Clustering points in a vector space or nodes in a graph is a ubiquitous primitive in statistical data analysis, and it is commonly used for exploratory data analysis. In practice, it is often of interest to "refine" or "improve" a given cluster that has been obtained by some other method. In this survey, we focus on principled algorithms for this cluster improvement problem. Many such cluster improvement algorithms are flow-based methods, by which we mean that operationally they require the solution of a sequence of maximum flow problems on a (typically implicitly) modified data graph. These cluster improvement algorithms are powerful, both in theory and in practice, but they have not been widely adopted for problems such as community detection, local graph clustering, semi-supervised learning, etc. Possible reasons for this are: the steep learning curve for these algorithms; the lack of efficient and easy to use software; and the lack of detailed numerical experiments on real-world data that demonstrate their usefulness. Our objective here is to address these issues. To do so, we guide the reader through the whole process of understanding how to implement and apply these powerful algorithms. We present a unifying fractional programming optimization framework that permits us to distill, in a simple way, the crucial components of all these algorithms. It also makes apparent similarities and differences between related methods. Viewing these cluster improvement algorithms via a fractional programming framework suggests directions for future algorithm development. Finally, we develop efficient implementations of these algorithms in our LocalGraphClustering Python package, and we perform extensive numerical experiments to demonstrate the performance of these methods on social networks and image-based data graphs.

Learning arguments is highly relevant to the field of explainable artificial intelligence. It is a family of symbolic machine learning techniques that is particularly human-interpretable. These techniques learn a set of arguments as an intermediate representation. Arguments are small rules with exceptions that can be chained to larger arguments for making predictions or decisions. We investigate the learning of arguments, specifically the learning of arguments from a 'case model' proposed by Verheij [34]. The case model in Verheij's approach are cases or scenarios in a legal setting. The number of cases in a case model are relatively low. Here, we investigate whether Verheij's approach can be used for learning arguments from other types of data sets with a much larger number of instances. We compare the learning of arguments from a case model with the HeRO algorithm [15] and learning a decision tree.

We propose a general approach for distance based clustering, using the gradient of the cost function that measures clustering quality with respect to cluster assignments and cluster center positions. The approach is an iterative two step procedure (alternating between cluster assignment and cluster center updates) and is applicable to a wide range of functions, satisfying some mild assumptions. The main advantage of the proposed approach is a simple and computationally cheap update rule. Unlike previous methods that specialize to a specific formulation of the clustering problem, our approach is applicable to a wide range of costs, including non-Bregman clustering methods based on the Huber loss. We analyze the convergence of the proposed algorithm, and show that it converges to the set of appropriately defined fixed points, under arbitrary center initialization. In the special case of Bregman cost functions, the algorithm converges to the set of centroidal Voronoi partitions, which is consistent with prior works. Numerical experiments on real data demonstrate the effectiveness of the proposed method.

Learning is a distinctive feature of intelligent behaviour. High-throughput experimental data and Big Data promise to open new windows on complex systems such as cells, the brain or our societies. Yet, the puzzling success of Artificial Intelligence and Machine Learning shows that we still have a poor conceptual understanding of learning. These applications push statistical inference into uncharted territories where data is high-dimensional and scarce, and prior information on "true" models is scant if not totally absent. Here we review recent progress on understanding learning, based on the notion of "relevance". The relevance, as we define it here, quantifies the amount of information that a dataset or the internal representation of a learning machine contains on the generative model of the data. This allows us to define maximally informative samples, on one hand, and optimal learning machines on the other. These are ideal limits of samples and of machines, that contain the maximal amount of information about the unknown generative process, at a given resolution (or level of compression). Both ideal limits exhibit critical features in the statistical sense: Maximally informative samples are characterised by a power-law frequency distribution (statistical criticality) and optimal learning machines by an anomalously large susceptibility. The trade-off between resolution (i.e. compression) and relevance distinguishes the regime of noisy representations from that of lossy compression. These are separated by a special point characterised by Zipf's law statistics. This identifies samples obeying Zipf's law as the most compressed loss-less representations that are optimal in the sense of maximal relevance. Criticality in optimal learning machines manifests in an exponential degeneracy of energy levels, that leads to unusual thermodynamic properties.

This article discusses a particular case of the data clustering problem, where it is necessary to find groups of adjacent text segments of the appropriate length that match a fuzzy pattern represented as a sequence of fuzzy properties. To solve this problem, a heuristic algorithm for finding a sufficiently large number of solutions is proposed. The key idea of the proposed algorithm is the use of the prefix structure to track the process of mapping text segments to fuzzy properties. An important special case of the text segmentation problem is the fuzzy string matching problem, when adjacent text segments have unit length and, accordingly, the fuzzy pattern is a sequence of fuzzy properties of text characters. It is proven that the heuristic segmentation algorithm in this case finds all text segments that match the fuzzy pattern. Finally, we consider the problem of a best segmentation of the entire text based on a fuzzy pattern, which is solved using the dynamic programming method.

Random partition models are widely used in Bayesian methods for various clustering tasks, such as mixture models, topic models, and community detection problems. While the number of clusters induced by random partition models has been studied extensively, another important model property regarding the balancedness of cluster sizes has been largely neglected. We formulate a framework to define and theoretically study the balancedness of exchangeable random partition models, by analyzing how a model assigns probabilities to partitions with different levels of balancedness. We demonstrate that the "rich-get-richer" characteristic of many existing popular random partition models is an inevitable consequence of two common assumptions: product-form exchangeability and projectivity. We propose a principled way to compare the balancedness of random partition models, which gives a better understanding of what model works better and what doesn't for different applications. We also introduce the "rich-get-poorer" random partition models and illustrate their application to entity resolution tasks.

A major archetype of artificial intelligence is developing algorithms facilitating temporal efficiency and accuracy while boosting the generalization performance. Even with the latest developments in machine learning, a key limitation has been the inefficient feature extraction from the initial data, which is essential in performance optimization. Here, we introduce a feature extraction method inspired by sensory cortical networks in the brain. Dubbed as bioinspired cortex, the algorithm provides convergence to orthogonal features from streaming signals with superior computational efficiency while processing data in compressed form. We demonstrate the performance of the new algorithm using artificially created complex data by comparing it with the commonly used traditional clustering algorithms, such as Birch, GMM, and K-means. While the data processing time is significantly reduced, seconds versus hours, encoding distortions remain essentially the same in the new algorithm providing a basis for better generalization. Although we show herein the superior performance of the cortex model in clustering and vector quantization, it also provides potent implementation opportunities for machine learning fundamental components, such as reasoning, anomaly detection and classification in large scope applications, e.g., finance, cybersecurity, and healthcare.

This paper tackles the problem of missing data imputation for noisy and non-Gaussian data. A classical imputation method, the Expectation Maximization (EM) algorithm for Gaussian mixture models, has shown interesting properties when compared to other popular approaches such as those based on k-nearest neighbors or on multiple imputations by chained equations. However, Gaussian mixture models are known to be not robust to heterogeneous data, which can lead to poor estimation performance when the data is contaminated by outliers or come from a non-Gaussian distributions. To overcome this issue, a new expectation maximization algorithm is investigated for mixtures of elliptical distributions with the nice property of handling potential missing data. The complete-data likelihood associated with mixtures of elliptical distributions is well adapted to the EM framework thanks to its conditional distribution, which is shown to be a Student distribution. Experimental results on synthetic data demonstrate that the proposed algorithm is robust to outliers and can be used with non-Gaussian data. Furthermore, experiments conducted on real-world datasets show that this algorithm is very competitive when compared to other classical imputation methods.

With the rapid expansion of urban areas and the increasingly use of electricity, the need for locating buried cables is becoming urgent. In this paper, a noval method to locate underground cables based on Ground Penetrating Radar (GPR) and Gaussian-process regression is proposed. Firstly, the coordinate system of the detected area is conducted, and the input and output of locating buried cables are determined. The GPR is moved along the established parallel detection lines, and the hyperbolic signatures generated by buried cables are identified and fitted, thus the positions and depths of some points on the cable could be derived. On the basis of the established coordinate system and the derived points on the cable, the clustering method and cable fitting algorithm based on Gaussian-process regression are proposed to find the most likely locations of the underground cables. Furthermore, the confidence intervals of the cable's locations are also obtained. Both the position and depth noises are taken into account in our method, ensuring the robustness and feasibility in different environments and equipments. Experiments on real-world datasets are conducted, and the obtained results demonstrate the effectiveness of the proposed method.

Data available in scholarly knowledge graphs (SKGs) - i.e., "a graph of data intended to accumulate and convey knowledge of the real world, whose nodes represent entities of interest and whose edges represent potentially different relations between these entities" [14] - is growing continuously every day, leading to a plethora of challenges concerning, for instance, article exploration and visualization [17], article recommendation [3], citation recommendation [11], and Author Name Disambiguation (AND) [24], which is relevant for the purposes of the present article. In particular, AND refers to a specific task of entity resolution which aims at resolving author mentions in bibliographic references to real-world people. Author persistent identifiers, such as ORCIDs and VIAFs, simplify the AND activity since such identifiers can be used for reconciling entities defined as different objects and representing the same real-world person. However, the availability of such persistent identifiers in SKGs - such as OpenCitations (OC) [22], AMiner [27] and Microsoft Academic Knowledge Graph (MAKG) [10] - is characterized by very low coverage and, as such, additional and computationally-oriented techniques must be adopted to identify different authors as the same person. In the past, many automatic approaches have been developed to automatically address AND by using publications metadata (e.g., title, abstract, keywords, venue, affiliation, etc.) to extract some features which can be used in the disambiguation task. These methods vary widely from supervised learning methods to unsupervised learning including recently developed deep neural network-based architectures [31]. However, the existing SKGs do not provide all the relevant contextual information necessary to reuse effectively and efficiently such approaches, that often rely on pure textual data. In contrast with the approaches mentioned above, this study focuses on performing AND for scholarly data represented as linked data or included in SKGs by considering the multi-modal information available in such collections, i.e., the structural information consisting of entities and relations between them as well as text or numeric values associated with the authors and publications defined in the form of literals (family name, given name, publication title, venue title, year of publication, etc.). The proposed framework to address this task is named Literally Author Name Disambiguation (LAND), which focuses on tackling the following research questions: - Can Knowledge Graph Embeddings (KGEs) - i.e. a technique that enables the creation of a "dense representation of the graph in a continuous, low-dimensional vector space that can then be used for machine learning tasks"[13] - be used effectively for the downstream task of clustering, more specifically for author name disambiguation?