Abstract Time series classification (TSC) is a challenging task due to the diversity of types of features that may be relevant for different classification tasks, including trends, variance, frequency, magnitude, and various patterns. To address this challenge, several alternative classes of approach have been developed. While kernel, neural network, and hybrid approaches perform well overall, some specialized approaches are better suited for specific tasks. In this paper, we propose a new similarity-based classifier, Proximity Forest version 2.0 (PF 2.0), which outperforms previous state-of-the-art similarity-based classifiers across the UCR benchmark and outperforms other state-of-the-art methods on specific datasets in the benchmark that are best addressed by similarity-base methods. PF 2.0 incorporates three recent advances in time series similarity measures — (1) computationally efficient early abandoning and pruning to speedup elastic similarity computations; (2) a new elastic similarity measure, Amerced Dynamic Time Warping ( $${{\,\textrm{ADTW}\,}}$$ ADTW ); and (3) cost function tuning. It rationalizes the set of similarity measures employed, reducing the eight base measures of the original PF to four and using the first derivative transform with all similarity measures, rather than a limited subset. It also incorporates HYDRA, a dictionary-based transform. We have re-implemented PF 1.0 and implemented PF 2.0 framework in Java, making the PF framework more efficient.

Crowdsourcing services provide a fast and cheap way to obtain substantial labeled data by employing crowd workers on the Internet. In crowdsourcing learning, two-stage methods have been widely used, which first infer the integrated label for each instance and then build a learning model using instances with their integrated labels. However, existing two-stage methods mainly focus on how to infer more accurate integrated labels, after that, most of them directly regard the integrated labels as class labels to build a learning model, which loses the detailed worker labeling information in multiple noisy labels and thus results in sub-optimal model accuracy. To solve this problem, in this study, we take the multiple noisy labels of each instance as its attribute value vector to construct another view in addition to the original attribute view, and propose a novel two-stage method called dual-view learning from crowds (DVLFC). In DVLFC, we first pick out workers with sufficient number of labels and augment the multiple noisy label set for each instance, then we build a supervised learning model in each view and at last we fuse their class-membership probabilities to get the final classification result. Extensive experiments on both real-world and artificial crowdsourced datasets prove the effectiveness of DVLFC.

In time series anomaly detection (TSAD), the scarcity of labeled data poses a challenge to the development of accurate models. Unsupervised domain adaptation (UDA) offers a solution by leveraging labeled data from a related domain to detect anomalies in an unlabeled target domain. However, existing UDA methods assume consistent anomalous classes across domains. To address this limitation, we propose a novel Domain Adaptation Contrastive learning model for Anomaly Detection in multivariate time series (DACAD), combining UDA with contrastive learning. DACAD utilizes an anomaly injection mechanism that enhances generalization across unseen anomalous classes, improving adaptability and robustness. Additionally, our model employs supervised contrastive loss for the source domain and self-supervised contrastive triplet loss for the target domain, ensuring comprehensive feature representation learning and domain-invariant feature extraction. Finally, an effective Center-based Entropy Classifier (CEC) accurately learns normal boundaries in the source domain. Extensive evaluations on multiple real-world datasets and a synthetic dataset highlight DACAD's superior performance in transferring knowledge across domains and mitigating the challenge of limited labeled data in TSAD.

Unsupervised graph representation learning (UGRL) based on graph neural networks (GNNs), has received increasing attention owing to its efficacy in handling graph-structured data. However, existing UGRL methods ideally assume that the node features are noise-free, which makes them fail to distinguish between useful information and noise when applied to real data with noisy features, thus affecting the quality of learned representations. This urges us to take node noisy features into account in real-world UGRL. With empirical analysis, we reveal that feature propagation, the essential operation in GNNs, acts as a "double-edged sword" in handling noisy features - it can both denoise and diffuse noise, leading to varying feature quality across nodes, even within the same node at different hops. Building on this insight, we propose a novel UGRL method based on Multi-hop feature Quality Estimation (MQE for short). Unlike most UGRL models that directly utilize propagation-based GNNs to generate representations, our approach aims to learn representations through estimating the quality of propagated features at different hops. Specifically, we introduce a Gaussian model that utilizes a learnable "meta-representation" as a condition to estimate the expectation and variance of multi-hop propagated features via neural networks. In this way, the ''meta representation'' captures the semantic and structural information underlying multiple propagated features but is naturally less susceptible to interference by noise, thereby serving as high-quality node representations beneficial for downstream tasks. Extensive experiments on multiple real-world datasets demonstrate that MQE in learning reliable node representations in scenarios with diverse types of feature noise.

Time series classification and regression are rapidly evolving fields that find areas of application in all domains of machine learning and data science. This hands on tutorial will provide an accessible overview of the recent research in these fields, using code examples to introduce the process of implementing and evaluating an estimator. We will show how to easily reproduce published results and how to compare a new algorithm to state-of-the-art. Finally, we will work through real world examples from the field of Electroencephalogram (EEG) classification and regression. EEG machine learning tasks arise in medicine, brain-computer interface research and psychology. We use these problems to how to compare algorithms on problems from a single domain and how to deal with data with different characteristics, such as missing values, unequal length and high dimensionality. The latest advances in the fields of time series classification and regression are all available through the aeon toolkit, an open source, scikit-learn compatible framework for time series machine learning which we use to provide our code examples.

Abstract We show that it is possible to achieve the same accuracy, on average, as the most accurate existing interval methods for time series classification on a standard set of benchmark datasets using a single type of feature (quantiles), fixed intervals, and an ‘off the shelf’ classifier. This distillation of interval-based approaches represents a fast and accurate method for time series classification, achieving state-of-the-art accuracy on the expanded set of 142 datasets in the UCR archive with a total compute time (training and inference) of less than 15 min using a single CPU core.

Abstract We argue that time series analysis is fundamentally different in nature to either vision or natural language processing with respect to the forms of meaningful self-supervised learning tasks that can be defined. Motivated by this insight, we introduce a novel approach called Series2Vec for self-supervised representation learning. Unlike the state-of-the-art methods in time series which rely on hand-crafted data augmentation, Series2Vec is trained by predicting the similarity between two series in both temporal and spectral domains through a self-supervised task. By leveraging the similarity prediction task, which has inherent meaning for a wide range of time series analysis tasks, Series2Vec eliminates the need for hand-crafted data augmentation. To further enforce the network to learn similar representations for similar time series, we propose a novel approach that applies order-invariant attention to each representation within the batch during training. Our evaluation of Series2Vec on nine large real-world datasets, along with the UCR/UEA archive, shows enhanced performance compared to current state-of-the-art self-supervised techniques for time series. Additionally, our extensive experiments show that Series2Vec performs comparably with fully supervised training and offers high efficiency in datasets with limited-labeled data. Finally, we show that the fusion of Series2Vec with other representation learning models leads to enhanced performance for time series classification. Code and models are open-source at https://github.com/Navidfoumani/Series2Vec

Abstract Transformers have demonstrated outstanding performance in many applications of deep learning. When applied to time series data, transformers require effective position encoding to capture the ordering of the time series data. The efficacy of position encoding in time series analysis is not well-studied and remains controversial, e.g., whether it is better to inject absolute position encoding or relative position encoding, or a combination of them. In order to clarify this, we first review existing absolute and relative position encoding methods when applied in time series classification. We then proposed a new absolute position encoding method dedicated to time series data called time Absolute Position Encoding (tAPE). Our new method incorporates the series length and input embedding dimension in absolute position encoding. Additionally, we propose computationally Efficient implementation of Relative Position Encoding (eRPE) to improve generalisability for time series. We then propose a novel multivariate time series classification model combining tAPE/eRPE and convolution-based input encoding named ConvTran to improve the position and data embedding of time series data. The proposed absolute and relative position encoding methods are simple and efficient. They can be easily integrated into transformer blocks and used for downstream tasks such as forecasting, extrinsic regression, and anomaly detection. Extensive experiments on 32 multivariate time-series datasets show that our model is significantly more accurate than state-of-the-art convolution and transformer-based models. Code and models are open-sourced at https://github.com/Navidfoumani/ConvTran .

Abstract The ability to compute the exact divergence between two high-dimensional distributions is useful in many applications, but doing so naively is intractable. Computing the $$\alpha \beta $$ α β -divergence—a family of divergences that includes the Kullback–Leibler divergence and Hellinger distance—between the joint distribution of two decomposable models, i.e., chordal Markov networks, can be done in time exponential in the treewidth of these models. Extending this result, we propose an approach to compute the exact $$\alpha \beta $$ α β -divergence between any marginal or conditional distribution of two decomposable models. In order to do so tractably, we provide a decomposition over the marginal and conditional distributions of decomposable models. We then show how our method can be used to analyze distributional changes by first applying it to the benchmark image dataset QMNIST and a dataset containing observations from various areas at the Roosevelt Nation Forest and their cover type. Finally, based on our framework, we propose a novel way to quantify the error in contemporary superconducting quantum computers.

The ability to compute the exact divergence between two high-dimensional distributions is useful in many applications but doing so naively is intractable. Computing the alpha-beta divergence—a family of divergences that includes the Kullback-Leibler divergence and Hellinger distance—between the joint distribution of two decomposable models, i.e chordal Markov networks, can be done in time exponential in the treewidth of these models. However, reducing the dissimilarity between two high-dimensional objects to a single scalar value can be uninformative. Furthermore, in applications such as supervised learning, the divergence over a conditional distribution might be of more interest. Therefore, we propose an approach to compute the exact alpha-beta divergence between any marginal or conditional distribution of two decomposable models. Doing so tractably is non-trivial as we need to decompose the divergence between these distributions and therefore, require a decomposition over the marginal and conditional distributions of these models. Consequently, we provide such a decomposition and also extend existing work to compute the marginal and conditional alpha-beta divergence between these decompositions. We then show how our method can be used to analyze distributional changes by first applying it to a benchmark image dataset. Finally, based on our framework, we propose a novel way to quantify the error in contemporary superconducting quantum computers. Code for all experiments is available at: https://lklee.dev/pub/2023-icdm/code

Abstract We demonstrate a simple connection between dictionary methods for time series classification, which involve extracting and counting symbolic patterns in time series, and methods based on transforming input time series using convolutional kernels, namely Rocket and its variants. We show that by adjusting a single hyperparameter it is possible to move by degrees between models resembling dictionary methods and models resembling Rocket . We present Hydra , a simple, fast, and accurate dictionary method for time series classification using competing convolutional kernels, combining key aspects of both Rocket and conventional dictionary methods. Hydra is faster and more accurate than the most accurate existing dictionary methods, achieving similar accuracy to several of the most accurate current methods for time series classification. Hydra can also be combined with Rocket and its variants to significantly improve the accuracy of these methods.

Abstract Dynamic time warping (DTW) is a popular time series distance measure that aligns the points in two series with one another. These alignments support warping of the time dimension to allow for processes that unfold at differing rates. The distance is the minimum sum of costs of the resulting alignments over any allowable warping of the time dimension. The cost of an alignment of two points is a function of the difference in the values of those points. The original cost function was the absolute value of this difference. Other cost functions have been proposed. A popular alternative is the square of the difference. However, to our knowledge, this is the first investigation of both the relative impacts of using different cost functions and the potential to tune cost functions to different time series classification tasks. We do so in this paper by using a tunable cost function $$\lambda _{\gamma }$$ λ γ with parameter $$\gamma $$ γ . We show that higher values of $$\gamma $$ γ place greater weight on larger pairwise differences, while lower values place greater weight on smaller pairwise differences. We demonstrate that training $$\gamma $$ γ significantly improves the accuracy of both the $${ DTW }$$ DTW nearest neighbor and Proximity Forest classifiers.

Abstract This paper contributes multivariate versions of seven commonly used elastic similarity and distance measures for time series data analytics. Elastic similarity and distance measures can compensate for misalignments in the time axis of time series data. We adapt two existing strategies used in a multivariate version of the well-known Dynamic Time Warping (DTW), namely, Independent and Dependent DTW, to these seven measures. While these measures can be applied to various time series analysis tasks, we demonstrate their utility on multivariate time series classification using the nearest neighbor classifier. On 23 well-known datasets, we demonstrate that each of the measures but one achieves the highest accuracy relative to others on at least one dataset, supporting the value of developing a suite of multivariate similarity and distance measures. We also demonstrate that there are datasets for which either the dependent versions of all measures are more accurate than their independent counterparts or vice versa. In addition, we also construct a nearest neighbor-based ensemble of the measures and show that it is competitive to other state-of-the-art single-strategy multivariate time series classifiers.

Abstract Nearest neighbour similarity measures are widely used in many time series data analysis applications. They compute a measure of similarity between two time series. Most applications require tuning of these measures’ meta-parameters in order to achieve good performance. However, most measures have at least $$O(L^2)$$ O ( L 2 ) complexity, making them computationally expensive and the process of learning their meta-parameters burdensome, requiring days even for datasets containing only a few thousand series. In this paper, we propose UltraFastMPSearch, a family of algorithms to learn the meta-parameters for different types of time series distance measures. These algorithms are significantly faster than the prior state of the art. Our algorithms build upon the state of the art, exploiting the properties of a new efficient exact algorithm which supports early abandoning and pruning for most time series distance measures. We show on 128 datasets from the UCR archive that our new family of algorithms are up to an order of magnitude faster than the previous state of the art.

Many real-world data streams are non-stationary. Subject to concept drift, the distributions change over time. To retain accuracy in the face of such drift, online decision tree learners must discard parts of the tree that are no longer accurate and replace them by new subtrees that reflect the new distribution. The longstanding state-of-the-art online decision tree learner for non-stationary streams is Hoeffding Adaptive Tree (HAT), which adds a drift detection and response mechanism to the classic Very Fast Decision Tree (VFDT) online decision tree learner. However, for stationary distributions, VFDT has been superseded by Extremely Fast Decision Tree (EFDT), which uses a statistically more efficient learning mechanism than VFDT. This learning mechanism needs to be coupled with a compensatory revision mechanism that can compensate for circumstances where the learning mechanism is too eager. The current work develops a strategy to combine the best of both these state-of-the-art approaches, exploiting both the statistically efficient learning mechanism from EFDT and the highly effective drift detection and response mechanism of HAT. To do so requires decoupling of the EFDT splitting and revision mechanisms, as the latter incorrectly triggers the HAT drift detection mechanism. The resulting learner, Extremely Fast Hoeffding Adaptive Tree, responds to drift more rapidly and effectively than either HAT or EFDT, and attains a statistically significant advantage in accuracy even on stationary streams.

Abstract We propose MultiRocket, a fast time series classification (TSC) algorithm that achieves state-of-the-art accuracy with a tiny fraction of the time and without the complex ensembling structure of many state-of-the-art methods. MultiRocket improves on MiniRocket, one of the fastest TSC algorithms to date, by adding multiple pooling operators and transformations to improve the diversity of the features generated. In addition to processing the raw input series, MultiRocket also applies first order differences to transform the original series. Convolutions are applied to both representations, and four pooling operators are applied to the convolution outputs. When benchmarked using the University of California Riverside TSC benchmark datasets, MultiRocket is significantly more accurate than MiniRocket, and competitive with the best ranked current method in terms of accuracy, HIVE-COTE 2.0, while being orders of magnitude faster.

Kernel-based models have a strong generalization ability, but most, including SVM, are vulnerable to the curse of kernelization. Moreover, their predictive performance is sensitive to hyperparameter tuning, which demands high computational resources. These problems render kernel methods problematic when dealing with large-scale datasets. To this end, we first formulate the optimization problem in a kernel-based learning setting as a posterior inference problem, and then develop a rich family of Recurrent Neural Network-based variational inference techniques. Unlike existing literature, which stops at the variational distribution and uses it as the surrogate for the true posterior distribution, here we further leverage Stein Variational Gradient Descent to further bring the variational distribution closer to the true posterior, we refer to this step asStein Refinement. Putting these altogether, we arrive at a robust and efficient variational learning method for multiclass kernel machines with extremely accurate approximation. Moreover, our formulation enables efficient learning of kernel parameters and hyperparameters which robustifies the proposed method against data uncertainties. The extensive experiments show that without tuning any parameter on modest quantities of data our method obtains comparable accuracy to LIBSVM, a well-known implementation of SVM, and outperforms other baselines, while being able to seamlessly scale with large-scale datasets.

The Dynamic Time Warping (DTW) similarity measure is widely used in many time series data mining applications. It computes the cost of aligning two series, smaller costs indicating more similar series. Most applications require tuning of DTW’s Warping Window (WW) parameter in order to achieve good performance. This parameter controls the amount of warping allowed, reducing pathological alignments, with the added benefit of speeding up computation. However, since DTW is in itself very costly, learning the WW is a burdensome process, requiring days even for datasets containing only a few thousand series. In this paper, we propose ULTRAFASTWWSEARCH, a new algorithm able to learn the WW significantly faster than the state-of-the-art FASTWWSEARCH method. ULTRAFASTWWSEARCH builds upon the latter, exploiting the properties of a new efficient exact DTW algorithm which supports early abandoning and pruning (EAP). We show on 128 datasets from the UCR archive that ULTRAFASTWWSEARCH is up to an order of magnitude faster than the previous state of the art.

Rocket achieves state-of-the-art accuracy for time series classification with a fraction of the computational expense of most existing methods by transforming input time series using random convolutional kernels, and using the transformed features to train a linear classifier. We reformulate Rocket into a new method, MiniRocket. MiniRocket is up to 75 times faster than Rocket on larger datasets, and almost deterministic (and optionally, fully deterministic), while maintaining essentially the same accuracy. Using this method, it is possible to train and test a classifier on all of 109 datasets from the UCR archive to state-of-the-art accuracy in under 10 minutes. MiniRocket is significantly faster than any other method of comparable accuracy (including Rocket), and significantly more accurate than any other method of remotely similar computational expense.

Rule ensembles are designed to provide a useful trade-off between predictive accuracy and model interpretability. However, the myopic and random search components of current rule ensemble methods can compromise this goal: they often need more rules than necessary to reach a certain accuracy level or can even outright fail to accurately model a distribution that can actually be described well with a few rules. Here, we present a novel approach aiming to fit rule ensembles of maximal predictive power for a given ensemble size (and thus model comprehensibility). In particular, we present an efficient branch-and-bound algorithm that optimally solves the per-rule objective function of the popular second-order gradient boosting framework. Our main insight is that the boosting objective can be tightly bounded in linear time of the number of covered data points. Along with an additional novel pruning technique related to rule redundancy, this leads to a computationally feasible approach for boosting optimal rules that, as we demonstrate on a wide range of common benchmark problems, consistently outperforms the predictive performance of boosting greedy rules.

Spatio-temporal data sets such as satellite image series are of utmost importance for understanding global developments like climate change or urbanization. However, incompleteness of data can greatly impact usability and knowledge discovery. In fact, there are many cases where not a single data point in the set is fully observed. For filling gaps, we introduce a novel approach that utilizes Markov random fields (MRFs). We extend the probabilistic framework to also consider empirical prior information, which allows to train even on highly incomplete data. Moreover, we devise a way to make discrete MRFs predict continuous values via state superposition. Experiments on real-world remote sensing imagery suffering from cloud cover show that the proposed approach outperforms state-of-the-art gap filling techniques.

The Nearest Neighbour algorithm coupled with the Dynamic Time Warping similarity measure (NN-DTW) is at the core of state-of-the-art classification algorithms including Ensemble of Elastic Distances and Collection of Transformation-Based Ensemble. DTW's complexity makes NN-DTW highly computationally demanding. To combat this, lower bounds to DTW are used to minimize the number of times the expensive DTW need be computed during NN-DTW search. Effective lower bounds must balance ‘time to calculate’ vs ‘tightness to DTW.‘ On the one hand, the tighter the bound the fewer the calls to the full DTW. On the other, calculating tighter bounds usually requires greater computation. Numerous lower bounds have been proposed. Different bounds provide different trade-off between computational time and tightness. In this work, we present a new class of lower bounds that are tighter than the popular Keogh lower bound, while requiring similar computation time. Our new lower bounds take advantage of the DTW boundary condition, monotonicity and continuity constraints. In contrast to most existing bounds, they remain relatively tight even for large windows. A single parameter to these new lower bounds controls the speed-tightness trade-off. We demonstrate that these new lower bounds provide an exceptional balance between computation time and tightness for the NN-DTW time series classification task, resulting in greatly improved efficiency for NN-DTW lower bound search.

Statistically sound pattern discovery harnesses the rigour of statistical hypothesis testing to overcome many of the issues that have hampered standard data mining approaches to pattern discovery. Most importantly, application of appropriate statistical tests allows precise control over the risk of false discoveries—patterns that are found in the sample data but do not hold in the wider population from which the sample was drawn. Statistical tests can also be applied to filter out patterns that are unlikely to be useful, removing uninformative variations of the key patterns in the data. This tutorial introduces the key statistical and data mining theory and techniques that underpin this fast developing field. We concentrate on two general classes of patterns: dependency rules that express statistical dependencies between condition and consequent parts and dependency sets that express mutual dependence between set elements. We clarify alternative interpretations of statistical dependence and introduce appropriate tests for evaluating statistical significance of patterns in different situations. We also introduce special techniques for controlling the likelihood of spurious discoveries when multitudes of patterns are evaluated. The paper is aimed at a wide variety of audiences. It provides the necessary statistical background and summary of the state-of-the-art for any data mining researcher or practitioner wishing to enter or understand statistically sound pattern discovery research or practice. It can serve as a general introduction to the field of statistically sound pattern discovery for any reader with a general background in data sciences.

We introduce a novel incremental decision tree learning algorithm, Hoeffding Anytime Tree, that is statistically more efficient than the current state-of-the-art, Hoeffding Tree. We demonstrate that an implementation of Hoeffding Anytime Tree---"Extremely Fast Decision Tree'', a minor modification to the MOA implementation of Hoeffding Tree---obtains significantly superior prequential accuracy on most of the largest classification datasets from the UCI repository. Hoeffding Anytime Tree produces the asymptotic batch tree in the limit, is naturally resilient to concept drift, and can be used as a higher accuracy replacement for Hoeffding Tree in most scenarios, at a small additional computational cost.

Kernel methods are powerful supervised machine learning models for their strong generalization ability, especially on limited data to effectively generalize on unseen data. However, most kernel methods, including the state-of-the-art LIBSVM, are vulnerable to the curse of kernelization, making them infeasible to apply to large-scale datasets. This issue is exacerbated when kernel methods are used in conjunction with a grid search to tune their kernel parameters and hyperparameters which brings in the question of model robustness when applied to real datasets. In this paper, we propose a robust Bayesian Kernel Machine (BKM) - a Bayesian kernel machine that exploits the strengths of both the Bayesian modelling and kernel methods. A key challenge for such a formulation is the need for an efficient learning algorithm. To this end, we successfully extended the recent Stein variational theory for Bayesian inference for our proposed model, resulting in fast and efficient learning and prediction algorithms. Importantly our proposed BKM is resilient to the curse of kernelization, hence making it applicable to large-scale datasets and robust to parameter tuning, avoiding the associated expense and potential pitfalls with current practice of parameter tuning. Our extensive experimental results on 12 benchmark datasets show that our BKM without tuning any parameter can achieve comparable predictive performance with the state-of-the-art LIBSVM and significantly outperforms other baselines, while obtaining significantly speedup in terms of the total training time compared with its rivals

Time series classification maps time series to labels. The nearest neighbor algorithm (NN) using the Dynamic Time Warping (DTW) similarity measure is a leading algorithm for this task and a component of the current best ensemble classifiers for time series. However, NN-DTW is only a winning combination when its meta-parameter – its warping window – is learned from the training data. The warping window (WW) intuitively controls the amount of distortion allowed when comparing a pair of time series. With a training database of N time series of lengths L, a naive approach to learning the WW requires Θ(N2·L3) operations. This often results in NN-DTW requiring days for training on datasets containing a few thousand time series only. In this paper, we introduce FastWWSearch: an efficient and exact method to learn WW. We show on 86 datasets that our method is always faster than the state of the art, with at least one order of magnitude and up to 1000x speed-up.

Machine learning researchers are facing a data deluge quantities of training data have been increasing at a rapid rate. However, most of machine learning algorithms were proposed in the context of learning from relatively smaller quantities of data. We argue that a big data classifier should have superior feature engineering capability, minimal tuning parameters and should be able to learn decision boundaries in fewer passes through the data. In this paper, we have proposed an (computationally) efficient yet (classification-wise) effective family of learning algorithms that fulfils these properties. The proposed family of learning algorithms is based on recently proposed accelerated higher-order logistic regression algorithm: ALRn. The contributions of this work are three-fold. First, we have added the functionality of out-of-core learning in ALRn, resulting in a limited pass learning algorithm. Second, superior feature engineering capabilities are built and third, a far more efficient (memory-wise) implementation has been proposed. We demonstrate the competitiveness of our proposed algorithm by comparing its performance not only with state-of-the-art classifier in out-of-core learning such as Selective KDB but also with state-of-the-art in in-core learning such as Random Forest.

Spatial association rule mining (SARM) is an important data mining task for understanding implicit and sophisticated interactions in spatial data. The usefulness of SARM results, represented as sets of rules, depends on their reliability: the abundance of rules, control over the risk of spurious rules, and accuracy of rule interestingness measure (RIM) values. This study presents crisp-fuzzy SARM, a novel SARM method that can enhance the reliability of resultant rules. The method firstly prunes dubious rules using statistically sound tests and crisp supports for the patterns involved, and then evaluates RIMs of accepted rules using fuzzy supports. For the RIM evaluation stage, the study also proposes a Gaussian-curve-based fuzzy data discretization model for SARM with improved design for spatial semantics. The proposed techniques were evaluated by both synthetic and real-world data. The synthetic data was generated with predesigned rules and RIM values, thus the reliability of SARM results could be confidently and quantitatively evaluated. The proposed techniques showed high efficacy in enhancing the reliability of SARM results in all three aspects. The abundance of resultant rules was improved by 50% or more compared with using conventional fuzzy SARM. Minimal risk of spurious rules was guaranteed by statistically sound tests. The probability that the entire result contained any spurious rules was below 1%. The RIM values also avoided large positive errors committed by crisp SARM, which typically exceeded 50% for representative RIMs. The real-world case study on New York City points of interest reconfirms the improved reliability of crisp-fuzzy SARM results, and demonstrates that such improvement is critical for practical spatial data analytics and decision support.

In machine learning, data augmentation is the process of creating synthetic examples in order to augment a dataset used to learn a model. One motivation for data augmentation is to reduce the variance of a classifier, thereby reducing error. In this paper, we propose new data augmentation techniques specifically designed for time series classification, where the space in which they are embedded is induced by Dynamic Time Warping (DTW). The main idea of our approach is to average a set of time series and use the average time series as a new synthetic example. The proposed methods rely on an extension of DTW Barycentric Averaging (DBA), the averaging technique that is specifically developed for DTW. In this paper, we extend DBA to be able to calculate a weighted average of time series under DTW. In this case, instead of each time series contributing equally to the final average, some can contribute more than others. This extension allows us to generate an infinite number of new examples from any set of given time series. To this end, we propose three methods that choose the weights associated to the time series of the dataset. We carry out experiments on the 85 datasets of the UCR archive and demonstrate that our method is particularly useful when the number of available examples is limited (e.g. 2 to 6 examples per class) using a 1-NN DTW classifier. Furthermore, we show that augmenting full datasets is beneficial in most cases, as we observed an increase of accuracy on 56 datasets, no effect on 7 and a slight decrease on only 22.

We present theoretical analysis and a suite of tests and procedures for addressing a broad class of redundant and misleading association rules we call specious rules. Specious dependencies, also known as spurious, apparent, or illusory associations, refer to a well-known phenomenon where marginal dependencies are merely products of interactions with other variables and disappear when conditioned on those variables. The most extreme example is Yule-Simpson's paradox where two variables present positive dependence in the marginal contingency table but negative in all partial tables defined by different levels of a confounding factor. It is accepted wisdom that in data of any nontrivial dimensionality it is infeasible to control for all of the exponentially many possible confounds of this nature. In this paper, we consider the problem of specious dependencies in the context of statistical association rule mining. We define specious rules and show they offer a unifying framework which covers many types of previously proposed redundant or misleading association rules. After theoretical analysis, we introduce practical algorithms for detecting and pruning out specious association rules efficiently under many key goodness measures, including Mutual information and exact hypergeometric probabilities. We demonstrate that the procedure greatly reduces the number of associations discovered, providing an elegant and effective solution to the problem of association mining discovering large numbers of misleading and redundant rules.

Time series classification maps time series to labels. The nearest neighbour algorithm (NN) using the Dynamic Time Warping (DTW) similarity measure is a leading algorithm for this task. NN compares each time series to be classified to every time series in the training database. With a training database of N time series of lengths L, each classification requires ν(N · L2) computations. The databases used in almost all prior research have been relatively small (with less than 10,000 samples) and much of the research has focused on making DTW's complexity linear with L, leading to a runtime complexity of O(N · L). As we demonstrate with an example in remote sensing, real-world time series databases are now reaching the million-to-billion scale. This wealth of training data brings the promise of higher accuracy, but raises a significant challenge because N is becoming the limiting factor. As DTW is not a metric, indexing objects induced by its space is extremely challenging. We tackle this task in this paper. We develop TSI, a novel algorithm for Time Series Indexing which combines a hierarchy of K-means clustering with DTW-based lower-bounding. We show that, on large databases, TSI makes it possible to classify time series orders of magnitude faster than the state of the art.

With the emergence of big data, there has been a growing interest in optimization routines that lead to faster convergence of Logistic Regression (LR). Among many optimization methods such as Gradient Descent, Quasi-Newton, Conjugate Gradient, etc., the Trust-region based truncated Newton method (TRON) algorithm has been shown to converge the fastest. The TRON algorithm also forms an important component of the highly efficient and widely used liblinear package. It has been shown that the WANBIA-C trick of scaling with the log of the naive Bayes conditional probabilities can greatly accelerate the convergence of LR trained using (first-order) Gradient Descent and (approximate second-order) Quasi-Newton optimization. In this work we study the applicability of the WANBIA-C trick to TRON. We first devise a TRON algorithm optimizing the softmax objective function and then demonstrate that WANBIA-C style preconditioning can be beneficial for TRON, leading to an extremely fast (batch) LR algorithm. Second, we present a comparative analysis of one-vs-all LR and softmax LR in terms of the 0–1 Loss, Bias, Variance, RMSE, Log-Loss, Training and Classification time, and show that softmax LR leads to significantly better RMSE and Log-Loss. We evaluate our proposed approach on 51 benchmark datasets.

More and more applications have come with large data sets in the past decade. However, existing algorithms cannot guarantee to scale well on large data. Averaged n-Dependence Estimators (AnDE) allows for flexible learning from out-of-core data, by varying the value of n (number of super parents). Hence, AnDE is especially appropriate for large data learning. In this paper, we propose a sample-based attribute selection technique for AnDE. It needs one more pass through the training data, in which a multitude of approximate AnDE models are built and efficiently assessed by leave-one-out cross validation. The use of a sample reduces the training time. Experiments on 15 large data sets demonstrate that the proposed technique significantly reduces AnDE's error at the cost of a modest increase in training time. This efficient and scalable out-of-core approach delivers superior or comparable performance to typical in-core Bayesian network classifiers.

From understanding the structure of data, to classification and topic modeling, graphical models are core tools in machine learning and data mining. They combine probability and graph theories to form a compact representation of probability distributions. In the last decade, as data stores became larger and higher-dimensional, traditional algorithms for learning graphical models from data, with their lack of scalability, became less and less usable, thus directly decreasing the potential benefits of this core technology. To scale graphical modeling techniques to the size and dimensionality of most modern data stores, data science researchers and practitioners now have to meld the most recent advances in numerous specialized fields including graph theory, statistics, pattern mining and graphical modeling.

Statistical hypothesis testing is a popular and powerful tool for inferring knowledge from data. For every such test performed, there is always a non-zero probability of making a false discovery, i.e.~rejecting a null hypothesis in error. Familywise error rate (FWER) is the probability of making at least one false discovery during an inference process. The expected FWER grows exponentially with the number of hypothesis tests that are performed, almost guaranteeing that an error will be committed if the number of tests is big enough and the risk is not managed; a problem known as the multiple testing problem. State-of-the-art methods for controlling FWER in multiple comparison settings require that the set of hypotheses be predetermined. This greatly hinders statistical testing for many modern applications of statistical inference, such as model selection, because neither the set of hypotheses that will be tested, nor even the number of hypotheses, can be known in advance.

Association discovery is a fundamental data mining task. The primary statistical approach to association discovery between variables is log-linear analysis. Classical approaches to log-linear analysis do not scale beyond about ten variables. We have recently shown that, if we ensure that the graph supporting the log-linear model is chordal, log-linear analysis can be applied to datasets with hundreds of variables without sacrificing the statistical soundness [21]. However, further scalability remained limited, because state-of-the-art techniques have to examine every edge at every step of the search. This paper makes the following contributions: 1) we prove that only a very small subset of edges has to be considered at each step of the search; 2) we demonstrate how to efficiently find this subset of edges and 3) we show how to efficiently keep track of the best edges to be subsequently added to the initial model. Our experiments, carried out on real datasets with up to 2000 variables, show that our contributions make it possible to gain about 4 orders of magnitude, making log-linear analysis of datasets with thousands of variables possible in seconds instead of days.

Log-linear analysis is the primary statistical approach to discovering conditional dependencies between the variables of a dataset. A good log-linear analysis method requires both high precision and statistical efficiency. High precision means that the risk of false discoveries should be kept very low. Statistical efficiency means that the method should discover actual associations with as few samples as possible. Classical approaches to log-linear analysis make use of χ2tests to control this balance between quality and complexity. We present an information-theoretic approach to log-linear analysis. We show that our approach 1) requires significantly fewer samples to discover the true associations than statistical approaches -- statistical efficiency -- 2) controls for the risk of false discoveries as well as statistical approaches -- high precision - and 3) can perform the discovery on datasets with hundreds of variables on a standard desktop computer -- computational efficiency.

Recent years have seen significant progress in improving both the efficiency and effectiveness of time series classification. However, because the best solution is typically the Nearest Neighbor algorithm with the relatively expensive Dynamic Time Warping as the distance measure, successful deployments on resource constrained devices remain elusive. Moreover, the recent explosion of interest in wearable devices, which typically have limited computational resources, has created a growing need for very efficient classification algorithms. A commonly used technique to glean the benefits of the Nearest Neighbor algorithm, without inheriting its undesirable time complexity, is to use the Nearest Centroid algorithm. However, because of the unique properties of (most) time series data, the centroid typically does not resemble any of the instances, an unintuitive and underappreciated fact. In this work we show that we can exploit a recent result to allow meaningful averaging of 'warped' times series, and that this result allows us to create ultra-efficient Nearest 'Centroid' classifiers that are at least as accurate as their more lethargic Nearest Neighbor cousins.

Discretization of streaming data has received surprisingly little attention. This might be because streaming data require incremental discretization with cut points that may vary over time and this is perceived as undesirable. We argue, to the contrary, that it can be desirable for a discretization to evolve in synchronization with an evolving data stream, even when the learner assumes that attribute values' meanings remain invariant over time. We examine the issues associated with discretization in the context of distribution drift and develop computationally efficient incremental discretization algorithms. We show that discretization can reduce the error of a classical incremental learner and that allowing a discretization to drift in synchronization with distribution drift can further reduce error.

We propose an alternative parameterization of Logistic Regression (LR) for the categorical data, multi-class setting. LR optimizes the conditional log-likelihood over the training data and is based on an iterative optimization procedure to tune this objective function. The optimization procedure employed may be sensitive to scale and hence an effective pre-conditioning method is recommended. Many problems in machine learning involve arbitrary scales or categorical data (where simple standardization of features is not applicable). The problem can be alleviated by using optimization routines that are invariant to scale such as (second-order) Newton methods. However, computing and inverting the Hessian is a costly procedure and not feasible for big data. Thus one must often rely on first-order methods such as gradient descent (GD), stochastic gradient descent (SGD) or approximate second-order such as quasi-Newton (QN) routines, which are not invariant to scale. This paper proposes a simple yet effective pre-conditioner for speeding-up LR based on naive Bayes conditional probability estimates. The idea is to scale each attribute by the log of the conditional probability of that attribute given the class. This formulation substantially speeds-up LR's convergence. It also provides a weighted naive Bayes formulation which yields an effective framework for hybrid generative-discriminative classification.

Pattern discovery is a core data mining activity. Initial approaches were dominated by the frequent pattern discovery paradigm -- only patterns that occur frequently in the data were explored. Having been thoroughly researched and its limitations now well understood, this paradigm is giving way to a new one, which can be called statistically sound pattern discovery. In this paradigm, the main impetus is to discover statistically significant patterns, which are unlikely to have occurred by chance and are likely to hold in future data. Thus, the new paradigm provides a strict control over false discoveries and overfitting.

When data-driven improvements involve personally identifiable data, or even data that can be used to infer sensitive information about individuals, we face the dilemma that we potentially risk compromising privacy. As we see increased emphasis on using data mining to effect improvements in a range of socially beneficial activities, from improving matching of talented students to opportunities for higher education, or improving allocation of funds across competing school programs, or reducing hospitalization time following surgery, the dilemma can often be especially acute. The data involved often is personally identifiable or revealing and sensitive, and many of the institutions that must be involved in gathering and maintaining custody of the data are not equipped to adequately secure the data, raising the risk of privacy breaches. How should we approach this trade-off? Can we assess the risks? Can we control or mitigate them? Can we develop guidelines for when the risk is or is not worthwhile, and for how best to handle data in different common scenarios? Chairs Raghu Ramakrishnan and Geoffrey I. Webb bring this panel of leading data miners and privacy experts together to address these critical issues.

Association discovery is a fundamental data mining task. The primary statistical approach to association discovery between variables is log-linear analysis. Classical approaches to log-linear analysis do not scale beyond about ten variables. We develop an efficient approach to log-linear analysis that scales to hundreds of variables by melding the classical statistical machinery of log-linear analysis with advanced data mining techniques from association discovery and graphical modeling.

No abstract available.

Self-sufficient itemsets have been proposed as an effective approach to summarizing the key associations in data. However, their computation appears highly demanding, as assessing whether an itemset is self-sufficient requires consideration of all pairwise partitions of the itemset into pairs of subsets as well as consideration of all supersets. This article presents the first published algorithm for efficiently discovering self-sufficient itemsets. This branch-and-bound algorithm deploys two powerful pruning mechanisms based on upper bounds on itemset value and statistical significance level. It demonstrates that finding top- k productive and nonredundant itemsets, with postprocessing to identify those that are not independently productive, can efficiently identify small sets of key associations. We present extensive evaluation of the strengths and limitations of the technique, including comparisons with alternative approaches to finding the most interesting associations.

Self-sufficient itemsets are those whose frequency cannot be explained solely by the frequency of either their subsets or of their supersets. We argue that itemsets that are not self-sufficient will often be of little interest to the data analyst, as their frequency should be expected once that of the itemsets on which their frequency depends is known. We present tests for statistically sound discovery of self-sufficient itemsets, and computational techniques that allow those tests to be applied as a post-processing step for any itemset discovery algorithm. We also present a measure for assessing the degree of potential interest in an itemset that complements these statistical measures.

With this issue, Data Mining and Knowledge Discovery celebrates 10 years of publication.Data Mining is arguably the most successful area of research to emerge from Artificial Intelligence.It has had a major impact in industry and society.At the same time, research in the field has achieved tremendous advances.These advances continue apace, and the field remains as active and innovative as ever.This journal has grown alongside the research field it serves.As the premier journal on Data Mining, DMKD has helped foster the discipline and has in turn been nurtured by the discipline's growth and strength, leading to its current high impact rating of 2.105.The journal has a proud record of high standards, provides rapid assessment of submissions and allows authors to retain copyright of their published articles.To mark this tenth anniversary, we have invited some of the field's leading contributors to provide position papers on topics of their choice.They have been asked to share their insights without the usual emphasis on theoretical and empirical evidence.Each of the six contributions has exploited this opportunity in a different and interesting way.Faloutsos and Megalooikonomou (this issue) argue that compression and Kolmogorov Complexity provide unifying frameworks for the field of data mining and explore the consequences that follow from that viewpoint.Domingos (this issue) argues for the need to augment traditional data mining processes with a capacity to utilize more knowledge.He provides a summary

We conduct a large-scale comparative study on linearly combining superparent-one-dependence estimators (SPODEs), a popular family of seminaive Bayesian classifiers. Altogether, 16 model selection and weighing schemes, 58 benchmark data sets, and various statistical tests are employed. This paper's main contributions are threefold. First, it formally presents each scheme's definition, rationale, and time complexity and hence can serve as a comprehensive reference for researchers interested in ensemble learning. Second, it offers bias-variance analysis for each scheme's classification error performance. Third, it identifies effective schemes that meet various needs in practice. This leads to accurate and fast classification algorithms which have an immediate and significant impact on real-world applications. Another important feature of our study is using a variety of statistical tests to evaluate multiple learning methods across multiple data sets.

In many applications, association rules will only be interesting if they represent non-trivial correlations between all constituent items. Numerous techniques have been developed that seek to avoid false discoveries. However, while all provide useful solutions to aspects of this problem, none provides a generic solution that is both flexible enough to accommodate varying definitions of true and false discoveries and powerful enough to provide strict control over the risk of false discoveries. This paper presents generic techniques that allow definitions of true and false discoveries to be specified in terms of arbitrary statistical hypothesis tests and which provide strict control over the experiment wise risk of false discoveries.

Considerable progress has been made on how to reduce the number of spurious exploratory rules with quantitative attributes. However, little has been done for rules with undiscretized quantitative attributes. It is argued that propositional rules can not effectively describe the interactions between quantitative and qualitative attributes. Aumann and Lindell proposed quantitative association rules to provide a better description of such relationship, together with a rule pruning techniques. Since their technique is based on the frequent itemset framework, it is not suitable for rule discovery in large, dense databases. In this paper, an efficient technique for automatically discarding insignificant rules during rule discovery is proposed, based on the OPUS search algorithm. Experiments demonstrate that the algorithm we propose can efficiently remove potentially uninteresting rules even in very large, dense databases.

Ensemble learning strategies, especially boosting and bagging decision trees, have demonstrated impressive capacities to improve the prediction accuracy of base learning algorithms. Further gains have been demonstrated by strategies that combine simple ensemble formation approaches. We investigate the hypothesis that the improvement in accuracy of multistrategy approaches to ensemble learning is due to an increase in the diversity of ensemble members that are formed. In addition, guided by this hypothesis, we develop three new multistrategy ensemble learning techniques. Experimental results in a wide variety of natural domains suggest that these multistrategy ensemble learning techniques are, on average, more accurate than their component ensemble learning techniques.

Understanding the differences between contrasting groups is a fundamental task in data analysis. This realization has led to the development of a new special purpose data mining technique, contrast-set mining. We undertook a study with a retail collaborator to compare contrast-set mining with existing rule-discovery techniques. To our surprise we ob-served that straightforward application of an existing com-mercial rule-discovery system, Magnum Opus, could suc-cessfully perform the contrast-set-mining task. This led to the realization that contrast-set mining is a special case of the more general rule-discovery task. We present the results of our study together with a proof of this conclusion. Categories and Subject Descriptors

We present a method for continuous database marketing that identifies target customers for a number of marketing offers using predictive models. The algorithm then selects the appropriate offer for the customer. Experimental design principles are encapsulated to capture more information that will be used to monitor and refine the predictive models. The updated predictive models are then used for the next round of marketing offers.

The naive Bayes classifier is widely used in interactive applications due to its computational efficiency, direct theoretical base, and competitive accuracy. However its attribute independence assumption can result in sub-optimal accuracy. A number of techniques have explored simple relaxations of the attribute independence assumption in order to increase accuracy. Among these, the lazy Bayesian rule (LBR) and the tree-augmented naive Bayes (TAN) have demonstrated strong prediction accuracy. However their relative performance has never been evaluated. The paper compares and contrasts these two techniques, finding that they have comparable accuracy and hence should be selected according to computational profile. LBR is desirable when small numbers of objects are to be classified while TAN is desirable when large numbers of objects are to be classified.

This paper further develops Aumann and Lindell's [3] proposal for a variant of association rules for which the consequent is a numeric variable. It is argued that these rules can discover useful interactions with numeric data that cannot be discovered directly using traditional association rules with discretization. Alternative measures for identifying interesting rules are proposed. Efficient algorithms are presented that enable these rules to be discovered for dense data sets for which application of Auman and Lindell's algorithm is infeasible.

This paper argues that for some applications direct search for association rules can be more ecient than the tw o stage process of the Apriori algorithm which rst nds large itemsets whic hare then used to iden tify associations.In particular, it is argued, Apriori can impose large computational overheads when the number of frequen titemsets is very large.This will often be the case when association rule analysis is performed on domains other than basket analysis or when it is performed for basket analysis with basket information augmented b y other customer information.An algorithm is presented that is computationally ecient for association rule analyses during which the n um ber of rules to be found can be constrained and all data can be maintained in memory.