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Dimensionality reduction and manifold learning methods such as t-distributed stochastic neighbor embedding (t-SNE) are frequently used to map high-dimensional data into a two-dimensional space to visualize and explore that data. Going beyond the specifics of t-SNE, there are two substantial limitations of any such approach: (1) not all information can be captured in a single two-dimensional embedding, and (2) to well-informed users, the salient structure of such an embedding is often already known, preventing that any real new insights can be obtained. Currently, it is not known how to extract the remaining information in a similarly effective manner. We introduce conditional t-SNE (ct-SNE), a generalization of t-SNE that discounts prior information in the form of labels. This enables obtaining more informative and more relevant embeddings. To achieve this, we propose a conditioned version of the t-SNE objective, obtaining an elegant method with a single integrated objective. We show how to efficiently optimize the objective and study the effects of the extra parameter that ct-SNE has over t-SNE. Qualitative and quantitative empirical results on synthetic and real data show ct-SNE is scalable, effective, and achieves its goal: it allows complementary structure to be captured in the embedding and provided new insights into real data.

The connectivity structure of graphs is typically related to the attributes of the vertices. In social networks for example, the probability of a friendship between any pair of people depends on a range of attributes, such as their age, residence location, workplace, and hobbies. The high-level structure of a graph can thus possibly be described well by means of patterns of the form ‘the subgroup of all individuals with certain properties X are often (or rarely) friends with individuals in another subgroup defined by properties Y’, ideally relative to their expected connectivity. Such rules present potentially actionable and generalizable insight into the graph. Prior work has already considered the search for dense subgraphs (‘communities’) with homogeneous attributes. The first contribution in this paper is to generalize this type of pattern to densities between apair of subgroups, as well as betweenall pairs from a set of subgroups that partition the vertices. Second, we develop a novel information-theoretic approach for quantifying the subjective interestingness of such patterns, by contrasting them with prior information an analyst may have about the graph’s connectivity. We demonstrate empirically that in the special case of dense subgraphs, this approach yields results that are superior to the state-of-the-art. Finally, we propose algorithms for efficiently finding interesting patterns of these different types.

The democratization of AI tools for content generation, combined with unrestricted access to mass media for all (e.g. through microblogging and social media), makes it increasingly hard for people to distinguish fact from fiction. This raises the question of how individual opinions evolve in such a networked environment without grounding in a known reality. The dominant approach to studying this problem uses simple models from the social sciences on how individuals change their opinions when exposed to their social neighborhood, and applies them on large social networks. We propose a novel model that incorporates two known social phenomena: (i)Biased Assimilation: the tendency of individuals to adopt other opinions if they are similar to their own; (ii)Backfire Effect: the fact that an opposite opinion may further entrench people in their stances, making their opinions more extreme instead of moderating them. To the best of our knowledge, this is the first DeGroot-type opinion formation model that captures the Backfire Effect. A thorough theoretical and empirical analysis of the proposed model reveals intuitive conditions for polarization and consensus to exist, as well as the properties of the resulting opinions.

This book contains a selection of the best papers of the 32nd Benelux Conference on Artificial Intelligence, BNAIC/Benelearn 2020, held in Leiden, The Netherlands, in November 2020. Due to the COVID-19 pandemic the conference was held online. The 12 papers presented in this volume were carefully reviewed and selected from 41 regular submissions. They address various aspects of artificial intelligence such as natural language processing, agent technology, game theory, problem solving, machine learning, human-agent interaction, AI and education, and data analysis.

In this paper, we explore the rate of language change in the history of English. Our main focus is on detecting periods of accelerated change in Middle English (1150–1500), but we also compare the Middle English data with the Early Modern period (1500–1700) in order to establish a longer diachrony for the pace at which English has changed over time. Our study is based on a meta-analysis of existing corpus research, which is made available through a new linguistic resource, the Language Change Database (LCD). By aggregating the rates of 44 individual changes, we provide a critical assessment of how well the theory of punctuated equilibria (Dixon, Robert M. W. 1997. The rise and fall of languages. Cambridge: Cambridge University Press) fits with our results. More specifically, by comparing the rate of language change with major language-external events, such as the Norman Conquest and the Black Death, we provide the first corpus-based meta-analysis of whether these events, which had significant societal consequences, also had an impact on the rate of language change. Our results indicate that major changes in the rate of linguistic change in the late medieval period could indeed be connected to the social and cultural after-effects of the Norman Conquest. We also make a methodological contribution to the field of English historical linguistics: by re-using data from existing research, linguists can start to ask new, fundamental questions about the ways in which language change progresses.

Social networks often provide only a binary perspective on social ties: two individuals are either connected or not. While sometimes external information can be used to infer thestrengthof social ties, access to such information may be restricted or impractical to obtain. Sintos and Tsaparas (KDD 2014) first suggested to infer the strength of social ties from the topology of the network alone, by leveraging theStrong Triadic Closure(STC) property. The STC property states that if personAhas strong social ties with personsBandC,BandCmust be connected to each other as well (whether with a weak or strong tie). They exploited this property to formulate the inference of the strength of social ties as a NP-hard maximization problem, and proposed two approximation algorithms. We refine and improve this line of work, by developing a sequence of linear relaxations of the problem, which can be solved exactly in polynomial time. Usefully, these relaxations infer more fine-grained levels of tie strength (beyond strong and weak), which also allows one to avoid making arbitrary strong/weak strength assignments when the network topology provides inconclusive evidence. Moreover, these relaxations allow us to easily change the objective function to more sensible alternatives, instead of simply maximizing the number of strong edges. An extensive theoretical analysis leads to two efficient algorithmic approaches. Finally, our experimental results elucidate the strengths of the proposed approach, while at the same time questioning the validity of leveraging the STC property for edge strength inference in practice.

Data clustering, local pattern mining, and community detection in graphs are three mature areas of data mining and machine learning. In recent years, attributed subgraph mining has emerged as a new powerful data mining task in the intersection of these areas. Given a graph and a set of attributes for each vertex, attributed subgraph mining aims to find cohesive subgraphs for which (some of) the attribute values have exceptional values. The principled integration of graph and attribute data poses two challenges: (1) the definition of a pattern syntax (the abstract form of patterns) that is intuitive and lends itself to efficient search, and (2) the formalization of the interestingness of such patterns. We propose an integrated solution to both of these challenges. The proposed pattern syntax improves upon prior work in being both highly flexible and intuitive. Plus, we define an effective and principled algorithm to enumerate patterns of this syntax. The proposed approach for quantifying interestingness of these patterns is rooted in information theory, and is able to account for background knowledge on the data. While prior work quantified the interestingness for the cohesion of the subgraph and for the exceptionality of its attributes separately, then combining these in a parameterized trade-off, we instead handle this trade-off implicitly in a principled, parameter-free manner. Empirical results confirm we can efficiently find highly interesting subgraphs.

Many real-world problems can be formalized as predicting links in a partially observed network. Examples include Facebook friendship suggestions, the prediction of protein–protein interactions, and the identification of hidden relationships in a crime network. Several link prediction algorithms, notably those recently introduced using network embedding, are capable of doing this by just relying on the observed part of the network. Often, whether two nodes are linked can be queried, albeit at a substantial cost (e.g., by questionnaires, wet lab experiments, or undercover work). Such additional information can improve the link prediction accuracy, but owing to the cost, the queries must be made with due consideration. Thus, we argue that an active learning approach is of great potential interest and developed ALPINE (Active Link Prediction usIng Network Embedding), a framework that identifies the most useful link status by estimating the improvement in link prediction accuracy to be gained by querying it. We proposed several query strategies for use in combination with ALPINE, inspired by the optimal experimental design and active learning literature. Experimental results on real data not only showed that ALPINE was scalable and boosted link prediction accuracy with far fewer queries, but also shed light on the relative merits of the strategies, providing actionable guidance for practitioners.

Network embedding methods map a network's nodes to vectors in an embedding space, in such a way that these representations are useful for estimating some notion of similarity or proximity between pairs of nodes in the network. The quality of these node representations is then showcased through results of downstream prediction tasks. Commonly used benchmark tasks such as link prediction, however, present complex evaluation pipelines and an abundance of design choices. This, together with a lack of standardized evaluation setups can obscure the real progress in the field. In this paper, we aim to shed light on the state-of-the-art of network embedding methods for link prediction and show, using a consistent evaluation pipeline, that only thin progress has been made over the last years. The newly conducted benchmark that we present here, including 17 embedding methods, also shows that many approaches are outperformed even by simple heuristics. Finally, we argue that standardized evaluation tools can repair this situation and boost future progress in this field.

The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between any pair of people depends on a range of attributes, such as their age, residence location, workplace, and hobbies. The high-level structure of a graph can thus possibly be described well by means of patterns of the form `the subgroup of all individuals with a certain properties X are often (or rarely) friends with individuals in another subgroup defined by properties Y', in comparison to what is expected. Such rules present potentially actionable and generalizable insight into the graph. We present a method that finds node subgroup pairs between which the edge density is interestingly high or low, using an information-theoretic definition of interestingness. Additionally, the interestingness is quantified subjectively, to contrast with prior information an analyst may have about the connectivity. This view immediatly enables iterative mining of such patterns. This is the first method aimed at graph connectivity relations between different subgroups. Our method generalizes prior work on dense subgraphs induced by a subgroup description. Although this setting has been studied already, we demonstrate for this special case considerable practical advantages of our subjective interestingness measure with respect to a wide range of (objective) interestingness measures.

International audience; The local pattern mining literature has long struggled with the so-called pattern explosion problem: the size of the set of patterns found exceeds the size of the original data. This causes computational problems (enumerating a large set of patterns will inevitably take a substantial amount of time) as well as problems for interpretation and usabil-ity (trawling through a large set of patterns is often impractical). Two complementary research lines aim to address this problem. The first aims to develop better measures of interestingness, in order to reduce the number of uninteresting patterns that are returned [6, 10]. The second aims to avoid an exhaustive enumeration of all 'interesting' patterns (where interestingness is quantified in a more traditional way, e.g. frequency), by directly sampling from this set in a way that more 'interest-ing' patterns are sampled with higher probability [2]. Unfortunately, the first research line does not reduce computational cost, while the second may miss out on the most interesting patterns. In this paper, we combine the best of both worlds for mining interesting tiles [8] from binary databases. Specifically, we propose a new pattern sampling approach based on Gibbs sampling, where the probability of sampling a pattern is proportional to their subjective interest-ingness [6]-an interestingness measure reported to better represent true interestingness. The experimental evaluation confirms the theory, but also reveals an important weakness of the proposed approach which we speculate is shared with any other pattern sampling approach. We thus conclude with a broader discussion of this issue, and a forward look.

The information in high-dimensional datasets is often too complex for human users to perceive directly. Hence, it may be helpful to use dimensionality reduction methods to construct lower dimensional representations that can be visualized. The natural question that arises is how do we construct a most informative low dimensional representation? We study this question from an information-theoretic perspective and introduce a new method for linear dimensionality reduction. The obtained model that quantifies the informativeness also allows us to flexibly account for prior knowledge a user may have about the data. This enables us to provide representations that are subjectively interesting. We title the method Subjectively Interesting Component Analysis (SICA) and expect it is mainly useful for iterative data mining. SICA is based on a model of a user’s belief state about the data. This belief state is used to search for surprising views. The initial state is chosen by the user (it may be empty up to the data format) and is updated automatically as the analysis progresses. We study several types of prior beliefs: if a user only knows the scale of the data, SICA yields the same cost function as Principal Component Analysis (PCA), while if a user expects the data to have outliers, we obtain a variant that we term t-PCA. Finally, scientifically more interesting variants are obtained when a user has more complicated beliefs, such as knowledge about similarities between data points. The experiments suggest that SICA enables users to find subjectively more interesting representations.

Cycles in graphs often signify interesting processes. For example, cyclic trading patterns can indicate inefficiencies or economic dependencies in trade networks, cycles in food webs can identify fragile dependencies in ecosystems, and cycles in financial transaction networks can be an indication of money laundering. Identifying such interesting cycles, which can also be constrained to contain a given set of query nodes, although not extensively studied, is thus a problem of considerable importance. In this paper, we introduce the problem of discovering interesting cycles in graphs. We first address the problem of quantifying the extent to which a given cycle is interesting for a particular analyst. We then show that finding cycles according to this interestingness measure is related to the longest cycle and maximum mean-weight cycle problems (in the unconstrained setting) and to the maximum Steiner cycle and maximum mean Steiner cycle problems (in the constrained setting). A complexity analysis shows that finding interesting cycles is NP-hard, and is NP-hard to approximate within a constant factor in the unconstrained setting, and within a factor polynomial in the input size for the constrained setting. The latter inapproximability result implies a similar result for the maximum Steiner cycle and maximum mean Steiner cycle problems. Motivated by these hardness results, we propose a number of efficient heuristic algorithms. We verify the effectiveness of the proposed methods and demonstrate their practical utility on two real-world use cases: a food web and an international trade-network dataset., Accepted for CIKM'19

International audience; Concepts are often described in terms of positive integer-valued attributes that are organized in a hierarchy. For example, cities can be described in terms of how many places there are of various types (e.g. nightlife spots, residences, food venues), and these places are organized in a hierarchy (e.g. a Portuguese restaurant is a type of food venue). This hierarchy imposes particular constraints on the values of related attributes---e.g. there cannot be more Portuguese restaurants than food venues. Moreover, knowing that a city has many food venues makes it less surprising that it also has many Portuguese restaurants, and vice versa. In the present paper, we attempt to characterize such concepts in terms of so-called contrastive antichains: particular kinds of subsets of their attributes and their values. We address the question of when a contrastive antichain is interesting, in the sense that it concisely describes the unique aspects of the concept, and this while duly taking into account the known attribute dependencies implied by the hierarchy. Our approach is capable of accounting for previously identified contrastive antichains, making iterative mining possible. Besides the interestingness measure, we also present an algorithm that scales well in practice, and demonstrate the usefulness of the method in an extensive empirical results section.

Numerical time series data are pervasive, originating from sources as diverse as wearable devices, medical equipment, to sensors in industrial plants. In many cases, time series contain interesting information in terms of subsequences that recur in approximate form, so-called motifs. Major open challenges in this area include how one can formalize the interestingness of such motifs and how the most interesting ones can be found. We introduce a novel approach that tackles these issues. We formalize the notion of such subsequence patterns in an intuitive manner and present an information-theoretic approach for quantifying their interestingness with respect to any prior expectation a user may have about the time series. The resulting interestingness measure is thus a subjective measure, enabling a user to find motifs that are truly interesting to them. Although finding the best motif appears computationally intractable, we develop relaxations and a branch-and-bound approach implemented in a constraint programming solver. As shown in experiments on synthetic data and two real-world datasets, this enables us to mine interesting patterns in small or mid-sized time series.

Network embedding (NE) methods aim to learn low-dimensional representations of network nodes as vectors, typically in Euclidean space. These representations are then validated on a variety of downstream prediction tasks. Link prediction is one of the most popular choices for assessing the performance of NE methods. However, the complexity of link prediction requires a carefully designed evaluation pipeline in order to provide consistent, reproducible and comparable results. We argue this has not been considered sufficiently in many recent works. The main goal of this paper is to overcome difficulties associated with evaluation pipelines and reproducibility of results. We introduce EvalNE, an evaluation framework to transparently assess and compare the performance of NE methods on link prediction. EvalNE provides automation and abstraction for tasks such as hyper-parameter tuning, model validation, edge sampling, computation of edge embeddings and model validation. The framework integrates efficient procedures for edge and non-edge sampling and can be used to easily evaluate any off-the-shelf embedding method. The framework is freely available as a Python toolbox. Finally, demonstrating the usefulness of EvalNE in practice, we conduct an empirical study in which we try to replicate and analyse experimental sections of several influential papers.

Cycles in graphs often signify interesting processes. For example, cyclic trading patterns can indicate inefficiencies or economic dependencies in trade networks, cycles in food webs can identify fragile dependencies in ecosystems, and cycles in financial transaction networks can be an indication of money laundering. Identifying such interesting cycles, which can also be constrained to contain a given set of query nodes, although not extensively studied, is thus a problem of considerable importance. In this paper, we introduce the problem of discovering interesting cycles in graphs. We first address the problem of quantifying the extent to which a given cycle is interesting for a particular analyst. We then show that finding cycles according to this interestingness measure is related to the longest cycle and maximum mean-weight cycle problems (in the unconstrained setting) and to the maximum Steiner cycle and maximum mean Steiner cycle problems (in the constrained setting). We show that the problems of finding the most interesting cycle and Steiner cycle are both NP-hard, and are NP-hard to approximate within a constant factor in the unconstrained setting, and within a factor polynomial in the input size for the constrained setting. We also show that the latter inapproximability result implies a similar result for the maximum Steiner cycle and maximum mean Steiner cycle problems. Motivated by these hardness results, we propose a number of efficient heuristic algorithms. Through extensive experiments, we verify the effectiveness of proposed methods and demonstrate their practical utility on real-world use cases.

Consider a large graph or network, and a user-provided set of query vertices between which the user wishes to explore relations. For example, a researcher may want to connect research papers in a citation network, an analyst may wish to connect organized crime suspects in a communication network, or an internet user may want to organize their bookmarks given their location in the world wide web. A natural way to do this is to connect the vertices in the form of a tree structure that is present in the graph. However, in sufficiently dense graphs, most such trees will be large or somehow trivial (e.g. involving high degree vertices) and thus not insightful. Extending previous research, we define and investigate the new problem of mining subjectively interesting trees connecting a set of query vertices in a graph, i.e., trees that are highly surprising to the specific user at hand. Using information theoretic principles, we formalize the notion of interestingness of such trees mathematically, taking in account certain prior beliefs the user has specified about the graph. A remaining problem is efficiently fitting a prior belief model. We show how this can be done for a large class of prior beliefs. Given a specified prior belief model, we then propose heuristic algorithms to find the best trees efficiently. An empirical validation of our methods on a large real graphs evaluates the different heuristics and validates the interestingness of the given trees.

Defining and computing distances between tree structures is a classical area of study in theoretical computer science, with practical applications in the areas of computational biology, information retrieval, text analysis, and many others. In this paper, we focus on rooted, unordered, uniquely-labelled trees such as taxonomies and other hierarchies. For trees as these, we introduce the intuitive concept of a ‘local move’ operation as an atomic edit of a tree. We then introduce SuMoTED, a new edit distance measure between such trees, defined as the minimal number of local moves required to convert one tree into another. We show how SuMoTED can be computed using a scalable algorithm with quadratic time complexity. Finally, we demonstrate its use on a collection of music genre taxonomies.

Finding out whether a word occurs significantly more often in one text or corpus than in another is an important question in analysing corpora. As noted by Kilgarriff (Language is never, ever, ever, random, Corpus Linguistics and Linguistic Theory, 2005; 1(2): 263–76.), the use of the X2 and log-likelihood ratio tests is problematic in this context, as they are based on the assumption that all samples are statistically independent of each other. However, words within a text are not independent. As pointed out in Kilgarriff (Comparing corpora, International Journal of Corpus Linguistics, 2001; 6(1): 1–37) and Paquot and Bestgen (Distinctive words in academic writing: a comparison of three statistical tests for keyword extraction. In Jucker, A., Schreier, D., and Hundt, M. (eds), Corpora: Pragmatics and Discourse. Amsterdam: Rodopi, 2009, pp. 247–69), it is possible to represent the data differently and employ other tests, such that we assume independence at the level of texts rather than individual words. This allows us to account for the distribution of words within a corpus. In this article we compare the significance estimates of various statistical tests in a controlled resampling experiment and in a practical setting, studying differences between texts produced by male and female fiction writers in the British National Corpus. We find that the choice of the test, and hence data representation, matters. We conclude that significance testing can be used to find consequential differences between corpora, but that assuming independence between all words may lead to overestimating the significance of the observed differences, especially for poorly dispersed words. We recommend the use of the t-test, Wilcoxon rank sum test, or bootstrap test for comparing word frequencies across corpora.

Controversy, disagreement, conflict, polarization and opinion divergence in social networks have been the subject of much recent research. In particular, researchers have addressed the question of how such concepts can be quantified given people’s prior opinions, and how they can be optimized by influencing the opinion of a small number of people or by editing the network’s connectivity. Here, rather than optimizing such concepts given a specific set of prior opinions, we study whether they can be optimized in the average case and in the worst case over all sets of prior opinions. In particular, we derive the worst-case and average-case conflict risk of networks, and we propose algorithms for optimizing these. For some measures of conflict, these are non-convex optimization problems with many local minima. We provide a theoretical and empirical analysis of the nature of some of these local minima, and show how they are related to existing organizational structures. Empirical results show how a small number of edits quickly decreases its conflict risk, both average-case and worst-case. Furthermore, it shows that minimizing average-case conflict risk often does not reduce worst-case conflict risk. Minimizing worst-case conflict risk on the other hand, while computationally more challenging, is generally effective at minimizing both worst-case as well as average-case conflict risk.

Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that 'similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such as link prediction (if 'similar' means being 'more likely to be connected') or classification (if 'similar' means 'being more likely to have the same label'). In recent years various methods for NE have been introduced, all following a similar strategy: defining a notion of similarity between nodes (typically some distance measure within the network), a distance measure in the embedding space, and a loss function that penalizes large distances for similar nodes and small distances for dissimilar nodes. A difficulty faced by existing methods is that certain networks are fundamentally hard to embed due to their structural properties: (approximate) multipartiteness, certain degree distributions, assortativity, etc. To overcome this, we introduce a conceptual innovation to the NE literature and propose to create \emph{Conditional Network Embeddings} (CNEs); embeddings that maximally add information with respect to given structural properties (e.g. node degrees, block densities, etc.). We use a simple Bayesian approach to achieve this, and propose a block stochastic gradient descent algorithm for fitting it efficiently. We demonstrate that CNEs are superior for link prediction and multi-label classification when compared to state-of-the-art methods, and this without adding significant mathematical or computational complexity. Finally, we illustrate the potential of CNE for network visualization.

This paper introduces an approach to find motifs in time series that are \emph{subjectively interesting}. That is, the aim is to find motifs that are surprising given an informative background distribution, which may for example correspond to the prior knowledge of a user of the tool. We quantify this surprisal using information theory, and more particularly the FORSIED framework. The resulting interestingness function according to which motifs are ranked is then subjective in the statistical sense, enabling us to find subsequence patterns (i.e., motifs and outliers) that are more truly interesting. Although finding the best motif appears intractable, we develop relaxations and a branch-and-bound approach that is implemented in a constraint programming solver. As shown in experiments on synthetic data and two real-world data sets this enables us to mine interesting patterns in small or mid-sized time series.

Deriving insights from high-dimensional data is one of the core problems in data mining. The difficulty mainly stems from the fact that there are exponentially many variable combinations to potentially consider, and there are infinitely many if we consider weighted combinations, even for linear combinations. Hence, an obvious question is whether we can automate the search for interesting patterns and visualizations. In this paper, we consider the setting where a user wants to learn as efficiently as possible about real-valued attributes. For example, to understand the distribution of crime rates in different geographic areas in terms of other (numerical, ordinal and/or categorical) variables that describe the areas. We introduce a method to find subgroups in the data that are maximally informative (in the formal Information Theoretic sense) with respect to a single or set of real-valued target attributes. The subgroup descriptions are in terms of a succinct set of arbitrarily-typed other attributes. The approach is based on the Subjective Interestingness framework FORSIED to enable the use of prior knowledge when finding most informative non-redundant patterns, and hence the method also supports iterative data mining., 12 pages, 10 figures, 2 tables, conference submission

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

Visual exploration of high-dimensional real-valued datasets is a fundamental task in exploratory data analysis (EDA). Existing methods use predefined criteria to choose the representation of data. There is a lack of methods that (i) elicit from the user what she has learned from the data and (ii) show patterns that she does not know yet. We construct a theoretical model where identified patterns can be input as knowledge to the system. The knowledge syntax here is intuitive, such as "this set of points forms a cluster", and requires no knowledge of maths. This background knowledge is used to find a Maximum Entropy distribution of the data, after which the system provides the user data projections in which the data and the Maximum Entropy distribution differ the most, hence showing the user aspects of the data that are maximally informative given the user's current knowledge. We provide an open source EDA system with tailored interactive visualizations to demonstrate these concepts. We study the performance of the system and present use cases on both synthetic and real data. We find that the model and the prototype system allow the user to learn information efficiently from various data sources and the system works sufficiently fast in practice. We conclude that the information theoretic approach to exploratory data analysis where patterns observed by a user are formalized as constraints provides a principled, intuitive, and efficient basis for constructing an EDA system., Comment: 12 pages, 9 figures, 2 tables, conference submission

Consider a large network, and a user-provided set of query nodes between which the user wishes to explore relations. For example, a researcher may want to connect research papers in a citation network, an analyst may wish to connect organized crime suspects in a communication network, or an internet user may want to organize their bookmarks given their location in the world wide web. A natural way to show how query nodes are related is in the form of a tree in the network that connects them. However, in sufficiently dense networks, most such trees will be large or somehow trivial (e.g. involving high degree nodes) and thus not insightful. In this paper, we define and investigate the new problem of mining subjectively interesting trees connecting a set of query nodes in a network, i.e., trees that are highly surprising to the specific user at hand. Using information theoretic principles, we formalize the notion of interestingness of such trees mathematically, taking in account any prior beliefs the user has specified about the network. We then propose heuristic algorithms to find the best trees efficiently, given a specified prior belief model. Modeling the user's prior belief state is however not necessarily computationally tractable. Yet, we show how a highly generic class of prior beliefs, namely about individual node degrees in combination with the density of particular sub-networks, can be dealt with in a tractable manner. Such types of beliefs can be used to model knowledge of a partial or total order of the network nodes, e.g. where the nodes represent events in time (such as papers in a citation network). An empirical validation of our methods on a large real network evaluates the different heuristics and validates the interestingness of the given trees.

Hierarchical classification is commonly defined as multi-class classification where the classes are hierarchically nested. Many practical hierarchical classification problems also share features with multi-label classification (i.e., each data point can have any number of labels, even non-hierarchically related) and novelty detection (i.e., some data points are novelties at some level of the hierarchy). A further complication is that it is common for training data to be incompletely labelled, e.g. the most specific labels are not always provided. In music genre classification for example, there are numerous music genres (multi-class) which are hierarchically related. Songs can belong to different (even non-nested) genres (multi-label), and a song labelled as Rock may not belong to any of its sub-genres, such that it is a novelty within this genre (novelty-detection). Finally, the training data may label a song as Rock whereas it really could be labelled correctly as the more specific genre Blues Rock. In this paper we develop a new method for hierarchical classification that naturally accommodates every one of these properties. To achieve this we develop a novel approach, modelling it as a Hierarchical Novelty Detection problem that can be trained through a single convex second-order cone programming problem. This contrasts with most existing approaches that typically require a model to be trained for each layer or internal node in the label hierarchy. Empirical results on a music genre classification problem are reported, comparing with a state-of-the-art method as well as simple benchmarks.

Data visualization and iterative/interactive data mining are growing rapidly in attention, both in research as well as in industry. However, while there are a plethora of advanced data mining methods and lots of works in the field of visualization, integrated methods that combine advanced visualization and/or interaction with data mining techniques in a principled way are rare. We present a framework based on constrained randomization which lets users explore high-dimensional data via 'subjectively informative' two-dimensional data visualizations. The user is presented with 'interesting' projections, allowing users to express their observations using visual interactions that update a background model representing the user's belief state. This background model is then considered by a projection-finding algorithm employing data randomization to compute a new 'interesting' projection. By providing users with information that contrasts with the background model, we maximize the chance that the user encounters striking new information present in the data. This process can be iterated until the user runs out of time or until the difference between the randomized and the real data is insignificant. We present two case studies, one controlled study on synthetic data and another on census data, using the proof-of-concept tool SIDE that demonstrates the presented framework.

Hypothesis testing using constrained null models can be used to compute the significance of data mining results given what is already known about the data. We study the novel problem of finding the smallest set of patterns that explains most about the data in terms of a global p value. The resulting set of patterns, such as frequent patterns or clusterings, is the smallest set that statistically explains the data. We show that the newly formulated problem is, in its general form, NP-hard and there exists no efficient algorithm with finite approximation ratio. However, we show that in a special case a solution can be computed efficiently with a provable approximation ratio. We find that a greedy algorithm gives good results on real data and that, using our approach, we can formulate and solve many known data-mining tasks. We demonstrate our method on several data mining tasks. We conclude that our framework is able to identify in various settings a small set of patterns that statistically explains the data and to formulate data mining problems in the terms of statistical significance.

Methods that find insightful low-dimensional projections are essential to effectively explore high-dimensional data. Principal Component Analysis is used pervasively to find low dimensional projections, not only because it is straightforward to use, but it is also often effective, because the variance in data is often dominated by relevant structure. However, even if the projections highlight real structure in the data, not all structure is interesting to every user. If a user is already aware of, or not interested in the dominant structure, Principal Component Analysis is less effective for finding interesting components. We introduce a new method called Subjectively Interesting Component Analysis (SICA), designed to find data projections that are subjectively interesting, i.e, projections that truly surprise the end-user. It isrooted in information theory and employs an explicit model of a user's prior expectations about the data. The corresponding optimization problem is a simple eigenvalue problem, and the result is a trade-o between explained variance and novelty. We present five case studies on synthetic data, images, time-series, and spatial data, to illustrate how SICA enables users to find (subjectively) interesting projections.

Data is typically complex and relational. Therefore, the development of relational data mining methods is an in- creasingly active topic of research. Recent work has resulted in new formalisations of patterns in relational data and in a way to quantify their interestingness in a subjective manner, taking into account the data analyst’s prior beliefs about the data. Yet, a scalable algorithm to find such most interesting patterns is lacking. We introduce a new algorithm based on two notions: (1) the use of Constraint Programming, which results in a notably shorter development time, faster runtimes, and more flexibility for extensions such as branch-and-bound search; and (2), the direct search for the most interesting patterns only, instead of exhaustive enumeration of patterns before ranking them. Through empirical evaluation, we find that our novel bounds yield speedups up to several orders of magnitude, especially on dense data with a simple schema. This makes it possible to mine the most subjectively-interesting relational patterns present in databases where this was previously impractical or impossible. ispartof: pages:913-918 ispartof: Proceedings of the 2016 IEEE International Conference on Data Mining (ICDM 2016) pages:913-918 ispartof: IEEE International Conference on Data Mining (ICDM 2015) location:Barcelona, Spain date:13 Dec - 15 Dec 2016 status: published

Data visualization and iterative/interactive data mining are growing rapidly in attention, both in research as well as in industry. However, integrated methods and tools that combine advanced visualization and data mining techniques are rare, and those that exist are often specialized to a single problem or domain. In this paper, we introduce a novel generic method for interactive visual exploration of high-dimensional data. In contrast to most visualization tools, it is not based on the traditional dogma of manually zooming and rotating data. Instead, the tool initially presents the user with an ‘interesting’ projection of the data and then employs data randomization with constraints to allow users to flexibly and intuitively express their interests or beliefs using visual interactions that correspond to exactly defined constraints. These constraints expressed by the user are then taken into account by a projection-finding algorithm to compute a new ‘interesting’ projection, a process that can be iterated until the user runs out of time or finds that constraints explain everything she needs to find from the data. We present the tool by means of two case studies, one controlled study on synthetic data and another on real census data. The data and software related to this paper are available at http://​www.​interesting-patterns.​net/​forsied/​interactive-visual-data-exploration-with-subjective-feedback/​.

We present SIDE, a tool for Subjective and Interactive Visual Data Exploration, which lets users explore high dimensional data via subjectively informative 2D data visualizations. Many existing visual analytics tools are either restricted to specific problems and domains or they aim to find visualizations that align with user’s belief about the data. In contrast, our generic tool computes data visualizations that are surprising given a user’s current understanding of the data. The user’s belief state is represented as a set of projection tiles. Hence, this user-awareness offers users an efficient way to interactively explore yet-unknown features of complex high dimensional datasets.

Detecting underlying trends in time series is important in many settings, such as market analysis (stocks, social media coverage) and system monitoring (production facilities, networks). Although many properties of the trends are common across different domains, others are domain-specific. In particular, modelling human activities such as their behaviour on social media, often leads to sharply defined events separated by periods without events. This paper is motivated by time series representing the number of tweets per day addressed to a specific Twitter user. Such time series are characterized by the combination of (1) an underlying trend, (2) concentrated bursts of activity that can be arbitrarily large, often attributable to an event, e.g., a tweet that goes viral or a real-world event, and (3) random fluctuations/noise. We present a new probabilistic model that accurately models such time series in terms of peaks on top of a piece-wise exponential trend. Fitting this model can be done by solving an efficient convex optimization problem. As an empirical validation of the approach, we illustrate how this model performs on a set of Twitter time series, each one addressing a particular music artist, which we manually annotated with events as a reference.

As in any dynamic market, supply and demand of music are in a constant state of disequilibrium. Music charts have for many years documented the demand for the most popular music, but a more comprehensive understanding of this market has remained beyond reach. In this paper, we provide a proof of concept for how web resources now make it possible to study both demand and supply sides, accounting also for smaller, independent artists.

In this article we will focus on premodifying -ing participles in English. By premodifying -ing participles we refer to NP-internal -ing forms, such as the ones found in a charming man or a barking dog. Our first goal is to see how these participles are used in four registers of Present-Day English: academic prose, newspaper articles, fiction and conversations. Furthermore, we will attempt to find corpus evidence for Vartiainen (forthcoming), where it was suggested that there are solid grounds for dividing the class of premodifying -ing participles into adjectival and verbal -ing participles. Our hypothesis is that if this division is evident in the syntactic behaviour of the participles, then it might also be reflected in the way -ing participles are used in different registers.

Comparing frequency counts over texts or corpora is an important task in many applications and scientific disciplines. Given a text corpus, we want to test a hypothesis, such as "word X is frequent", "word X has become more frequent over time", or "word X is more frequent in male than in female speech". For this purpose we need a null model of word frequencies. The commonly used bag-of-words model, which corresponds to a Bernoulli process with fixed parameter, does not account for any structure present in natural languages. Using this model for word frequencies results in large numbers of words being reported as unexpectedly frequent. We address how to take into account the inherent occurrence patterns of words in significance testing of word frequencies. Based on studies of words in two large corpora, we propose two methods for modeling word frequencies that both take into account the occurrence patterns of words and go beyond the bag-of-words assumption. The first method models word frequencies based on the spatial distribution of individual words in the language. The second method is based on bootstrapping and takes into account only word frequency at the text level. The proposed methods are compared to the current gold standard in a series of experiments on both corpora. We find that words obey different spatial patterns in the language, ranging from bursty to non-bursty/uniform, independent of their frequency, showing that the traditional approach leads to many false positives.

We study the performance of three dynamic programming methods on music retrieval. The methods are designed for time series matching but can be directly applied to retrieval of music. Dynamic Time Warping (DTW) identifies an optimal alignment between two time series, and computes the matching cost corresponding to that alignment. Significant speed-ups can be achieved by constrained Dynamic Time Warping (cDTW), which narrows down the set of positions in one time series that can be matched with specific positions in the other time series. Both methods are designed for full sequence matching but can also be applied for subsequence matching, by using a sliding window over each database sequence to compute a matching score for each database subsequence. In addition, SPRING is a dynamic programming approach designed for subsequence matching, where the query is matched with a database subsequence without requiring the match length to be equal to the query length. SPRING has a lower computational cost than DTW and cDTW. Our database consists of a set of MIDI files taken from the web. Each MIDI file has been converted to a 2-dimensional time series, taking into account both note pitches and durations. We have used synthetic queries of fixed size and different noise levels. Surprisingly, when looking for the top-K best matches, all three approaches show similar behavior in terms of retrieval accuracy for small values of K. This suggests that for the specific application area, a computationally cheaper method, such as SPRING, is sufficient to retrieve the best top-K matches.