Accelerating Kernel Neural Gas

Basic program for a significance test for two clusters in euclidean space as measured by their overlap

The interstitial space in a cluster of spheres is examined to determine the largest sphere that can be placed in its voids. A method is given for obtaining the interstitial sphere belonging to a group of arbitrarily arranged spheres by examining tetrahedral configurations. Given the coordinates of the centers and the radii of the spheres of a tetrahedral group, the coordinates and radius of the tetrahedral interstitial sphere can be found. The method can be applied to interstices of any coordination number. It is applicable to sphere packings with or without crystallographic symmetry.

Rooted Mahalanobis distance based Gustafson-Kessel fuzzy C-means

In this paper we present an active learning approach used to create an annotated corpus of literal and nonliteral usages of verbs. The model uses nearly unsupervised word-sense disambiguation and clustering techniques. We report on experiments in which a human expert is asked to correct system predictions in different stages of learning: (i) after the last iteration when the clustering step has converged, or (ii) during each iteration of the clustering algorithm. The model obtains an f-score of 53.8% on a dataset in which literal/nonliteral usages of 25 verbs were annotated by human experts. In comparison, the same model augmented with active learning obtains 64.91%. We also measure the number of examples required when model confidence is used to select examples for human correction as compared to random selection. The results of this active learning system have been compiled into a freely available annotated corpus of literal/nonliteral usage of verbs in context.

This paper discusses two cluster validity indices that quantify the quality of a putative clustering in terms of label-homogeneity and connectivity. Because the indices are defined in terms of local data-density, they do not favour spherical or ellipsoidal clusters as other validity indices tend to do. A statistics-based decision framework is outlined that uses these indices to decide on the correct number of clusters.

Labeling data to train visual concept classifiers requires significant human effort. Active learning addresses labeling overhead by selecting a meaningful subset of data, but often these approaches assume that the set of visual concepts is known in advance. Clustering approaches perform bottom-up discovery of concepts, and reduce labeling effort by moving from instance-based to group-based labeling. Unfortunately, clustering techniques assume a one-to-one mapping between clusters and visual concepts even though learned groups are often not coherent and fail to represent all concepts. We introduce Selective Guidance, a technique that hierarchically clusters data and selectively queries labels of coherent clusters representing different visual concepts. Unlike most active learning and clustering techniques, Selective Guidance does not require any a priori knowledge. Using benchmark data sets we show that Selective Guidance achieves classification accuracy better than active learning and clustering approaches with fewer labeling queries.

Pastoralists' settlement patterns in Kenya have been studied for decades using various statistical and mathematical models. However, traditional models have often relied on restrictive assumptions, such as the normality of the data or the linearity of relationships. In this paper, we apply a Bayesian nonparametric approach to model the settlement patterns of pastoralists in Kenya, allowing for more flexible and realistic representations of the data. We first collected settlement data for pastoralists in Kenya and compiled a database of environmental covariates, such as distance to water sources, vegetation cover, and road networks. We then applied a Bayesian nonparametric clustering method to identify distinct settlement patterns and tested the performance of the model against other commonly used clustering techniques. Our results indicate that the Bayesian nonparametric approach outperforms other clustering techniques in terms of model fit and accuracy in identifying distinct settlement patterns. Additionally, we conducted a spatial regression analysis to investigate the relationship between settlement patterns and environmental covariates, revealing that distance to water sources and road networks are significant predictors of settlement patterns. Overall, our study highlights the usefulness of Bayesian nonparametric methods in modelling settlement patterns of pastoralists in Kenya and provides valuable insights into the relationship between environmental factors and settlement patterns.

31 Nonparametric methods in directional data analysis

Bibliometric reviews of research have gained increased popularity since the mid-2010s. Yet, many readers may be uncertain as to the purpose and method of bibliometric reviews. This article provides an introduction to bibliometric review methods, clarifying their purpose, as well as methods of data collection, analysis, and interpretation. The latter portion of the article is devoted to a state-of-the-science, bibliometric review of research on problem-based learning. In this review, the author applied descriptive statistics, citation analysis, and co-citation analysis to a database of 5,764 Scopus-indexed documents on problem-based learning published between 2017 and 2021. The analyses found increasing diversity of the PBL knowledge base with respect to both geographical, subject area origins, and focus of the research when compared with findings reported in past reviews. Author co-citation analysis visualized the intellectual structure of this recent PBL literature revealing four dominant schools of thought: Interdisciplinary PBL Theory and Practice, Active Learning, Social and Experiential Learning, PBL Process. This finding highlights the increasing integration of PBL with other methods of experiential and active learning.

Clustering multi-dimensional points is a fundamental task in many fields, and density-based clustering supports many applications because it can discover clusters of arbitrary shapes. This article addresses the problem of Density-Peaks Clustering (DPC) in Euclidean space. DPC already has many applications, but its straightforward implementation incurs O ( n 2 ) time, where n is the number of points, thereby does not scale to large datasets. To enable DPC on large datasets, we first propose empirically efficient exact DPC algorithm, Ex-DPC. Although this algorithm is much faster than the straightforward implementation, it still suffers from O ( n 2 ) time theoretically. We hence propose a new exact algorithm, Ex-DPC++, that runs in o ( n 2 ) time. We accelerate their efficiencies by leveraging multi-threading. Moreover, real-world datasets may have arbitrary updates (point insertions and deletions). It is hence important to support efficient cluster updates. To this end, we propose D-DPC for fully dynamic DPC. We conduct extensive experiments using real datasets, and our experimental results demonstrate that our algorithms are efficient and scalable.

The standard Coupling From The Past (CFTP) algorithm is an interesting tool to sample from exact stationary distribution of a Markov chain. But it is very expensive in time consuming for large chains. There is a monotone version of CFTP, called MCFTP, that is less time consuming for monotone chains. In this work, we propose two techniques to get monotone chain allowing use of MCFTP: widening technique based on adding two fictitious states and clustering technique based on partitioning the state space in clusters. Usefulness and efficiency of our approaches are showed through a sample of Markov Chain Monte Carlo simulations.

Representing the reservoir as a network of discrete compartments with neighbor and non-neighbor connections is a fast, yet accurate method for analyzing oil and gas reservoirs. Automatic and rapid detection of coarse-scale compartments with distinct static and dynamic properties is an integral part of such high-level reservoir analysis. In this work, we present a hybrid framework specific to reservoir analysis for an automatic detection of clusters in space using spatial and temporal field data, coupled with a physics-based multiscale modeling approach. A novel and rigorous non-local formulation for flow in porous media is presented, in which the reservoir is represented by an adjacency matrix describing the connectivities of comprising compartments. We automatically divide the reservoir into a number of distinct compartments, in which the direction-dependent multiphase flow communication is a function of non-local phase potential differences. Our proposed clustering framework begins with a mixed-type raw dataset which can be categorical/numerical, spatial/temporal, and discrete/continuous. The dataset can contain noisy/missing values of different data types including but not limited to well production/injection history, well location, well type, geological features, PVT measurements, perforation data, etc. Unsupervised clustering techniques suited to the input data types (e.g. k-prototypes, spectral, Gaussian Mixtures, and hierarchical clustering), and appropriate distance measures (such as Euclidean distance, soft dynamic time warping, and mode) are used. The input data is standardized, and upon convergence check, the best clustering representation is obtained. Finally, Support-Vector-Machine technique is utilized in the kernel space to trace a demarcating hyperplane for the clusters. The proposed framework is successfully applied to more than five mature fields in the Middle East, South and North America, each with more than a thousand wells. In a specific case study reported here, the proposed workflow is applied to a major field with a couple of hundreds of wells with more than 40 years of production history. Leveraging the fast forward model, an efficient ensemble-based history matching framework is applied to reduce the uncertainty of the global reservoir parameters such as inter-blocks and aquifer-reservoir communications, fault transmissibilities, and block-based oil in place. The ensemble of history matched models are then used to provide a probabilistic forecast for different field development scenarios. In addition, the clustering framework enables us to treat missing data and use the augmented dataset for improving the clustering accuracy. In summary, in this work a novel hybrid approach is presented in which we couple a physics-based non-local modeling framework with data-driven clustering techniques to provide a fast and accurate multiscale modeling of compartmentalized reservoirs. This research also adds to the literature by presenting a comprehensive work on spatio-temporal clustering for reservoir studies applications that well considers the clustering complexities, the intrinsic sparse and noisy nature of the data, and the interpretability of the outcome.

Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of model-based methods, in this article, we study model-free subsampling methods, which aim to identify a subsample, that is, not confined by model assumptions. Existing model-free subsampling methods are usually built upon clustering techniques or kernel tricks. Most of these methods suffer from either a large computational burden or a theoretical weakness. In particular, the theoretical weakness is that the empirical distribution of the selected subsample may not necessarily converge to the population distribution. Such computational and theoretical limitations hinder the broad applicability of model-free subsampling methods in practice. We propose a novel model-free subsampling method by using optimal transport techniques. Moreover, we develop an efficient subsampling algorithm, that is, adaptive to the unknown probability density function. Theoretically, we show the selected subsample can be used for efficient density estimation by deriving the convergence rate for the proposed subsample kernel density estimator. We also provide the optimal bandwidth for the proposed estimator. Numerical studies on synthetic and real-world datasets demonstrate the performance of the proposed method is superior.

Electronic structure and optical property of semiconductor nanocrystallites

Active learning with fairness-aware clustering for fair classification considering multiple sensitive attributes