Data clustering is a common unsupervised learning method frequently used in exploratory data analysis. However, identifying relevant structures in unlabeled, high-dimensional data is nontrivial, requiring iterative experimentation with clustering parameters as well as data features and instances. The space of possible clusterings for a typical dataset is vast, and navigating in this vast space is also challenging. The absence of ground-truth labels makes it impossible to define an optimal solution, thus requiring user judgment to establish what can be considered a satisfiable clustering result. Data scientists need adequate interactive tools to effectively explore and navigate the large space of clusterings so as to improve the effectiveness of exploratory clustering analysis. We introduce \textit{Clustrophile 2}, a new interactive tool for guided clustering analysis. \textit{Clustrophile 2} guides users in clustering-based exploratory analysis, adapts user feedback to improve user guidance, facilitates the interpretation of clusters, and helps quickly reason about differences between clusterings. To this end, \textit{Clustrophile 2} contributes a novel feature, the clustering tour, to help users choose clustering parameters and assess the quality of different clustering results in relation to current analysis goals and user expectations. We evaluate \textit{Clustrophile 2} through a user study with 12 data scientists, who used our tool to explore and interpret sub-cohorts in a dataset of Parkinson's disease patients. Results suggest that \textit{Clustrophile 2} improves the speed and effectiveness of exploratory clustering analysis for both experts and non-experts.

Data-driven spatial filtering approaches are commonly used to assess rhythmic brain activity from multichannel recordings such as electroencephalography (EEG). As spatial filter estimation is prone to noise, non-stationarity effects and limited data, a high model variability induced by slight changes of, e.g., involved hyperparameters is generally encountered. These aspects challenge the assessment of functionally relevant features which are of special importance in closed-loop applications as, e.g., in the field of rehabilitation. We propose a data-driven method to identify groups of reliable and functionally relevant oscillatory components computed by a spatial filtering approach. Therefore, we initially embrace the variability of decoding models in a large configuration space before condensing information by density-based clustering of components' functional signatures. Exemplified for a hand force task with rich within-trial structure, the approach was evaluated on EEG data of 18 healthy subjects. We found that functional characteristics of single components are revealed by distinct temporal dynamics of their event-related power changes. Based on a within-subject analysis, our clustering revealed seven groups of homogeneous envelope dynamics on average. To support introspection by practitioners, we provide a set of metrics to characterize and validate single clusterings. We show that identified clusters contain components of strictly confined frequency ranges, dominated by the alpha and beta band. Our method is applicable to any spatial filtering algorithm. Despite high model variability, it allows capturing and monitoring relevant oscillatory features. We foresee its application in closed-loop applications such as brain-computer interface based protocols in stroke rehabilitation.

The recent framework of compressive statistical learning aims at designing tractable learning algorithms that use only a heavily compressed representation-or sketch-of massive datasets. Compressive K-Means (CKM) is such a method: it estimates the centroids of data clusters from pooled, non-linear, random signatures of the learning examples. While this approach significantly reduces computational time on very large datasets, its digital implementation wastes acquisition resources because the learning examples are compressed only after the sensing stage. The present work generalizes the sketching procedure initially defined in Compressive K-Means to a large class of periodic nonlinearities including hardware-friendly implementations that compressively acquire entire datasets. This idea is exemplified in a Quantized Compressive K-Means procedure, a variant of CKM that leverages 1-bit universal quantization (i.e. retaining the least significant bit of a standard uniform quantizer) as the periodic sketch nonlinearity. Trading for this resource-efficient signature (standard in most acquisition schemes) has almost no impact on the clustering performances, as illustrated by numerical experiments.

Feature engineering plays an important role in the success of a machine learning model. Most of the effort in training a model goes into data preparation and choosing the right representation. In this paper, we propose a robust feature engineering method, Randomized Union of Locally Linear Subspaces (RULLS). We generate sparse, non-negative, and rotation invariant features in an unsupervised fashion. RULLS aggregates features from a random union of subspaces by describing each point using globally chosen landmarks. These landmarks serve as anchor points for choosing subspaces. Our method provides a way to select features that are relevant in the neighborhood around these chosen landmarks. Distances from each data point to $k$ closest landmarks are encoded in the feature matrix. The final feature representation is a union of features from all chosen subspaces. The effectiveness of our algorithm is shown on various real-world datasets for tasks such as clustering and classification of raw data and in the presence of noise. We compare our method with existing feature generation methods. Results show a high performance of our method on both classification and clustering tasks.

HIV RNA viral load (VL) is an important outcome variable in studies of HIV infected persons. There exists only a handful of methods which classify patients by viral load patterns. Most methods place limits on the use of viral load measurements, are often specific to a particular study design, and do not account for complex, temporal variation. To address this issue, we propose a set of four unambiguous computable characteristics (features) of time-varying HIV viral load patterns, along with a novel centroid-based classification algorithm, which we use to classify a population of 1,576 HIV positive clinic patients into one of five different viral load patterns (clusters) often found in the literature: durably suppressed viral load (DSVL), sustained low viral load (SLVL), sustained high viral load (SHVL), high viral load suppression (HVLS), and rebounding viral load (RVL). The centroid algorithm summarizes these clusters in terms of their centroids and radii. We show that this allows new viral load patterns to be assigned pattern membership based on the distance from the centroid relative to its radius, which we term radial normalization classification. This method has the benefit of providing an objective and quantitative method to assign viral load pattern membership with a concise and interpretable model that aids clinical decision making. This method also facilitates meta-analyses by providing computably distinct HIV categories. Finally we propose that this novel centroid algorithm could also be useful in the areas of cluster comparison for outcomes research and data reduction in machine learning.

Minimum sum-of-squares clustering (MSSC) is a widely used clustering model, of which the popular K-means algorithm constitutes a local minimizer. It is well known that the solutions of K-means can be arbitrarily distant from the true MSSC global optimum, and dozens of alternative heuristics have been proposed for this problem. However, no other algorithm has been commonly adopted in the literature. This may be related to differences of computational effort, or to the assumption that a better solution of the MSSC has only a minor impact on classification or generalization capabilities. In this article, we dispute this belief. We introduce an efficient population-based metaheuristic that uses K-means as a local search in combination with problem-tailored crossover, mutation, and diversification operators. This algorithm can be interpreted as a multi-start K-means, in which the initial center positions are carefully sampled based on the search history. The approach is scalable and accurate, outperforming all recent state-of-the-art algorithms for MSSC in terms of solution quality, measured by the depth of local minima. This enhanced accuracy leads to classification results which are significantly closer to the ground truth than those of other algorithms, for overlapping Gaussian-mixture datasets with a large number of features and clusters. Therefore, improved global optimization methods appear to be essential to better exploit the MSSC model in high dimension.

During the last decades Network Science field has been rediscovered and addressed as the "new science" [2], [3]. A lot of issues have been (re-)examined thanks to Network Science techniques, which are nowadays permeating the way we face the world as a unique interconnected component. The presence and the immediate availability of a huge amount of digital data describing every kind of network and the way in which its nodes interact, has made possible an interdisciplinary analysis of many large-scale systems. Similar techniques have been recently applied also to professional sports, in order to discover complex interactions phenomena and universal rules which are almost invisible and difficult to recognize restricting the attention to small networks or to microscopic level. For example, complexnetwork analysis were conducted on soccer (e.g. in [4] and [5]), football ([6] and [7]), basket ([8] and [9]), baseball ([10]) and cricket ([11] and [12]), just to name a few. In professional tennis as well, there are few studies examining how to map matches into complex networks and then developing new ranking methods alternative to the ATP (Association of Tennis Professionals) official one. The first work of this kind is represented by [13], where the authors explained the network generation and then they performed some simple analysis on single Grand Slams tournaments matches only (i.e.

We present ElPiGraph, a method for approximating data distributions having non-trivial topological features such as the existence of excluded regions or branching structures. Unlike many existing methods, ElPiGraph is not based on the construction of a k-nearest neighbour graph, a procedure that can perform poorly in the case of multidimensional and noisy data. Instead, ElPiGraph constructs elastic principal graphs in a more robust way by minimizing elastic energy, applying graph grammars and explicitly controlling topological complexity. Using trimmed approximation error function makes ElPiGraph extremely robust to the presence of background noise without decreasing computational performance and allows it to deal with complex cases of manifold learning (for example, ElPiGraph can learn disconnected intersecting manifolds). Thanks to the quasi-quadratic nature of the elastic function, ElPiGraph performs almost as fast as a simple k-means clustering and, therefore, is much more scalable than alternative methods, and can work on large datasets containing millions of high dimensional points on a personal computer. The excellent performance of the method opens the possibility to apply resampling and to approximate complex data structures via principal graph ensembles which can be used to construct consensus principal graphs. ElPiGraph is currently implemented in five programming languages and accompanied by a graphical user interface, which makes it a versatile tool to deal with complex data in various fields from molecular biology, where it can be used to infer pseudo-time trajectories from single-cell RNASeq, to astronomy, where it can be used to approximate complex structures in the distribution of galaxies.

We show a sufficient condition on the dissimilarity measure that leads to the consistency of the algorithms for clustering offline and online data settings, respectively. As an example of application, clustering synthetic data sampled from multifractional Brownian motions is provided.

A key aspect of a sustainable urban transportation system is the effectiveness of transportation policies. To be effective, a policy has to consider a broad range of elements, such as pollution emission, traffic flow, and human mobility. Due to the complexity and variability of these elements in the urban area, to produce effective policies remains a very challenging task. With the introduction of the smart city paradigm, a widely available amount of data can be generated in the urban spaces. Such data can be a fundamental source of knowledge to improve policies because they can reflect the sustainability issues underlying the city. In this context, we propose an approach to exploit urban positioning data based on stigmergy, a bio-inspired mechanism providing scalar and temporal aggregation of samples. By employing stigmergy, samples in proximity with each other are aggregated into a functional structure called trail. The trail summarizes relevant dynamics in data and allows matching them, providing a measure of their similarity. Moreover, this mechanism can be specialized to unfold specific dynamics. Specifically, we identify high-density urban areas (i.e hotspots), analyze their activity over time, and unfold anomalies. Moreover, by matching activity patterns, a continuous measure of the dissimilarity with respect to the typical activity pattern is provided. This measure can be used by policy makers to evaluate the effect of policies and change them dynamically. As a case study, we analyze taxi trip data gathered in Manhattan from 2013 to 2015.