Identifying mobility behaviors in rich trajectory data is of great economic and social interest to various applications including urban planning, marketing and intelligence. Existing work on trajectory clustering often relies on similarity measurements that utilize raw spatial and/or temporal information of trajectories. These measures are incapable of identifying similar moving behaviors that exhibit varying spatio-temporal scales of movement. In addition, the expense of labeling massive trajectory data is a barrier to supervised learning models. To address these challenges, we propose an unsupervised neural approach for mobility behavior clustering, called the Deep Embedded TrajEctory ClusTering network (DETECT). DETECT operates in three parts: first it transforms the trajectories by summarizing their critical parts and augmenting them with context derived from their geographical locality (e.g., using POIs from gazetteers). In the second part, it learns a powerful representation of trajectories in the latent space of behaviors, thus enabling a clustering function (such as $k$-means) to be applied. Finally, a clustering oriented loss is directly built on the embedded features to jointly perform feature refinement and cluster assignment, thus improving separability between mobility behaviors. Exhaustive quantitative and qualitative experiments on two real-world datasets demonstrate the effectiveness of our approach for mobility behavior analyses.

The application of unsupervised learning approaches, and in particular of clustering techniques, represents a powerful exploration means for the analysis of network measurements. Discovering underlying data characteristics, grouping similar measurements together, and identifying eventual patterns of interest are some of the applications which can be tackled through clustering. Being unsupervised, clustering does not always provide precise and clear insight into the produced output, especially when the input data structure and distribution are complex and difficult to grasp. In this paper we introduce EXPLAIN-IT, a methodology which deals with unlabeled data, creates meaningful clusters, and suggests an explanation to the clustering results for the end-user. EXPLAIN-IT relies on a novel explainable Artificial Intelligence (AI) approach, which allows to understand the reasons leading to a particular decision of a supervised learning-based model, additionally extending its application to the unsupervised learning domain. We apply EXPLAIN-IT to the problem of YouTube video quality classification under encrypted traffic scenarios, showing promising results.

In this paper, we study correlation clustering under fairness constraints. Fair variants of $k$-median and $k$-center clustering have been studied recently, and approximation algorithms using a notion called fairlet decomposition have been proposed. We obtain approximation algorithms for fair correlation clustering under several important types of fairness constraints. Our results hinge on obtaining a fairlet decomposition for correlation clustering by introducing a novel combinatorial optimization problem. We define a fairlet decomposition with cost similar to the $k$-median cost and this allows us to obtain approximation algorithms for a wide range of fairness constraints. We complement our theoretical results with an in-depth analysis of our algorithms on real graphs where we show that fair solutions to correlation clustering can be obtained with limited increase in cost compared to the state-of-the-art (unfair) algorithms.

Artificial intelligence has been applied in wildfire science and management since the 1990s, with early applications including neural networks and expert systems. Since then the field has rapidly progressed congruently with the wide adoption of machine learning (ML) in the environmental sciences. Here, we present a scoping review of ML in wildfire science and management. Our objective is to improve awareness of ML among wildfire scientists and managers, as well as illustrate the challenging range of problems in wildfire science available to data scientists. We first present an overview of popular ML approaches used in wildfire science to date, and then review their use in wildfire science within six problem domains: 1) fuels characterization, fire detection, and mapping; 2) fire weather and climate change; 3) fire occurrence, susceptibility, and risk; 4) fire behavior prediction; 5) fire effects; and 6) fire management. We also discuss the advantages and limitations of various ML approaches and identify opportunities for future advances in wildfire science and management within a data science context. We identified 298 relevant publications, where the most frequently used ML methods included random forests, MaxEnt, artificial neural networks, decision trees, support vector machines, and genetic algorithms. There exists opportunities to apply more current ML methods (e.g., deep learning and agent based learning) in wildfire science. However, despite the ability of ML models to learn on their own, expertise in wildfire science is necessary to ensure realistic modelling of fire processes across multiple scales, while the complexity of some ML methods requires sophisticated knowledge for their application. Finally, we stress that the wildfire research and management community plays an active role in providing relevant, high quality data for use by practitioners of ML methods.

We study the forecasting of the power consumptions of a population of households and of subpopulations thereof. These subpopulations are built according to location, to exogenous information and/or to profiles we determined from historical households consumption time series. Thus, we aim to forecast the electricity consumption time series at several levels of households aggregation. These time series are linked through some summation constraints which induce a hierarchy. Our approach consists in three steps: feature generation, aggregation and projection. Firstly (feature generation step), we build, for each considering group for households, a benchmark forecast (called features), using random forests or generalized additive models. Secondly (aggregation step), aggregation algorithms, run in parallel, aggregate these forecasts and provide new predictions. Finally (projection step), we use the summation constraints induced by the time series underlying hierarchy to re-conciliate the forecasts by projecting them in a well-chosen linear subspace. We provide some theoretical guaranties on the average prediction error of this methodology, through the minimization of a quantity called regret. We also test our approach on households power consumption data collected in Great Britain by multiple energy providers in the Energy Demand Research Project context. We build and compare various population segmentations for the evaluation of our approach performance.

Cluster algorithms are gaining in popularity due to their compelling ability to identify discrete subgroups in data, and their increasing accessibility in mainstream programming languages and statistical software. While researchers can follow guidelines to choose the right algorithms, and to determine what constitutes convincing clustering, there are no firmly established ways of computing a priori statistical power for cluster analysis. Here, we take a simulation approach to estimate power and classification accuracy for popular analysis pipelines. We systematically varied cluster size, number of clusters, number of different features between clusters, effect size within each different feature, and cluster covariance structure in generated datasets. We then subjected these datasets to common dimensionality reduction approaches (none, multi-dimensional scaling, or uniform manifold approximation and projection) and cluster algorithms (k-means, hierarchical agglomerative clustering with Ward linkage and Euclidean distance, or average linkage and cosine distance, HDBSCAN). Furthermore, we simulated additional datasets to explore the effect of sample size and cluster separation on statistical power and classification accuracy. We found that clustering outcomes were driven by large effect sizes or the accumulation of many smaller effects across features, and were mostly unaffected by differences in covariance structure. Sufficient statistical power can be achieved with relatively small samples (N=20 per subgroup), provided cluster separation is large ({\Delta}=4). Finally, we discuss whether fuzzy clustering (c-means) could provide a more parsimonious alternative for identifying separable multivariate normal distributions, particularly those with lower centroid separation.

We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this information be known a priori. The framework proposed in this article allows for simultaneous estimation of the precision matrices and relationships between the precision matrices, jointly. Sparse and non-sparse estimators are proposed, both of which require solving a non-convex optimization problem. To compute our proposed estimators, we use an iterative algorithm which alternates between a convex optimization problem solved by blockwise coordinate descent and a k-means clustering problem. Blockwise updates for computing the sparse estimator require solving an elastic net penalized precision matrix estimation problem, which we solve using a proximal gradient descent algorithm. We prove that this subalgorithm has a linear rate of convergence. In simulation studies and two real data applications, we show that our method can outperform competitors that ignore relevant relationships between precision matrices and performs similarly to methods which use prior information often uknown in practice.

Conventional survival analysis approaches estimate risk scores or individualized time-to-event distributions conditioned on covariates. In practice, there is often great population-level phenotypic heterogeneity, resulting from (unknown) subpopulations with diverse risk profiles or survival distributions. As a result, there is an unmet need in survival analysis for identifying subpopulations with distinct risk profiles, while jointly accounting for accurate individualized time-to-event predictions. An approach that addresses this need is likely to improve characterization of individual outcomes by leveraging regularities in subpopulations, thus accounting for population-level heterogeneity. In this paper, we propose a Bayesian nonparametrics approach that represents observations (subjects) in a clustered latent space, and encourages accurate time-to-event predictions and clusters (subpopulations) with distinct risk profiles. Experiments on real-world datasets show consistent improvements in predictive performance and interpretability relative to existing state-of-the-art survival analysis models.

Currently, high-dimensional data is ubiquitous in data science, which necessitates the development of techniques to decompose and interpret such multidimensional (aka tensor) datasets. Finding a low dimensional representation of the data, that is, its inherent structure, is one of the approaches that can serve to understand the dynamics of low dimensional latent features hidden in the data. Nonnegative RESCAL is one such technique, particularly well suited to analyze self-relational data, such as dynamic networks found in international trade flows. Nonnegative RESCAL computes a low dimensional tensor representation by finding the latent space containing multiple modalities. Estimating the dimensionality of this latent space is crucial for extracting meaningful latent features. Here, to determine the dimensionality of the latent space with nonnegative RESCAL, we propose a latent dimension determination method which is based on clustering of the solutions of multiple realizations of nonnegative RESCAL decompositions. We demonstrate the performance of our model selection method on synthetic data and then we apply our method to decompose a network of international trade flows data from International Monetary Fund and validate the resulting features against empirical facts from economic literature.

Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a complicated way. To improve interpretability, we consider using a small decision tree to partition a data set into clusters, so that clusters can be characterized in a straightforward manner. We study this problem from a theoretical viewpoint, measuring cluster quality by the $k$-means and $k$-medians objectives: Must there exist a tree-induced clustering whose cost is comparable to that of the best unconstrained clustering, and if so, how can it be found? In terms of negative results, we show, first, that popular top-down decision tree algorithms may lead to clusterings with arbitrarily large cost, and second, that any tree-induced clustering must in general incur an $\Omega(\log k)$ approximation factor compared to the optimal clustering. On the positive side, we design an efficient algorithm that produces explainable clusters using a tree with $k$ leaves. For two means/medians, we show that a single threshold cut suffices to achieve a constant factor approximation, and we give nearly-matching lower bounds. For general $k \geq 2$, our algorithm is an $O(k)$ approximation to the optimal $k$-medians and an $O(k^2)$ approximation to the optimal $k$-means. Prior to our work, no algorithms were known with provable guarantees independent of dimension and input size.