The implementation of road user models that realistically reproduce a credible behavior in a multi-agentsimulation is still an open problem. A data-driven approach consists on to deduce behaviors that may exist in real situation to obtain different types of trajectories from a large set of observations. The data, and its classification, could then be used to train models capable to extrapolate such behavior. Cars and two different types of Vulnerable Road Users (VRU) will be considered by the trajectory clustering methods proposed: pedestrians and cyclists. The results reported here evaluate methods to extract well-defined trajectory classes from raw data without the use of map information while also separating ''eccentric'' or incomplete trajectories from the ones that are complete and representative in any scenario. Two environments will serve as test for the methods develop, three different intersections and one roundabout. The resulting clusters of trajectories can then be used for prediction or learning tasks or discarded if it is composed by outliers.

In this paper, we present an information-theoretic method for clustering mixed-type data, that is, data consisting of both continuous and categorical variables. The method is a variant of the Deterministic Information Bottleneck algorithm which optimally compresses the data while retaining relevant information about the underlying structure. We compare the performance of the proposed method to that of three well-established clustering methods (KAMILA, K-Prototypes, and Partitioning Around Medoids with Gower's dissimilarity) on simulated and real-world datasets. The results demonstrate that the proposed approach represents a competitive alternative to conventional clustering techniques under specific conditions.

Clustering, informally understood as the grouping of data, is a central task in statistics and computer science with broad applications. Modern clustering algorithms originated in the work of numerical taxonomists, who developed methods to identify hierarchical structures in the classification of plant and animal species. Since then clustering has been used in disciplines such as medicine, astronomy, anthropology, economics, etc., with aims such as exploratory analysis, data summarization, the identification of salient structures in data, and information organization. The notion of a "good" or "accurate" clustering varies between fields and applications. For example, to some computer scientists, the correct clustering of a dataset is often defined as the solution to an optimization problem (think K-means) and a good algorithm either solves or approximates a solution to this problem, ideally with some guarantees [14, 31].

Supervised machine learning methods for geological mapping via remote sensing face limitations due to the scarcity of accurately labelled training data that can be addressed by unsupervised learning, such as dimensionality reduction and clustering. Dimensionality reduction methods have the potential to play a crucial role in improving the accuracy of geological maps. Although conventional dimensionality reduction methods may struggle with nonlinear data, unsupervised deep learning models such as autoencoders can model non-linear relationships. Stacked autoencoders feature multiple interconnected layers to capture hierarchical data representations useful for remote sensing data. This study presents an unsupervised machine learning-based framework for processing remote sensing data using stacked autoencoders for dimensionality reduction and k-means clustering for mapping geological units. We use Landsat 8, ASTER, and Sentinel-2 datasets to evaluate the framework for geological mapping of the Mutawintji region in Western New South Wales, Australia. We also compare stacked autoencoders with principal component analysis and canonical autoencoders. Our results reveal that the framework produces accurate and interpretable geological maps, efficiently discriminating rock units. We find that the accuracy of stacked autoencoders ranges from 86.6 % to 90 %, depending on the remote sensing data type, which is superior to their counterparts. We also find that the generated maps align with prior geological knowledge of the study area while providing novel insights into geological structures.

Establishing the chronology of the Vedas has interested scholars for the last two centuries. The oldest among them is Rig-Veda which has ten Mandalas, each composed separately. In this paper, we look at deciphering plausible pointers to the internal chronology of the Mandalas, by focusing on Gods and Goddesses worshiped in different Mandalas. We apply text analysis to the Mandalas using Clustering Techniques based on Cosine Similarity. Then we represent the association of deities with Mandalas using a grid-based Social Network that is amenable to chronological analysis and demonstrates the benefits of using Social Network Analysis for the problem at hand. Further, we analyze references to rivers to arrive at additional correlations. The approach used can be deployed generically to analyze other kinds of references and mentions and arrive at more substantive inferences.

This study proposes CGRclust, a novel combination of unsupervised twin contrastive clustering of Chaos Game Representations (CGR) of DNA sequences, with convolutional neural networks (CNNs). To the best of our knowledge, CGRclust is the first method to use unsupervised learning for image classification (herein applied to two-dimensional CGR images) for clustering datasets of DNA sequences. CGRclust overcomes the limitations of traditional sequence classification methods by leveraging unsupervised twin contrastive learning to detect distinctive sequence patterns, without requiring DNA sequence alignment or biological/taxonomic labels. CGRclust accurately clustered twenty-five diverse datasets, with sequence lengths ranging from 664 bp to 100 kbp, including mitochondrial genomes of fish, fungi, and protists, as well as viral whole genome assemblies and synthetic DNA sequences. Compared with three recent clustering methods for DNA sequences (DeLUCS, iDeLUCS, and MeShClust v3.0.), CGRclust is the only method that surpasses 81.70% accuracy across all four taxonomic levels tested for mitochondrial DNA genomes of fish. Moreover, CGRclust also consistently demonstrates superior performance across all the viral genomic datasets. The high clustering accuracy of CGRclust on these twenty-five datasets, which vary significantly in terms of sequence length, number of genomes, number of clusters, and level of taxonomy, demonstrates its robustness, scalability, and versatility.

Individual brains vary greatly in morphology, connectivity and organization. The applicability of group-level parcellations is limited by the rapid development of precision medicine today because they do not take into account the variation of parcels at the individual level. Accurate mapping of brain functional regions at the individual level is pivotal for a comprehensive understanding of the variations in brain function and behaviors, early and precise identification of brain abnormalities, as well as personalized treatments for neuropsychiatric disorders. With the development of neuroimaging and machine learning techniques, studies on individual brain parcellation are booming. In this paper, we offer an overview of recent advances in the methodologies of individual brain parcellation, including optimization- and learning-based methods. Comprehensive evaluation metrics to validate individual brain mapping have been introduced. We also review the studies of how individual brain mapping promotes neuroscience research and clinical medicine. Finally, we summarize the major challenges and important future directions of individualized brain parcellation. Collectively, we intend to offer a thorough overview of individual brain parcellation methods, validations, and applications, along with highlighting the current challenges that call for an urgent demand for integrated platforms that integrate datasets, methods, and validations.

Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis. In numerous applications, it is necessary to align and jointly embed multiple datasets from different studies or experimental conditions. Such datasets may share underlying structures of interest but exhibit individual distortions, resulting in misaligned embeddings using traditional techniques. In this work, we propose \textit{Entropic Optimal Transport (EOT) eigenmaps}, a principled approach for aligning and jointly embedding a pair of datasets with theoretical guarantees. Our approach leverages the leading singular vectors of the EOT plan matrix between two datasets to extract their shared underlying structure and align the datasets accordingly in a common embedding space. We interpret our approach as an inter-data variant of the classical Laplacian eigenmaps and diffusion maps embeddings, showing that it enjoys many favorable analogous properties. We then analyze a data-generative model where two observed high-dimensional datasets share latent variables on a common low-dimensional manifold, but each dataset is subject to data-specific translation, scaling, nuisance structures, and noise. We show that in a high-dimensional asymptotic regime, the EOT plan recovers the shared manifold structure by approximating a kernel function evaluated at the locations of the latent variables. Subsequently, we provide a geometric interpretation of our embedding by relating it to the eigenfunctions of population-level operators encoding the density and geometry of the shared manifold. Finally, we showcase the performance of our approach for data integration and embedding through simulations and analyses of real-world biological data, demonstrating its advantages over alternative methods in challenging scenarios.

Facilitated by the powerful feature extraction ability of neural networks, deep clustering has achieved great success in analyzing high-dimensional and complex real-world data. The performance of deep clustering methods is affected by various factors such as network structures and learning objectives. However, as pointed out in this survey, the essence of deep clustering lies in the incorporation and utilization of prior knowledge, which is largely ignored by existing works. From pioneering deep clustering methods based on data structure assumptions to recent contrastive clustering methods based on data augmentation invariances, the development of deep clustering intrinsically corresponds to the evolution of prior knowledge. In this survey, we provide a comprehensive review of deep clustering methods by categorizing them into six types of prior knowledge. We find that in general the prior innovation follows two trends, namely, i) from mining to constructing, and ii) from internal to external. Besides, we provide a benchmark on five widely-used datasets and analyze the performance of methods with diverse priors. By providing a novel prior knowledge perspective, we hope this survey could provide some novel insights and inspire future research in the deep clustering community.

Graph condensation (GC) has recently garnered considerable attention due to its ability to reduce large-scale graph datasets while preserving their essential properties. The core concept of GC is to create a smaller, more manageable graph that retains the characteristics of the original graph. Despite the proliferation of graph condensation methods developed in recent years, there is no comprehensive evaluation and in-depth analysis, which creates a great obstacle to understanding the progress in this field. To fill this gap, we develop a comprehensive Graph Condensation Benchmark (GC-Bench) to analyze the performance of graph condensation in different scenarios systematically. Specifically, GC-Bench systematically investigates the characteristics of graph condensation in terms of the following dimensions: effectiveness, transferability, and complexity. We comprehensively evaluate 12 state-of-the-art graph condensation algorithms in node-level and graph-level tasks and analyze their performance in 12 diverse graph datasets. Further, we have developed an easy-to-use library for training and evaluating different GC methods to facilitate reproducible research. The GC-Bench library is available at https://github.com/RingBDStack/GC-Bench.