Determining the number of clusters in a dataset is a fundamental issue in data clustering. Many methods have been proposed to solve the problem of selecting the number of clusters, considering it to be a problem with regard to model selection. This paper proposes an efficient algorithm that automatically selects a suitable number of clusters based on a probability distribution model framework. The algorithm includes the following two components. First, a generalization of Kohonen's self-organizing map (SOM) is introduced. In Kohonen's SOM, clusters are modeled as mean vectors. In the generalized SOM, each cluster is modeled as a probabilistic distribution and constructed by samples classified based on the likelihood. Second, the dynamically updating method of the SOM structure is introduced. In Kohonen's SOM, each cluster is tied to a node of a fixed two-dimensional lattice space and learned using neighborhood relations between nodes based on Euclidean distance. The extended SOM defines a graph with clusters as vertices and neighborhood relations as links and updates the graph structure by cutting weakly-connection and unnecessary vertex deletions. The weakness of a link is measured using the Kullback--Leibler divergence, and the redundancy of a vertex is measured using the minimum description length. Those extensions make it efficient to determine the appropriate number of clusters. Compared with existing methods, the proposed method is computationally efficient and can accurately select the number of clusters.

Data-driven decision making is becoming an integral part of manufacturing companies. Data is collected and commonly used to improve efficiency and produce high quality items for the customers. IoT-based and other forms of object tracking are an emerging tool for collecting movement data of objects/entities (e.g. human workers, moving vehicles, trolleys etc.) over space and time. Movement data can provide valuable insights like process bottlenecks, resource utilization, effective working time etc. that can be used for decision making and improving efficiency. Turning movement data into valuable information for industrial management and decision making requires analysis methods. We refer to this process as movement analytics. The purpose of this document is to review the current state of work for movement analytics both in manufacturing and more broadly. We survey relevant work from both a theoretical perspective and an application perspective. From the theoretical perspective, we put an emphasis on useful methods from two research areas: machine learning, and logic-based knowledge representation. We also review their combinations in view of movement analytics, and we discuss promising areas for future development and application. Furthermore, we touch on constraint optimization. From an application perspective, we review applications of these methods to movement analytics in a general sense and across various industries. We also describe currently available commercial off-the-shelf products for tracking in manufacturing, and we overview main concepts of digital twins and their applications.

We propose a simple but effective source-free domain adaptation (SFDA) method. Treating SFDA as an unsupervised clustering problem and following the intuition that local neighbors in feature space should have more similar predictions than other features, we propose to optimize an objective of prediction consistency. This objective encourages local neighborhood features in feature space to have similar predictions while features farther away in feature space have dissimilar predictions, leading to efficient feature clustering and cluster assignment simultaneously. For efficient training, we seek to optimize an upper-bound of the objective resulting in two simple terms. Furthermore, we relate popular existing methods in domain adaptation, source-free domain adaptation and contrastive learning via the perspective of discriminability and diversity. The experimental results prove the superiority of our method, and our method can be adopted as a simple but strong baseline for future research in SFDA. Our method can be also adapted to source-free open-set and partial-set DA which further shows the generalization ability of our method.

Acquiring commonsense knowledge and reasoning is an important goal in modern NLP research. Despite much progress, there is still a lack of understanding (especially at scale) of the nature of commonsense knowledge itself. A potential source of structured commonsense knowledge that could be used to derive insights is ConceptNet. In particular, ConceptNet contains several coarse-grained relations, including HasContext, FormOf and SymbolOf, which can prove invaluable in understanding broad, but critically important, commonsense notions such as 'context'. In this article, we present a methodology based on unsupervised knowledge graph representation learning and clustering to reveal and study substructures in three heavily used commonsense relations in ConceptNet. Our results show that, despite having an 'official' definition in ConceptNet, many of these commonsense relations exhibit considerable sub-structure. In the future, therefore, such relations could be sub-divided into other relations with more refined definitions. We also supplement our core study with visualizations and qualitative analyses.

LiDAR-based localization approach is a fundamental module for large-scale navigation tasks, such as last-mile delivery and autonomous driving, and localization robustness highly relies on viewpoints and 3D feature extraction. Our previous work provides a viewpoint-invariant descriptor to deal with viewpoint differences; however, the global descriptor suffers from a low signal-noise ratio in unsupervised clustering, reducing the distinguishable feature extraction ability. We develop SphereVLAD++, an attention-enhanced viewpoint invariant place recognition method in this work. SphereVLAD++ projects the point cloud on the spherical perspective for each unique area and captures the contextual connections between local features and their dependencies with global 3D geometry distribution. In return, clustered elements within the global descriptor are conditioned on local and global geometries and support the original viewpoint-invariant property of SphereVLAD. In the experiments, we evaluated the localization performance of SphereVLAD++ on both public KITTI360 datasets and self-generated datasets from the city of Pittsburgh. The experiment results show that SphereVLAD++ outperforms all relative state-of-the-art 3D place recognition methods under small or even totally reversed viewpoint differences and shows 0.69% and 15.81% successful retrieval rates with better than the second best. Low computation requirements and high time efficiency also help its application for low-cost robots.

As humans, we perceive the three-dimensional structure of the world around us with apparent ease. Think of how vivid the three-dimensional percept is when you look at a vase of flowers sitting on the table next to you. You can tell the shape and translucency of each petal through the subtle patterns of light and shading that play across its surface and effortlessly segment each flower from the background of the scene (Figure 1.1). Looking at a framed group por- trait, you can easily count (and name) all of the people in the picture and even guess at their emotions from their facial appearance. Perceptual psychologists have spent decades trying to understand how the visual system works and, even though they can devise optical illusions1 to tease apart some of its principles (Figure 1.3), a complete solution to this puzzle remains elusive (Marr 1982; Palmer 1999; Livingstone 2008).

We analyze 14,651 HIV1 reverse transcriptase (HIV RT) sequences from the Stanford HIV Drug Resistance Database labeled with treatment regimen in order to study the evolution this enzyme under drug selection in the clinic. Our goal is to identify distinct sectors of HIV RT's sequence space that are undergoing evolution as a way to identify individual selections and/or evolutionary solutions. We utilize Uniform Manifold Approximation and Projection (UMAP), a graph-based dimensionality reduction technique uniquely suited for the detection of non-linear dependencies and visualize the results using an unsupervised clustering algorithm based on density analysis. Our analysis produced 21 distinct clusters of sequences. Supporting the biological significance of these clusters, they tend to represent phylogenetically related sequences with strong correspondence to distinct treatment regimens. Thus, this method for visualization of areas of HIV RT undergoing evolution can help infer information about selective pressures, although it is correlative. The mutation signatures associated with each cluster may represent the higher-order epistatic context facilitating these evolutionary pathways, information that is generally not accessible by other types of mutational co-dependence analyses.

A new interpoint distance-based measure is proposed to identify the optimal number of clusters present in a data set. Designed in nonparametric approach, it is independent of the distribution of given data. Interpoint distances between the data members make our cluster validity index applicable to univariate and multivariate data measured on arbitrary scales, or having observations in any dimensional space where the number of study variables can be even larger than the sample size. Our proposed criterion is compatible with any clustering algorithm, and can be used to determine the unknown number of clusters or to assess the quality of the resulting clusters for a data set. Demonstration through synthetic and real-life data establishes its superiority over the well-known clustering accuracy measures of the literature.

Clustering based on the random walk operator has been proven effective for undirected graphs, but its generalization to directed graphs (digraphs) is much more challenging. Although the random walk operator is well-defined for digraphs, in most cases such graphs are not strongly connected, and hence the associated random walks are not irreducible, which is a crucial property for clustering that exists naturally in the undirected setting. To remedy this, the usual workaround is to either naively symmetrize the adjacency matrix or to replace the natural random walk operator by the teleporting random walk operator, but this can lead to the loss of valuable information carried by edge directionality. In this paper, we introduce a new clustering framework, the Parametrized Random Walk Diffusion Kernel Clustering (P-RWDKC), which is suitable for handling both directed and undirected graphs. Our framework is based on the diffusion geometry (Coifman & Lafon, 2006) and the generalized spectral clustering framework (Sevi et al., 2022). Accordingly, we propose an algorithm that automatically reveals the cluster structure at a given scale, by considering the random walk dynamics associated with a parametrized kernel operator, and by estimating its critical diffusion time. Experiments on K-NN graphs constructed from real-world datasets and real-world graphs show that our clustering approach performs well in all tested cases, and outperforms existing approaches in most of them.

Many models for undirected graphs are based on factorizing the graph's adjacency matrix; these models find a vector representation of each node such that the predicted probability of a link between two nodes increases with the similarity (dot product) of their associated vectors. Recent work has shown that these models are unable to capture key structures in real-world graphs, particularly heterophilous structures, wherein links occur between dissimilar nodes. In contrast, a factorization with two vectors per node, based on logistic principal components analysis (LPCA), has been proven not only to represent such structures, but also to provide exact low-rank factorization of any graph with bounded max degree. However, this bound has limited applicability to real-world networks, which often have power law degree distributions with high max degree. Further, the LPCA model lacks interpretability since its asymmetric factorization does not reflect the undirectedness of the graph. We address these issues in two ways. First, we prove a new bound for the LPCA model in terms of arboricity rather than max degree; this greatly increases the bound's applicability to many sparse real-world networks. Second, we propose an alternative graph model whose factorization is symmetric and nonnegative, which allows for link predictions to be interpreted in terms of node clusters. We show that the bounds for exact representation in the LPCA model extend to our new model. On the empirical side, our model is optimized effectively on real-world graphs with gradient descent on a cross-entropy loss. We demonstrate its effectiveness on a variety of foundational tasks, such as community detection and link prediction.