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.

Clustering in graphs has been a well-known research problem, particularly because most Internet and social network data is in the form of graphs. Organizations widely use spectral clustering algorithms to find clustering in graph datasets. However, applying spectral clustering to a large dataset is challenging due to computational overhead. While the distributed spectral clustering algorithm exists, they face the problem of data privacy and increased communication costs between the clients. Thus, in this paper, we propose a spectral clustering algorithm using federated learning (FL) to overcome these issues. FL is a privacy-protecting algorithm that accumulates model parameters from each local learner rather than collecting users' raw data, thus providing both scalability and data privacy. We developed two approaches: FedSpectral and FedSpectral+. FedSpectral is a baseline approach that uses local spectral clustering labels to aggregate the global spectral clustering by creating a similarity graph. FedSpectral+, a state-of-the-art approach, uses the power iteration method to learn the global spectral embedding by incorporating the entire graph data without access to the raw information distributed among the clients. We further designed our own similarity metric to check the clustering quality of the distributed approach to that of the original/non-FL clustering. The proposed approach FedSpectral+ obtained a similarity of 98.85% and 99.8%, comparable to that of global clustering on the ego-Facebook and email-Eu-core dataset.

Simulations of large-scale dynamical systems require expensive computations. Low-dimensional parametrization of high-dimensional states such as Proper Orthogonal Decomposition (POD) can be a solution to lessen the burdens by providing a certain compromise between accuracy and model complexity. However, for really low-dimensional parametrizations (for example for controller design) linear methods like the POD come to their natural limits so that nonlinear approaches will be the methods of choice. In this work we propose a convolutional autoencoder (CAE) consisting of a nonlinear encoder and an affine linear decoder and consider combinations with k-means clustering for improved encoding performance. The proposed set of methods is compared to the standard POD approach in two cylinder-wake scenarios modeled by the incompressible Navier-Stokes equations.

Despite the tremendous success of convolutional neural networks (CNNs) in computer vision, the mechanism of CNNs still lacks clear interpretation. Currently, class activation mapping (CAM), a famous visualization technique to interpret CNN's decision, has drawn increasing attention. Gradient-based CAMs are efficient while the performance is heavily affected by gradient vanishing and exploding. In contrast, gradient-free CAMs can avoid computing gradients to produce more understandable results. However, existing gradient-free CAMs are quite time-consuming because hundreds of forward interference per image are required. In this paper, we proposed Cluster-CAM, an effective and efficient gradient-free CNN interpretation algorithm. Cluster-CAM can significantly reduce the times of forward propagation by splitting the feature maps into clusters in an unsupervised manner. Furthermore, we propose an artful strategy to forge a cognition-base map and cognition-scissors from clustered feature maps. The final salience heatmap will be computed by merging the above cognition maps. Qualitative results conspicuously show that Cluster-CAM can produce heatmaps where the highlighted regions match the human's cognition more precisely than existing CAMs. The quantitative evaluation further demonstrates the superiority of Cluster-CAM in both effectiveness and efficiency.