variables, including traditional top-1 subgroup discovery in its definition. This novel model class allows us to formalise the problem of optimal robust subgroup discovery using the Minimum Description Length (MDL) principle, where we resort to optimal Normalised Maximum Likelihood and Bayesian encodings for nominal and numeric targets, respectively. Second, finding optimal subgroup lists is NP-hard. Therefore, we propose SSD++, a greedy heuristic that finds good subgroup lists and guarantees that the most significant subgroup found according to the MDL criterion is added in each iteration. In fact, the greedy gain is shown to be equivalent to a Bayesian one-sample proportion, multinomial, or t-test between the subgroup and dataset marginal target distributions plus a multiple hypothesis testing penalty. Furthermore, we empirically show on 54 datasets that SSD++ outperforms previous subgroup discovery methods in terms of quality, generalisation on unseen data, and subgroup list size.

OBJECTIVE: Privacy is a concern whenever individual patient health data is exchanged for scientific research. We propose using mixed sum-product networks (MSPNs) as private representations of data and take samples from the network to generate synthetic data that can be shared for subsequent statistical analysis. This anonymization method was evaluated with respect to privacy and information loss. MATERIALS AND METHODS: Using a simulation study, information loss was quantified by assessing whether synthetic data could reproduce regression parameters obtained from the original data. Predictors variable types were varied between continuous, count, categorical, and mixed discrete-continuous. Additionally, we measured whether the MSPN approach successfully anonymizes the data by removing associations between background and sensitive information for these datasets. RESULTS: The synthetic data generated with MSPNs yielded regression results highly similar to those generated with original data, differing less than 5% in most simulation scenarios. Standard errors increased compared to the original data. Particularly for smaller datasets (1000 records), this resulted in a discrepancy between the estimated and empirical standard errors. Sensitive values could no longer be inferred from background information for at least 99% of tested individuals. DISCUSSION: The proposed anonymization approach yields very promising results. Further research is required to evaluate its performance with other types of data and analyses, and to predict how user parameter choices affect a bias-privacy trade-off. CONCLUSION: Generating synthetic data from MSPNs is a promising, easy-to-use approach for anonymization of sensitive individual health data that yields informative and private data.

information for discrete-continuous mixtures using multi-dimensional adaptive histograms.

Abstract Many real-world phenomena can be represented as dynamic graphs, i.e., networks that change over time. The problem of dynamic graph summarization, i.e., to succinctly describe the evolution of a dynamic graph, has been widely studied. Existing methods typically use objective measures to find fixed structures such as cliques, stars, and cores. Most of the methods, however, do not consider the problem of online summarization, where the summary is incrementally conveyed to the analyst as the graph evolves, and (thus) do not take into account the knowledge of the analyst at a specific moment in time. We address this gap in the literature through a novel, generic framework for subjective interestingness for sequential data. Specifically, we iteratively identify atomic changes, called ‘actions’, that provide most information relative to the current knowledge of the analyst. For this, we introduce a novel information gain measure, which is motivated by the minimum description length (MDL) principle. With this measure, our approach discovers compact summaries without having to decide on the number of patterns. As such, we are the first to combine approaches for data mining based on subjective interestingness (using the maximum entropy principle) with pattern-based summarization (using the MDL principle). We instantiate this framework for dynamic graphs and dense subgraph patterns, and present DSSG, a heuristic algorithm for the online summarization of dynamic graphs by means of informative actions, each of which represents an interpretable change to the connectivity structure of the graph. The experiments on real-world data demonstrate that our approach effectively discovers informative summaries. We conclude with a case study on data from an airline network to show its potential for real-world applications.

We introduce geometric pattern mining, the problem of finding recurring local structure in discrete, geometric matrices. It differs from existing pattern mining problems by identifying complex spatial relations between elements, resulting in arbitrarily shaped patterns. After we formalise this new type of pattern mining, we propose an approach to selecting a set of patterns using the Minimum Description Length principle. We demonstrate the potential of our approach by introducing Vouw, a heuristic algorithm for mining exact geometric patterns. We show that Vouw delivers high-quality results with a synthetic benchmark.

Signature patterns have been introduced to model repetitive behavior, e.g., of customers repeatedly buying the same set of products in consecutive time periods. A disadvantage of existing approaches to signature discovery, however, is that the required number of occurrences of a signature needs to be manually chosen. To address this limitation, we formalize the problem of selecting the best signature using the minimum description length (MDL) principle. To this end, we propose an encoding for signature models and for any data stream given such a signature model. As finding the MDL-optimal solution is unfeasible, we propose a novel algorithm that is an instance of widening , i.e., a diversified beam search that heuristically explores promising parts of the search space. Finally, we demonstrate the effectiveness of the problem formalization and the algorithm on a real-world retail dataset, and show that our approach yields relevant signatures.

No abstract available.

Rank data, in which each row is a complete or partial ranking of available items (columns), is ubiquitous. Among others, it can be used to represent preferences of users, levels of gene expression, and outcomes of sports events. It can have many types of patterns, among which consistent rankings of a subset of the items in multiple rows, and multiple rows that rank the same subset of the items highly. In this article, we show that the problems of finding such patterns can be formulated within a single generic framework that is based on the concept of semiring matrix factorization. In this framework, we employ the max-product semiring rather than the plus-product semiring common in traditional linear algebra. We apply this semiring matrix factorization framework on two tasks: sparse rank matrix factorization and rank matrix tiling. Experiments on both synthetic and real world datasets show that the framework is capable of discovering different types of structure as well as obtaining high quality solutions.

Outlier detection in high-dimensional data is a challenging yet important task, as it has applications in, e.g., fraud detection and quality control. State-of-the-art density-based algorithms perform well because they 1) take the local neighbourhoods of data points into account and 2) consider feature subspaces. In highly complex and high-dimensional data, however, existing methods are likely to overlook important outliers because they do not explicitly take into account that the data is often a mixture distribution of multiple components. We therefore introduce GLOSS, an algorithm that performs local subspace outlier detection using global neighbourhoods. Experiments on synthetic data demonstrate that GLOSS more accurately detects local outliers in mixed data than its competitors. Moreover, experiments on real-world data show that our approach identifies relevant outliers overlooked by existing methods, confirming that one should keep an eye on the global perspective even when doing local outlier detection.

Two-view datasets are datasets whose attributes are naturally split into two sets, each providing a different view on the same set of objects. We introduce1 the exploratory data mining task of finding small and non-redundant sets of associations that describe how the two views are related. To achieve this, we propose a novel approach in which sets of rules are used to translate one view to the other and vice versa. Our models, dubbed translation tables, contain both unidirectional and bidirectional rules that span both views and provide lossless translation from either of the views to the opposite view. To be able to evaluate different translation tables and perform model selection, we present a score based on the Minimum Description Length (MDL) principle. Next, we introduce three TRANSLATOR algorithms to find good models according to this score. The first algorithm is parameter-free and iteratively adds the rule that improves compression most. The other two algorithms use heuristics to achieve better trade-offs between runtime and compression. The empirical evaluation on real-world data demonstrates that only modest numbers of associations are needed to characterize the two-view structure present in the data, while the obtained translation rules are easily interpretable and provide relevant insight into the data.

MOTIVATION: Subtyping cancer is key to an improved and more personalized prognosis/treatment. The increasing availability of tumor related molecular data provides the opportunity to identify molecular subtypes in a data-driven way. Molecular subtypes are defined as groups of samples that have a similar molecular mechanism at the origin of the carcinogenesis. The molecular mechanisms are reflected by subtype-specific mutational and expression features. Data-driven subtyping is a complex problem as subtyping and identifying the molecular mechanisms that drive carcinogenesis are confounded problems. Many current integrative subtyping methods use global mutational and/or expression tumor profiles to group tumor samples in subtypes but do not explicitly extract the subtype-specific features. We therefore present a method that solves both tasks of subtyping and identification of subtype-specific features simultaneously. Hereto our method integrates` mutational and expression data while taking into account the clonal properties of carcinogenesis. Key to our method is a formalization of the problem as a rank matrix factorization of ranked data that approaches the subtyping problem as multi-view bi-clustering RESULTS: We introduce a novel integrative framework to identify subtypes by combining mutational and expression features. The incomparable measurement data is integrated by transformation into ranked data and subtypes are defined as multi-view bi-clusters We formalize the model using rank matrix factorization, resulting in the SRF algorithm. Experiments on simulated data and the TCGA breast cancer data demonstrate that SRF is able to capture subtle differences that existing methods may miss. AVAILABILITY AND IMPLEMENTATION: The implementation is available at: https://github.com/rankmatrixfactorisation/SRF CONTACT: [email protected], [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The utility of a dense subgraph in gaining a better understanding of a graph has been formalised in numerous ways, each striking a different balance between approximating actual interestingness and computational efficiency. A difficulty in making this trade-off is that, while computational cost of an algorithm is relatively well-defined, a pattern’s interestingness is fundamentally subjective. This means that this latter aspect is often treated only informally or neglected, and instead some form of density is used as a proxy. We resolve this difficulty by formalising what makes a dense subgraph pattern interesting to a given user. Unsurprisingly, the resulting measure is dependent on the prior beliefs of the user about the graph. For concreteness, in this paper we consider two cases: one case where the user only has a belief about the overall density of the graph, and another case where the user has prior beliefs about the degrees of the vertices. Furthermore, we illustrate how the resulting interestingness measure is different from previous proposals. We also propose effective exact and approximate algorithms for mining the most interesting dense subgraph according to the proposed measure. Usefully, the proposed interestingness measure and approach lend themselves well to iterative dense subgraph discovery. Contrary to most existing approaches, our method naturally allows subsequently found patterns to be overlapping. The empirical evaluation highlights the properties of the new interestingness measure given different prior belief sets, and our approach’s ability to find interesting subgraphs that other methods are unable to find.

Influence maximization aims to find a set of persons in a social network that can be used as seeds for a viral marketing campaign, such that the expected spread of influence is maximized. Standard approaches to this problem produce a single seed set that either maximizes influence, or the “bang for the buck” if the vertices are associated with a cost. In this paper we consider the problem of finding the cost-influence skyline, i.e., the collection of all seed sets that are Pareto optimal w.r.t. seeding cost and expected influence. Computing the cost-influence skyline has a number of advantages over finding a single solution only. First, it provides a better understanding of the trade-off between cost and influence, which enables the user to make an informed choice regarding the budget. Second, by computing the cost-influence skyline we obtain the optimal seed set for any given seeding budget, not only the one that corresponds to singleton solutions found by existing algorithms. In practice, the problem is to discover the skyline w.r.t. two functions spanned by all subsets of size k of a set of vertices. Due to the extremely large number of such subsets, this is a very hard problem. We present an efficient heuristic algorithm for computing the skyline when one of the functions is linear (e.g., the seeding cost) and the other submodular (e.g., expected influence). The experiments show that the cost-influence skyline can be computed in reasonable time for networks with up to a million vertices.

Two-view datasets are datasets whose attributes are naturally split into two sets, each providing a different view on the same set of objects. We introduce the task of finding small and non-redundant sets of associations that describe how the two views are related. To achieve this, we propose a novel approach in which sets of rules are used to translate one view to the other and vice versa. Our models, dubbed translation tables, contain both unidirectional and bidirectional rules that span both views and provide lossless translation from either of the views to the opposite view. To be able to evaluate different translation tables and perform model selection, we present a score based on the Minimum Description Length (MDL) principle. Next, we introduce three TRANSLATOR algorithms to find good models according to this score. The first algorithm is parameter-free and iteratively adds the rule that improves compression most. The other two algorithms use heuristics to achieve better trade-offs between runtime and compression. The empirical evaluation on real-world data demonstrates that only modest numbers of associations are needed to characterize the two-view structure present in the data, while the obtained translation rules are easily interpretable and provide insight into the data.

Traditional approaches to community detection, as studied by physicists, sociologists, and more recently computer scientists, aim at simply partitioning the social network graph. However, with the advent of online social networking sites, richer data has become available: beyond the link information, each user in the network is annotated with additional information, for example, demographics, shopping behavior, or interests. In this context, it is therefore important to develop mining methods which can take advantage of all available information. In the case of community detection, this means finding good communities (a set of nodes cohesive in the social graph) which are associated with good descriptions in terms of user information (node attributes). Having good descriptions associated to our models make them understandable by domain experts and thus more useful in real-world applications. Another requirement dictated by real-world applications, is to develop methods that can use, when available, any domain-specific background knowledge. In the case of community detection the background knowledge could be a vague description of the communities sought in a specific application, or some prototypical nodes (e.g., good customers in the past), that represent what the analyst is looking for (a community of similar users). Towards this goal, in this article, we define and study the problem of finding a diverse set of cohesive communities with concise descriptions. We propose an effective algorithm that alternates between two phases: a hill-climbing phase producing (possibly overlapping) communities, and a description induction phase which uses techniques from supervised pattern set mining. Our framework has the nice feature of being able to build well-described cohesive communities starting from any given description or seed set of nodes, which makes it very flexible and easily applicable in real-world applications. Our experimental evaluation confirms that the proposed method discovers cohesive communities with concise descriptions in realistic and large online social networks such as D elicious , F lickr , and L ast FM.

Pattern mining provides useful tools for exploratory data analysis. Numerous efficient algorithms exist that are able to discover various types of patterns in large datasets. However, the problem of identifying patterns that are genuinely interesting to a particular user remains challenging. Current approaches generally require considerable data mining expertise or effort and hence cannot be used by typical domain experts. We show that it is possible to resolve this issue by interactive learning of user-specific pattern ranking functions, where a user ranks small sets of patterns and a general ranking function is inferred from this feedback by preference learning techniques. We present a general framework for learning pattern ranking functions and propose a number of active learning heuristics that aim at minimizing the required user effort. In particular we focus on Subgroup Discovery, a specific pattern mining task. We evaluate the capacity of the algorithm to learn a ranking of a subgroup set defined by a complex quality measure, given only reasonably small sample rankings. Experiments demonstrate that preference learning has the capacity to learn accurate rankings and that active learning heuristics help reduce the required user effort. Moreover, using learned ranking functions as search heuristics allows discovering subgroups of substantially higher quality than those in the given set. This shows that active preference learning is potentially an important building block of interactive pattern mining systems.

Large data is challenging for most existing discovery algorithms, for several reasons. First of all, such data leads to enormous hypothesis spaces, making exhaustive search infeasible. Second, many variants of essentially the same pattern exist, due to (numeric) attributes of high cardinality, correlated attributes, and so on. This causes top- k mining algorithms to return highly redundant result sets, while ignoring many potentially interesting results. These problems are particularly apparent with subgroup discovery (SD) and its generalisation, exceptional model mining. To address this, we introduce subgroup set discovery : one should not consider individual subgroups, but sets of subgroups. We consider three degrees of redundancy, and propose corresponding heuristic selection strategies in order to eliminate redundancy. By incorporating these (generic) subgroup selection methods in a beam search, the aim is to improve the balance between exploration and exploitation. The proposed algorithm, dubbed DSSD for diverse subgroup set discovery, is experimentally evaluated and compared to existing approaches. For this, a variety of target types with corresponding datasets and quality measures is used. The subgroup sets that are discovered by the competing methods are evaluated primarily on the following three criteria: (1) diversity in the subgroup covers (exploration), (2) the maximum quality found (exploitation), and (3) runtime. The results show that DSSD outperforms each traditional SD method on all or a (non-empty) subset of these criteria, depending on the specific setting. The more complex the task, the larger the benefit of using our diverse heuristic search turns out to be.

Motivated by sensor networks, mobility data, biology and life sciences, the area of mining uncertain data has recently received a great deal of attention. While various papers have focused on efficiently mining frequent patterns from uncertain data, the problem of discovering a small set of interesting patterns that provide an accurate and condensed description of a probabilistic database is still unexplored. In this paper we study the problem of discovering characteristic patterns in uncertain data through information theoretic lenses. Adopting the possible worlds interpretation of probabilistic data and a compression scheme based on the MDL principle, we formalize the problem of mining patterns that compress the database well in expectation. Despite its huge search space, we show that this problem can be accurately approximated. In particular, we devise a sequence of three methods where each new method improves the memory requirements orders of magnitudes compared to its predecessor, while giving up only a little in terms of approximation accuracy. We empirically compare our methods on both synthetic data and real data from life science. Results show that from a probabilistic matrix with more than one million rows and columns, we can extract a small set of meaningful patterns that accurately characterize the data distribution of any probable world.

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.

Whenever a dataset has multiple discrete target variables, we want our algorithms to consider not only the variables themselves, but also the interdependencies between them. We propose to use these interdependencies to quantify the quality of subgroups, by integrating Bayesian networks with the Exceptional Model Mining framework. Within this framework, candidate subgroups are generated. For each candidate, we fit a Bayesian network on the target variables. Then we compare the network's structure to the structure of the Bayesian network fitted on the whole dataset. To perform this comparison, we define an edit distance-based distance metric that is appropriate for Bayesian networks. We show interesting subgroups that we experimentally found with our method on datasets from music theory, semantic scene classification, biology and zoogeography.

We introduce a new approach to Exceptional Model Mining. Our algorithm, called EMDM, is an iterative method that alternates between Exception Maximisation and Description Minimisation. As a result, it finds maximally exceptional models with minimal descriptions. Exceptional Model Mining was recently introduced by Leman et al. (Exceptional model mining 1–16, 2008) as a generalisation of Subgroup Discovery. Instead of considering a single target attribute, it allows for multiple ‘model’ attributes on which models are fitted. If the model for a subgroup is substantially different from the model for the complete database, it is regarded as an exceptional model. To measure exceptionality, we propose two information-theoretic measures. One is based on the Kullback–Leibler divergence, the other on Krimp . We show how compression can be used for exception maximisation with these measures, and how classification can be used for description minimisation. Experiments show that our approach efficiently identifies subgroups that are both exceptional and interesting.

On photo sharing websites like Flickr and Zooomr, users are offered the possibility to assign tags to their uploaded pictures. Using these tags to find interesting groups of semantically related pictures in the result set of a given query is a problem with obvious applications. We analyse this problem from a Minimum Description Length (MDL) perspective and develop an algorithm that finds the most interesting groups. The method is based on Krimp, which finds small sets of patterns that characterise the data using compression. These patterns are sets of tags, often assigned together to photos. The better a database compresses, the more structure it contains and thus the more homogeneous it is. Following this observation we devise a compression-based measure. Our experiments on Flickr data show that the most interesting and homogeneous groups are found. We show extensive examples and compare to clusterings on the Flickr website.

Most, if not all, databases are mixtures of samples from different distributions. Transactional data is no exception. For the prototypical example, supermarket basket analysis, one also expects a mixture of different buying patterns. Households of retired people buy different collections of items than households with young children. Models that take such underlying distributions into account are in general superior to those that do not. In this paper we introduce two MDL-based algorithms that follow orthogonal approaches to identify the components in a transaction database. The first follows a model-based approach, while the second is data-driven. Both are parameter-free: the number of components and the components themselves are chosen such that the combined complexity of data and models is minimised. Further, neither prior knowledge on the distributions nor a distance metric on the data is required. Experiments with both methods show that highly characteristic components are identified.

Many databases will not or can not be disclosed without strong guarantees that no sensitive information can be extracted. To address this concern several data perturbation techniques have been proposed. However, it has been shown that either sensitive information can still be extracted from the perturbed data with little prior knowledge, or that many patterns are lost. In this paper we show that generating new data is an inherently safer alternative. We present a data generator based on the models obtained by the MDL-based KRIMP (Siebes et al., 2006) algorithm. These are accurate representations of the data distributions and can thus be used to generate data with the same characteristics as the original data. Experimental results show a very large pattern-similarity between the generated and the original data, ensuring that viable conclusions can be drawn from the anonymised data. Furthermore, anonymity is guaranteed for suited databases and the quality-privacy trade-off can be balanced explicitly.

Characterising the differences between two databases is an often occurring problem in Data Mining. Detection of change over time is a prime example, comparing databases from two branches is another one. The key problem is to discover the patterns that describe the difference. Emerging patterns provide only a partial answer to this question.

One of the major problems in frequent item set mining is the explosion of the number of results: it is difficult to find the most interesting frequent item sets. The cause of this explosion is that large sets of frequent item sets describe essentially the same set of transactions. In this paper we approach this problem using the MDL principle: the best set of frequent item sets is that set that compresses the database best. We introduce four heuristic algorithms for this task, and the experiments show that these algorithms give a dramatic reduction in the number of frequent item sets. Moreover, we show how our approach can be used to determine the best value for the min-sup threshold.