We study landmark-based SLAM with unknown data association: our robot navigates in a completely unknown environment and has to simultaneously reason over its own trajectory, the positions of an unknown number of landmarks in the environment, and potential data associations between measurements and landmarks. This setup is interesting since: (i) it arises when recovering from data association failures or from SLAM with information-poor sensors, (ii) it sheds light on fundamental limits (and hardness) of landmark-based SLAM problems irrespective of the front-end data association method, and (iii) it generalizes existing approaches where data association is assumed to be known or partially known. We approach the problem by splitting it into an inner problem of estimating the trajectory, landmark positions and data associations and an outer problem of estimating the number of landmarks. Our approach creates useful and novel connections with existing techniques from discrete-continuous optimization (e.g., k-means clustering), which has the potential to trigger novel research. We demonstrate the proposed approaches in extensive simulations and on real datasets and show that the proposed techniques outperform typical data association baselines and are even competitive against an "oracle" baseline which has access to the number of landmarks and an initial guess for each landmark.

Over the last few years Explainable Clustering has gathered a lot of attention. Dasgupta et al. [ICML'20] initiated the study of explainable k-means and k-median clustering problems where the explanation is captured by a threshold decision tree which partitions the space at each node using axis parallel hyperplanes. Recently, Laber et al. [Pattern Recognition'23] made a case to consider the depth of the decision tree as an additional complexity measure of interest. In this work, we prove that even when the input points are in the Euclidean plane, then any depth reduction in the explanation incurs unbounded loss in the k-means and k-median cost. Formally, we show that there exists a data set X in the Euclidean plane, for which there is a decision tree of depth k-1 whose k-means/k-median cost matches the optimal clustering cost of X, but every decision tree of depth less than k-1 has unbounded cost w.r.t. the optimal cost of clustering. We extend our results to the k-center objective as well, albeit with weaker guarantees.

With the advent of e-commerce platforms, reviews are crucial for customers to assess the credibility of a product. The star ratings do not always match the review text written by the customer. For example, a three star rating (out of five) may be incongruous with the review text, which may be more suitable for a five star review. A clustering approach can be used to relabel the correct star ratings by grouping the text reviews into individual groups. In this work, we explore the task of choosing different text embeddings to represent these reviews and also explore the impact the embedding choice has on the performance of various classes of clustering algorithms. We use contextual (BERT) and non-contextual (Word2Vec) text embeddings to represent the text and measure their impact of three classes on clustering algorithms - partitioning based (KMeans), single linkage agglomerative hierarchical, and density based (DBSCAN and HDBSCAN), each with various experimental settings. We use the silhouette score, adjusted rand index score, and cluster purity score metrics to evaluate the performance of the algorithms and discuss the impact of different embeddings on the clustering performance. Our results indicate that the type of embedding chosen drastically affects the performance of the algorithm, the performance varies greatly across different types of clustering algorithms, no embedding type is better than the other, and DBSCAN outperforms KMeans and single linkage agglomerative clustering but also labels more data points as outliers. We provide a thorough comparison of the performances of different algorithms and provide numerous ideas to foster further research in the domain of text clustering.

Automatic analysis of customer data for businesses is an area that is of interest to companies. Business to business data is studied rarely in academia due to the sensitive nature of such information. Applying natural language processing can speed up the analysis of prohibitively large sets of data. This paper addresses this subject and applies sentiment analysis, topic modelling and keyword extraction to a B2B data set. We show that accurate sentiment can be extracted from the notes automatically and the notes can be sorted by relevance into different topics. We see that without clear separation topics can lack relevance to a business context.

Graph contrastive learning (GCL) has attracted a surge of attention due to its superior performance for learning node/graph representations without labels. However, in practice, the underlying class distribution of unlabeled nodes for the given graph is usually imbalanced. This highly imbalanced class distribution inevitably deteriorates the quality of learned node representations in GCL. Indeed, we empirically find that most state-of-the-art GCL methods cannot obtain discriminative representations and exhibit poor performance on imbalanced node classification. Motivated by this observation, we propose a principled GCL framework on Imbalanced node classification (ImGCL), which automatically and adaptively balances the representations learned from GCL without labels. Specifically, we first introduce the online clustering based progressively balanced sampling (PBS) method with theoretical rationale, which balances the training sets based on pseudo-labels obtained from learned representations in GCL. We then develop the node centrality based PBS method to better preserve the intrinsic structure of graphs, by upweighting the important nodes of the given graph. Extensive experiments on multiple imbalanced graph datasets and imbalanced settings demonstrate the effectiveness of our proposed framework, which significantly improves the performance of the recent state-of-the-art GCL methods. Further experimental ablations and analyses show that the ImGCL framework consistently improves the representation quality of nodes in under-represented (tail) classes.

Clustering is at the very core of machine learning, and its applications proliferate with the increasing availability of data. However, as datasets grow, comparing clusterings with an adjustment for chance becomes computationally difficult, preventing unbiased ground-truth comparisons and solution selection. We propose FastAMI, a Monte Carlo-based method to efficiently approximate the Adjusted Mutual Information (AMI) and extend it to the Standardized Mutual Information (SMI). The approach is compared with the exact calculation and a recently developed variant of the AMI based on pairwise permutations, using both synthetic and real data. In contrast to the exact calculation our method is fast enough to enable these adjusted information-theoretic comparisons for large datasets while maintaining considerably more accurate results than the pairwise approach.

This work introduces Jacobian-scaled K-means (JSK-means) clustering, which is a physics-informed clustering strategy centered on the K-means framework. The method allows for the injection of underlying physical knowledge into the clustering procedure through a distance function modification: instead of leveraging conventional Euclidean distance vectors, the JSK-means procedure operates on distance vectors scaled by matrices obtained from dynamical system Jacobians evaluated at the cluster centroids. The goal of this work is to show how the JSK-means algorithm -- without modifying the input dataset -- produces clusters that capture regions of dynamical similarity, in that the clusters are redistributed towards high-sensitivity regions in phase space and are described by similarity in the source terms of samples instead of the samples themselves. The algorithm is demonstrated on a complex reacting flow simulation dataset (a channel detonation configuration), where the dynamics in the thermochemical composition space are known through the highly nonlinear and stiff Arrhenius-based chemical source terms. Interpretations of cluster partitions in both physical space and composition space reveal how JSK-means shifts clusters produced by standard K-means towards regions of high chemical sensitivity (e.g., towards regions of peak heat release rate near the detonation reaction zone). The findings presented here illustrate the benefits of utilizing Jacobian-scaled distances in clustering techniques, and the JSK-means method in particular displays promising potential for improving former partition-based modeling strategies in reacting flow (and other multi-physics) applications.

However, they are designed on of connected nodes belong to different classes (Pei et al., the homophilic assumption of graph and clustering 2020; Xie et al., 2023). Traditional GNNs learn representations on heterophilic graph is overlooked. Due to via message passing mechanism under the assumption the lack of labels, it is impossible to first identify of homophily (Fang et al., 2022). Facing heterophilic graphs, a graph as homophilic or heterophilic before a previous approaches mainly suffer two limitations. On the suitable GNN model can be found. Hence, clustering one hand, the local neighbors in a graph are nodes that are on real-world graph with various levels of proximally located, while nodes that are semantically similar homophily poses a new challenge to the graph might be far apart on heterophilic graph (Zhu et al., research community. To fill this gap, we propose 2020). Thus, existing techniques fail to capture long-range a novel graph clustering method, which contains information from distant nodes. On the other hand, they three key components: graph reconstruction, don't distinguish similar and dissimilar neighbors, which a mixed filter, and dual graph clustering carry different amounts of information.

In general, a similarity threshold (i.e., a vigilance parameter) for a node learning process in Adaptive Resonance Theory (ART)-based algorithms has a significant impact on clustering performance. In addition, an edge deletion threshold in a topological clustering algorithm plays an important role in adaptively generating well-separated clusters during a self-organizing process. In this paper, we propose a new parameter-free ART-based topological clustering algorithm capable of continual learning by introducing parameter estimation methods. Experimental results with synthetic and real-world datasets show that the proposed algorithm has superior clustering performance to the state-of-the-art clustering algorithms without any parameter pre-specifications.

This paper presents two novel deterministic initialization procedures for K-means clustering based on a modified crowding distance. The procedures, named CKmeans and FCKmeans, use more crowded points as initial centroids. Experimental studies on multiple datasets demonstrate that the proposed approach outperforms Kmeans and Kmeans++ in terms of clustering accuracy. The effectiveness of CKmeans and FCKmeans is attributed to their ability to select better initial centroids based on the modified crowding distance. Overall, the proposed approach provides a promising alternative for improving K-means clustering.