Time series clustering is an unsupervised learning method for classifying time series data into groups with similar behavior. It is used in applications such as healthcare, finance, economics, energy, and climate science. Several time series clustering methods have been introduced and used for over four decades. Most of them focus on measuring either Euclidean distances or association dissimilarities between time series. In this work, we propose a new dissimilarity measure called ranked Pearson correlation dissimilarity (RDPC), which combines a weighted average of a specified fraction of the largest element-wise differences with the well-known Pearson correlation dissimilarity. It is incorporated into hierarchical clustering. The performance is evaluated and compared with existing clustering algorithms. The results show that the RDPC algorithm outperforms others in complicated cases involving different seasonal patterns, trends, and peaks. Finally, we demonstrate our method by clustering a random sample of customers from a Thai electricity consumption time series dataset into seven groups with unique characteristics.

Semiconductor manufacturing generates vast amounts of image data, crucial for defect identification and yield optimization, yet often exceeds manual inspection capabilities. Traditional clustering techniques struggle with high-dimensional, unlabeled data, limiting their effectiveness in capturing nuanced patterns. This paper introduces an advanced clustering framework that integrates deep Topological Data Analysis (TDA) with self-supervised and transfer learning techniques, offering a novel approach to unsupervised image clustering. TDA captures intrinsic topological features, while self-supervised learning extracts meaningful representations from unlabeled data, reducing reliance on labeled datasets. Transfer learning enhances the framework's adaptability and scalability, allowing fine-tuning to new datasets without retraining from scratch. Validated on synthetic and open-source semiconductor image datasets, the framework successfully identifies clusters aligned with defect patterns and process variations. This study highlights the transformative potential of combining TDA, self-supervised learning, and transfer learning, providing a scalable solution for proactive process monitoring and quality control in semiconductor manufacturing and other domains with large-scale image datasets.

Clustering is a fundamental task in data mining and machine learning, particularly for analyzing large-scale data. In this paper, we introduce Clust-Splitter, an efficient algorithm based on nonsmooth optimization, designed to solve the minimum sum-of-squares clustering problem in very large datasets. The clustering task is approached through a sequence of three nonsmooth optimization problems: two auxiliary problems used to generate suitable starting points, followed by a main clustering formulation. To solve these problems effectively, the limited memory bundle method is combined with an incremental approach to develop the Clust-Splitter algorithm. We evaluate Clust-Splitter on real-world datasets characterized by both a large number of attributes and a large number of data points and compare its performance with several state-of-the-art large-scale clustering algorithms. Experimental results demonstrate the efficiency of the proposed method for clustering very large datasets, as well as the high quality of its solutions, which are on par with those of the best existing methods.

Clustering aims to form groups of similar data points in an unsupervised regime. Yet, clustering complex datasets containing critically intertwined shapes poses significant challenges. The prevailing clustering algorithms widely depend on evaluating similarity measures based on Euclidean metrics. Exploring topological characteristics to perform clustering of complex datasets inevitably presents a better scope. The topological clustering algorithms predominantly perceive the point set through the lens of Simplicial complexes and Persistent homology. Despite these approaches, the existing topological clustering algorithms cannot somehow fully exploit topological structures and show inconsistent performances on some highly complicated datasets. This work aims to mitigate the limitations by identifying topologically similar neighbors through the Vietoris-Rips complex and Betti number filtration. In addition, we introduce the concept of the Betti sequences to capture flexibly essential features from the topological structures. Our proposed algorithm is adept at clustering complex, intertwined shapes contained in the datasets. We carried out experiments on several synthetic and real-world datasets. Our algorithm demonstrated commendable performances across the datasets compared to some of the well-known topology-based clustering algorithms.

Urban transportation plays a vital role in modern city life, affecting how efficiently people and goods move around. This study analyzes transportation patterns using two datasets: the NYC Taxi Trip dataset from New York City and the Pathao Food Trip dataset from Dhaka, Bangladesh. Our goal is to identify key trends in demand, peak times, and important geographical hotspots. We start with Exploratory Data Analysis (EDA) to understand the basic characteristics of the datasets. Next, we perform geospatial analysis to map out high-demand and low-demand regions. We use the SARIMAX model for time series analysis to forecast demand patterns, capturing seasonal and weekly variations. Lastly, we apply clustering techniques to identify significant areas of high and low demand. Our findings provide valuable insights for optimizing fleet management and resource allocation in both passenger transport and food delivery services. These insights can help improve service efficiency, better meet customer needs, and enhance urban transportation systems in diverse urban environments.

Concept Factorization (CF) models have attracted widespread attention due to their excellent performance in data clustering. In recent years, many variant models based on CF have achieved great success in clustering by taking into account the internal geometric manifold structure of the dataset and using graph regularization techniques. However, their clustering performance depends greatly on the construction of the initial graph structure. In order to enable adaptive learning of the graph structure of the data, we propose a Concept Factorization Based on Self-Representation and Adaptive Graph Structure Learning (CFSRAG) Model. CFSRAG learns the affinity relationship between data through a self-representation method, and uses the learned affinity matrix to implement dynamic graph regularization constraints, thereby ensuring dynamic learning of the internal geometric structure of the data. Finally, we give the CFSRAG update rule and convergence analysis, and conduct comparative experiments on four real datasets. The results show that our model outperforms other state-of-the-art models.

We present Mixture of Discrete-time Gaussian Processes (MiDiGap), a novel approach for flexible policy representation and imitation learning in robot manipulation. MiDiGap enables learning from as few as five demonstrations using only camera observations and generalizes across a wide range of challenging tasks. It excels at long-horizon behaviors such as making coffee, highly constrained motions such as opening doors, dynamic actions such as scooping with a spatula, and multimodal tasks such as hanging a mug. MiDiGap learns these tasks on a CPU in less than a minute and scales linearly to large datasets. We also develop a rich suite of tools for inference-time steering using evidence such as collision signals and robot kinematic constraints. This steering enables novel generalization capabilities, including obstacle avoidance and cross-embodiment policy transfer. MiDiGap achieves state-of-the-art performance on diverse few-shot manipulation benchmarks. On constrained RLBench tasks, it improves policy success by 76 percentage points and reduces trajectory cost by 67%. On multimodal tasks, it improves policy success by 48 percentage points and increases sample efficiency by a factor of 20. In cross-embodiment transfer, it more than doubles policy success. We make the code publicly available at https://midigap.cs.uni-freiburg.de.

Partial label learning (PLL) is a significant weakly supervised learning framework, where each training example corresponds to a set of candidate labels and only one label is the ground-truth label. For the first time, this paper investigates the partial label clustering problem, which takes advantage of the limited available partial labels to improve the clustering performance. Specifically, we first construct a weight matrix of examples based on their relationships in the feature space and disambiguate the candidate labels to estimate the ground-truth label based on the weight matrix. Then, we construct a set of must-link and cannot-link constraints based on the disambiguation results. Moreover, we propagate the initial must-link and cannot-link constraints based on an adversarial prior promoted dual-graph learning approach. Finally, we integrate weight matrix construction, label disambiguation, and pairwise constraints propagation into a joint model to achieve mutual enhancement. We also theoretically prove that a better disambiguated label matrix can help improve clustering performance. Comprehensive experiments demonstrate our method realizes superior performance when comparing with state-of-the-art constrained clustering methods, and outperforms PLL and semi-supervised PLL methods when only limited samples are annotated. The code is publicly available at https://github.com/xyt-ml/PLC.

In Federated Learning, heterogeneity in client data distributions often means that a single global model does not have the best performance for individual clients. Consider for example training a next-word prediction model for keyboards: user-specific language patterns due to demographics (dialect, age, etc.), language proficiency, and writing style result in a highly non-IID dataset across clients. Other examples are medical images taken with different machines, or driving data from different vehicle types. To address this, we propose a simple yet effective personalized federated learning framework (pFedLIA) that utilizes a computationally efficient influence approximation, called `Lazy Influence', to cluster clients in a distributed manner before model aggregation. Within each cluster, data owners collaborate to jointly train a model that captures the specific data patterns of the clients. Our method has been shown to successfully recover the global model's performance drop due to the non-IID-ness in various synthetic and real-world settings, specifically a next-word prediction task on the Nordic languages as well as several benchmark tasks. It matches the performance of a hypothetical Oracle clustering, and significantly improves on existing baselines, e.g., an improvement of 17% on CIFAR100.

W e propose the Compact Clustering Attention (COCA) layer, an effective building block that introduces a hierarchical strategy for object-centric representation learning, while solving the unsupervised object discovery task on single images. COCA is an attention-based clustering module capable of extracting object-centric representations from multi-object scenes, when cascaded into a bottom-up hierarchical network architecture, referred to as COCA-Net. At its core, COCA utilizes a novel clustering algorithm that leverages the physical concept of compactness, to highlight distinct object centroids in a scene, providing a spatial inductive bias. Thanks to this strategy, COCA-Net generates high-quality segmentation masks on both the decoder side and, notably, the encoder side of its pipeline. Additionally, COCA-Net is not bound by a predetermined number of object masks that it generates and handles the segmentation of background elements better than its competitors. W e demonstrate COCA-Net's segmentation performance on six widely adopted datasets, achieving superior or competitive results against the state-of-the-art models across nine different evaluation metrics.