Clustering techniques are often validated using benchmark datasets where class labels are used as ground-truth clusters. However, depending on the datasets, class labels may not align with the actual data clusters, and such misalignment hampers accurate validation. Therefore, it is essential to evaluate and compare datasets regarding their cluster-label matching (CLM), i.e., how well their class labels match actual clusters. Internal validation measures (IVMs), like Silhouette, can compare CLM over different labeling of the same dataset, but are not designed to do so across different datasets. We thus introduce Adjusted IVMs as fast and reliable methods to evaluate and compare CLM across datasets. We establish four axioms that require validation measures to be independent of data properties not related to cluster structure (e.g., dimensionality, dataset size). Then, we develop standardized protocols to convert any IVM to satisfy these axioms, and use these protocols to adjust six widely used IVMs. Quantitative experiments (1) verify the necessity and effectiveness of our protocols and (2) show that adjusted IVMs outperform the competitors, including standard IVMs, in accurately evaluating CLM both within and across datasets. We also show that the datasets can be filtered or improved using our method to form more reliable benchmarks for clustering validation.

Wake vortices - strong, coherent air turbulences created by aircraft - pose a significant risk to aviation safety and therefore require accurate and reliable detection methods. In this paper, we present an advanced, explainable machine learning method that utilizes Light Detection and Ranging (LiDAR) data for effective wake vortex detection. Our method leverages a dynamic graph CNN (DGCNN) with semantic segmentation to partition a 3D LiDAR point cloud into meaningful segments. Further refinement is achieved through clustering techniques. A novel feature of our research is the use of a perturbation-based explanation technique, which clarifies the model's decision-making processes for air traffic regulators and controllers, increasing transparency and building trust. Our experimental results, based on measured and simulated LiDAR scans compared against four baseline methods, underscore the effectiveness and reliability of our approach. This combination of semantic segmentation and clustering for real-time wake vortex tracking significantly advances aviation safety measures, ensuring that these are both effective and comprehensible.

Improving clustering quality evaluation in noisy Gaussian mixtures Renato Cordeiro de Amorim Vladimir Makarenkov Abstract Clustering is a well-established technique in machine learning and data analysis, widely used across various domains. Cluster validity indices, such as the Average Silhouette Width, Calinski-Harabasz, and Davies-Bouldin indices, play a crucial role in assessing clustering quality when external ground truth labels are unavailable. However, these measures can be affected by the feature relevance issue, potentially leading to unreliable evaluations in high-dimensional or noisy data sets. We introduce a theoretically grounded Feature Importance Rescaling (FIR) method that enhances the quality of clustering validation by adjusting feature contributions based on their dispersion. It attenuates noise features, clarifies clustering compactness and separation, and thereby aligns clustering validation more closely with the ground truth. Through extensive experiments on synthetic data sets under different configurations, we demonstrate that FIR consistently improves the correlation between the values of cluster validity indices and the ground truth, particularly in settings with noisy or irrelevant features. The results show that FIR increases the robustness of clustering evaluation, reduces variability in performance across different data sets, and remains effective even when clusters exhibit significant overlap. These findings highlight the potential of FIR as a valuable enhancement of clustering validation, making it a practical tool for unsupervised learning tasks where labelled data is unavailable. Mila - Quebec AI Institute, Montreal, QC, Canada.Keywords: Cluster validity indices, data rescaling, noisy data. 1 Introduction Clustering is a fundamenta technique in machine learning and data analysis, which is central to many exploratory methods.

Curriculum learning is a training method in which an agent is first trained on a curriculum of relatively simple tasks related to a target task in an effort to shorten the time required to train on the target task. Autonomous curriculum design involves the design of such curriculum with no reliance on human knowledge and/or expertise. Finding an efficient and effective way of autonomously designing curricula remains an open problem. We propose a novel approach for automatically designing curricula by leveraging the learner's uncertainty to select curricula tasks. Our approach measures the uncertainty in the learner's policy using relative entropy, and guides the agent to states of high uncertainty to facilitate learning. Our algorithm supports the generation of autonomous curricula in a self-assessed manner by leveraging the learner's past and current policies but it also allows the use of teacher guided design in an instructive setting. We provide theoretical guarantees for the convergence of our algorithm using two time-scale optimization processes. Results show that our algorithm outperforms randomly generated curriculum, and learning directly on the target task as well as the curriculum-learning criteria existing in literature. We also present two additional heuristic distance measures that could be combined with our relative-entropy approach for further performance improvements.

Algorithmic solutions have significant potential to improve decision-making across various domains, from healthcare to e-commerce. However, the widespread adoption of these solutions is hindered by a critical challenge: the lack of human-interpretable explanations. Current approaches to Explainable AI (XAI) predominantly focus on complex machine learning models, often producing brittle and non-intuitive explanations. This project proposes a novel approach to developing explainable algorithms by starting with optimization problems, specifically the assignment problem. The developed software library enriches basic algorithms with human-understandable explanations through four key methodologies: generating meaningful alternative solutions, creating robust solutions through input perturbation, generating concise decision trees and providing reports with comprehensive explanation of the results. Currently developed tools are often designed with specific clustering algorithms in mind, which limits their adaptability and flexibility to incorporate alternative techniques. Additionally, many of these tools fail to integrate expert knowledge, which could enhance the clustering process by providing valuable insights and context. This lack of adaptability and integration can hinder the effectiveness and robustness of the clustering outcomes in various applications. The represents a step towards making algorithmic solutions more transparent, trustworthy, and accessible. By collaborating with industry partners in sectors such as sales, we demonstrate the practical relevance and transformative potential of our approach.

In density-based clustering, clusters are areas of high object density separated by lower object density areas. This notion supports arbitrarily shaped clusters and automatic detection of noise points that do not belong to any cluster. However, it is challenging to adequately evaluate the quality of density-based clustering results. Even though some existing cluster validity indices (CVIs) target arbitrarily shaped clusters, none of them captures the quality of the labeled noise. In this paper, we propose DISCO, a Density-based Internal Score for Clustering Outcomes, which is the first CVI that also evaluates the quality of noise labels. DISCO reliably evaluates density-based clusters of arbitrary shape by assessing compactness and separation. It also introduces a direct assessment of noise labels for any given clustering. Our experiments show that DISCO evaluates density-based clusterings more consistently than its competitors. It is additionally the first method to evaluate the complete labeling of density-based clustering methods, including noise labels.

Off-policy evaluation can leverage logged data to estimate the effectiveness of new policies in e-commerce, search engines, media streaming services, or automatic diagnostic tools in healthcare. However, the performance of baseline off-policy estimators like IPS deteriorates when the logging policy significantly differs from the evaluation policy. Recent work proposes sharing information across similar actions to mitigate this problem. In this work, we propose an alternative estimator that shares information across similar contexts using clustering. We study the theoretical properties of the proposed estimator, characterizing its bias and variance under different conditions. We also compare the performance of the proposed estimator and existing approaches in various synthetic problems, as well as a real-world recommendation dataset. Our experimental results confirm that clustering contexts improves estimation accuracy, especially in deficient information settings.

Automated machine learning (AutoML) is a research area focusing on using optimisation techniques to design machine learning (ML) algorithms, alleviating the need for a human to perform manual algorithm design. Real-time AutoML enables the design process to happen while the ML algorithm is being applied to a task. Real-time AutoML is an emerging research area, as such existing real-time AutoML techniques need improvement with respect to the quality of designs and time taken to create designs. To address these issues, this study proposes an Online Meta-learning for AutoML in Real-time (OnMAR) approach. Meta-learning gathers information about the optimisation process undertaken by the ML algorithm in the form of meta-features. Meta-features are used in conjunction with a meta-learner to optimise the optimisation process. The OnMAR approach uses a meta-learner to predict the accuracy of an ML design. If the accuracy predicted by the meta-learner is sufficient, the design is used, and if the predicted accuracy is low, an optimisation technique creates a new design. A genetic algorithm (GA) is the optimisation technique used as part of the OnMAR approach. Different meta-learners (k-nearest neighbours, random forest and XGBoost) are tested. The OnMAR approach is model-agnostic (i.e. not specific to a single real-time AutoML application) and therefore evaluated on three different real-time AutoML applications, namely: composing an image clustering algorithm, configuring the hyper-parameters of a convolutional neural network, and configuring a video classification pipeline. The OnMAR approach is effective, matching or outperforming existing real-time AutoML approaches, with the added benefit of a faster runtime.

This unsupervised learning method is widely used in various applications, including image analysis, information retrieval, text analysis, bioinformatics, and many more [1, 2, 3, 4]. Clustering helps uncover the underlying structure of the data, facilitates data summarization, and sometimes serves as a preprocessing step for other algorithms [2]. Despite its widespread use, one of the primary challenges many traditional clustering algorithms face is that they often assume that the data points form clusters with convex shapes. For example, centroid-based algorithms like k -means and distribution-based models like Gaussian Mixture Models (GMM) typically produce clusters that are hyperspherical or ellipsoidal [5]. Although this assumption simplifies the clustering process, it restricts the flexibility of these models to handle complex data distributions that do not conform to convex shapes.

Traditional clustering methods typically focus on either cluster-wise global clustering or point-wise local clustering to reveal the intrinsic structures in unlabeled data. Global clustering optimizes an objective function to explore the relationships between clusters, but this approach may inevitably lead to coarse partition. In contrast, local clustering heuristically groups data based on detailed point relationships, but it tends to be less coherence and efficient. To bridge the gap between these two concepts and utilize the strengths of both, we propose Graph Probability Aggregation Clustering (GPAC), a graph-based fuzzy clustering algorithm. GPAC unifies the global clustering objective function with a local clustering constraint. The entire GPAC framework is formulated as a multi-constrained optimization problem, which can be solved using the Lagrangian method. Through the optimization process, the probability of a sample belonging to a specific cluster is iteratively calculated by aggregating information from neighboring samples within the graph. We incorporate a hard assignment variable into the objective function to further improve the convergence and stability of optimization. Furthermore, to efficiently handle large-scale datasets, we introduce an acceleration program that reduces the computational complexity from quadratic to linear, ensuring scalability. Extensive experiments conducted on synthetic, real-world, and deep learning datasets demonstrate that GPAC not only exceeds existing state-of-the-art methods in clustering performance but also excels in computational efficiency, making it a powerful tool for complex clustering challenges.