Feature selection in clustering is a hard task which involves simultaneously the discovery of relevant clusters as well as relevant variables with respect to these clusters. While feature selection algorithms are often model-based through optimised model selection or strong assumptions on $p(\pmb{x})$, we introduce a discriminative clustering model trying to maximise a geometry-aware generalisation of the mutual information called GEMINI with a simple $\ell_1$ penalty: the Sparse GEMINI. This algorithm avoids the burden of combinatorial feature subset exploration and is easily scalable to high-dimensional data and large amounts of samples while only designing a clustering model $p_\theta(y|\pmb{x})$. We demonstrate the performances of Sparse GEMINI on synthetic datasets as well as large-scale datasets. Our results show that Sparse GEMINI is a competitive algorithm and has the ability to select relevant subsets of variables with respect to the clustering without using relevance criteria or prior hypotheses.

Density-based clustering is a commonly used tool in data science. Today many data science works are utilizing high-dimensional neural embeddings. However, traditional density-based clustering techniques like DBSCAN have a degraded performance on high-dimensional data. In this paper, we propose LAF, a generic learned accelerator framework to speed up the original DBSCAN and the sampling-based variants of DBSCAN on high-dimensional data with angular distance metric. This framework consists of a learned cardinality estimator and a post-processing module. The cardinality estimator can fast predict whether a data point is core or not to skip unnecessary range queries, while the post-processing module detects the false negative predictions and merges the falsely separated clusters. The evaluation shows our LAF-enhanced DBSCAN method outperforms the state-of-the-art efficient DBSCAN variants on both efficiency and quality.

Most existing causal structure learning methods assume data collected from one environment and independent and identically distributed (i.i.d.). In some cases, data are collected from different subjects from multiple environments, which provides more information but might make the data non-identical or non-independent distribution. Some previous efforts try to learn causal structure from this type of data in two independent stages, i.e., first discovering i.i.d. groups from non-i.i.d. samples, then learning the causal structures from different groups. This straightforward solution ignores the intrinsic connections between the two stages, that is both the clustering stage and the learning stage should be guided by the same causal mechanism. Towards this end, we propose a unified Causal Cluster Structures Learning (named CCSL) method for causal discovery from non-i.i.d. data. This method simultaneously integrates the following two tasks: 1) clustering samples of the subjects with the same causal mechanism into different groups; 2) learning causal structures from the samples within the group. Specifically, for the former, we provide a Causality-related Chinese Restaurant Process to cluster samples based on the similarity of the causal structure; for the latter, we introduce a variational-inference-based approach to learn the causal structures. Theoretical results provide identification of the causal model and the clustering model under the linear non-Gaussian assumption. Experimental results on both simulated and real-world data further validate the correctness and effectiveness of the proposed method.

Abstract--Self-supervised learning is a popular and powerful method for utilizing large amounts of unlabeled data, for which a wide variety of training objectives have been proposed in the literature. In this study, we perform a Bayesian analysis of state-of-the-art self-supervised learning objectives and propose a unified formulation based on likelihood learning. Our analysis suggests a simple method for integrating self-supervised learning with generative models, allowing for the joint training of these two seemingly distinct approaches. We refer to this combined framework as GEDI, which stands for GEnerative and DIscriminative training. Additionally, we demonstrate an instantiation of the GEDI framework by integrating an energy-based model with a cluster-based self-supervised learning model. Through experiments on synthetic and real-world data, including SVHN, CIFAR10, and CIFAR100, we show that GEDI outperforms existing self-supervised learning strategies in terms of clustering performance by a wide margin. We also demonstrate that GEDI can be integrated into a neural-symbolic framework to address tasks in the small data regime, where it can use logical constraints to further improve clustering and classification performance.

Unsupervised machine learning is a type of machine learning where the model is trained on a dataset without any labeled output. The goal of unsupervised learning is to uncover hidden patterns or relationships in the data. Unsupervised learning is useful when labeled data is not available or when the goal is to discover new relationships in the data. However, it can be more challenging to evaluate the results of unsupervised learning compared to supervised learning, as there is no clear metric to assess the performance of the model. In conclusion, unsupervised learning is a powerful tool for understanding and extracting information from complex and unlabeled data.

In this work, we study the problem of partitioning a set of graphs into different groups such that the graphs in the same group are similar while the graphs in different groups are dissimilar. This problem was rarely studied previously, although there have been a lot of work on node clustering and graph classification. The problem is challenging because it is difficult to measure the similarity or distance between graphs. One feasible approach is using graph kernels to compute a similarity matrix for the graphs and then performing spectral clustering, but the effectiveness of existing graph kernels in measuring the similarity between graphs is very limited. To solve the problem, we propose a novel method called Deep Graph-Level Clustering (DGLC). DGLC utilizes a graph isomorphism network to learn graph-level representations by maximizing the mutual information between the representations of entire graphs and substructures, under the regularization of a clustering module that ensures discriminative representations via pseudo labels. DGLC achieves graph-level representation learning and graph-level clustering in an end-to-end manner. The experimental results on six benchmark datasets of graphs show that our DGLC has state-of-the-art performance in comparison to many baselines.

In this paper we propose a new approach to detect clusters in undirected graphs with attributed vertices. We incorporate structural and attribute similarities between the vertices in an augmented graph by creating additional vertices and edges as proposed in [1, 2]. The augmented graph is then embedded in a Euclidean space associated to its Laplacian and we cluster vertices via a modified K-means algorithm, using a new vector-valued distance in the embedding space. Main novelty of our method, which can be classified as an early fusion method, i.e., a method in which additional information on vertices are fused to the structure information before applying clustering, is the interpretation of attributes as new realizations of graph vertices, which can be dealt with as coordinate vectors in a related Euclidean space. This allows us to extend a scalable generalized spectral clustering procedure which substitutes graph Laplacian eigenvectors with some vectors, named algebraically smooth vectors, obtained by a linear-time complexity Algebraic MultiGrid (AMG) method. We discuss the performance of our proposed clustering method by comparison with recent literature approaches and public available results. Extensive experiments on different types of synthetic datasets and real-world attributed graphs show that our new algorithm, embedding attributes information in the clustering, outperforms structure-only-based methods, when the attributed network has an ambiguous structure. Furthermore, our new method largely outperforms the method which originally proposed the graph augmentation, showing that our embedding strategy and vector-valued distance are very effective in taking advantages from the augmented-graph representation.

Due to their conceptual simplicity, k-means algorithm variants have been extensively used for unsupervised cluster analysis. However, one main shortcoming of these algorithms is that they essentially fit a mixture of identical spherical Gaussians to data that vastly deviates from such a distribution. In comparison, general Gaussian Mixture Models (GMMs) can fit richer structures but require estimating a quadratic number of parameters per cluster to represent the covariance matrices. This poses two main issues: (i) the underlying optimization problems are challenging due to their larger number of local minima, and (ii) their solutions can overfit the data. In this work, we design search strategies that circumvent both issues. We develop efficient global optimization algorithms for general GMMs, and we combine these algorithms with regularization strategies that avoid overfitting. Through extensive computational analyses, we observe that global optimization or regularization in isolation does not substantially improve cluster recovery. However, combining these techniques permits a completely new level of performance previously unachieved by k-means algorithm variants, unraveling vastly different cluster structures. These results shed new light on the current status quo between GMM and k-means methods and suggest the more frequent use of general GMMs for data exploration. To facilitate such applications, we provide open-source code as well as Julia packages ("UnsupervisedClustering.jl" and "RegularizedCovarianceMatrices.jl") implementing the proposed techniques.

In mining, grade control generally focuses on blast hole sampling and the estimation of ore control block models with little or no attention given to how the materials are being excavated from the ground. In the process of loading trucks, the underlying variability of the individual bucket load will determine the variability of truck payload. Hence, accurate material movement demands a good knowledge of the excavation process and the buckets interaction with the environment. However, equipment frequently goes into off nominal states due to unexpected delays, disturbances or faults. The large amount of such disturbances causes information loss that reduces the statistical power and biases estimates, leading to increased uncertainty in the production. A reliable method that inferences the missing knowledge about the interaction between the machine and the environment from the available data sources, is vital to accurately model the material movement. In this study, a twostep method was implemented that performed unsupervised clustering and then predicted the missing information. The first method is DBSCAN based spatial clustering which divides the diggers and buckets positional data into connected loading segments. Clear patterns of segmented bucket dig positions were observed. The second model utilized Gaussian process regression which was trained with the clustered data and the model was then used to infer the mean locations of the test clusters. Bucket dig locations were then simulated at the inferred mean locations for different durations and compared against the known bucket dig locations. This method was tested at an open pit mine in the Pilbara of Western Australia. The results demonstrate the advantage of the proposed method in inferencing the missing information of bucket environment interactions and therefore enables miners to continuously track the material movement.

Self-organization is ubiquitous in nature and mind. However, machine learning and theories of cognition still barely touch the subject. The hurdle is that general patterns are difficult to define in terms of dynamical equations and designing a system that could learn by reordering itself is still to be seen. Here, we propose a learning system, where patterns are defined within the realm of nonlinear dynamics with positive and negative feedback loops, allowing attractor-repeller pairs to emerge for each pattern observed. Experiments reveal that such a system can map temporal to spatial correlation, enabling hierarchical structures to be learned from sequential data. The results are accurate enough to surpass state-of-the-art unsupervised learning algorithms in seven out of eight experiments as well as two real-world problems. Interestingly, the dynamic nature of the system makes it inherently adaptive, giving rise to phenomena similar to phase transitions in chemistry/thermodynamics when the input structure changes. Thus, the work here sheds light on how self-organization can allow for pattern recognition and hints at how intelligent behavior might emerge from simple dynamic equations without any objective/loss function.