Structured point process data harvested from various platforms poses new challenges to the machine learning community. By imposing a matrix structure to repeatedly observed marked point processes, we propose a novel mixture model of multi-level marked point processes for identifying potential heterogeneity in the observed data. Specifically, we study a matrix whose entries are marked log-Gaussian Cox processes and cluster rows of such a matrix. An efficient semi-parametric Expectation-Solution (ES) algorithm combined with functional principal component analysis (FPCA) of point processes is proposed for model estimation. The effectiveness of the proposed framework is demonstrated through simulation studies and a real data analysis.

\textbf{A}ccuracy, \textbf{R}obustness to noises and scales, \textbf{I}nterpretability, \textbf{S}peed, and \textbf{E}asy to use (ARISE) are crucial requirements of a good clustering algorithm. However, achieving these goals simultaneously is challenging, and most advanced approaches only focus on parts of them. Towards an overall consideration of these aspects, we propose a novel clustering algorithm, namely GIT (Clustering Based on \textbf{G}raph of \textbf{I}ntensity \textbf{T}opology). GIT considers both local and global data structures: firstly forming local clusters based on intensity peaks of samples, and then estimating the global topological graph (topo-graph) between these local clusters. We use the Wasserstein Distance between the predicted and prior class proportions to automatically cut noisy edges in the topo-graph and merge connected local clusters as final clusters. Then, we compare GIT with seven competing algorithms on five synthetic datasets and nine real-world datasets. With fast local cluster detection, robust topo-graph construction and accurate edge-cutting, GIT shows attractive ARISE performance and significantly exceeds other non-convex clustering methods. For example, GIT outperforms its counterparts about $10\%$ (F1-score) on MNIST and FashionMNIST. Code is available at \color{red}{https://github.com/gaozhangyang/GIT}.

We investigate a clustering problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix. We start by considering Gaussian mixtures with two equally-sized components and derive a Max-Cut integer program based on maximum likelihood estimation. We prove its solutions achieve the optimal misclassification rate when the number of samples grows linearly in the dimension, up to a logarithmic factor. However, solving the Max-cut problem appears to be computationally intractable. To overcome this, we develop an efficient spectral algorithm that attains the optimal rate but requires a quadratic sample size. Although this sample complexity is worse than that of the Max-cut problem, we conjecture that no polynomial-time method can perform better. Furthermore, we gather numerical and theoretical evidence that supports the existence of a statistical-computational gap. Finally, we generalize the Max-Cut program to a $k$-means program that handles multi-component mixtures with possibly unequal weights. It enjoys similar optimality guarantees for mixtures of distributions that satisfy a transportation-cost inequality, encompassing Gaussian and strongly log-concave distributions.

We address the non-convex optimisation problem of finding a sparse matrix on the Stiefel manifold (matrices with mutually orthogonal columns of unit length) that maximises (or minimises) a quadratic objective function. Optimisation problems on the Stiefel manifold occur for example in spectral relaxations of various combinatorial problems, such as graph matching, clustering, or permutation synchronisation. Although sparsity is a desirable property in such settings, it is mostly neglected in spectral formulations since existing solvers, e.g. based on eigenvalue decomposition, are unable to account for sparsity while at the same time maintaining global optimality guarantees. We fill this gap and propose a simple yet effective sparsity-promoting modification of the Orthogonal Iteration algorithm for finding the dominant eigenspace of a matrix. By doing so, we can guarantee that our method finds a Stiefel matrix that is globally optimal with respect to the quadratic objective function, while in addition being sparse. As a motivating application we consider the task of permutation synchronisation, which can be understood as a constrained clustering problem that has particular relevance for matching multiple images or 3D shapes in computer vision, computer graphics, and beyond. We demonstrate that the proposed approach outperforms previous methods in this domain.

In the era of Big Data, businesses are faced with a deluge of time series data. This data is not just available in high volumes, but is also highly nuanced. Amazon Forecast Deep Learning algorithms such as DeepAR and CNN-QR build representations that effectively capture common trends and patterns across these numerous time series. These algorithms produce forecasts that perform better than traditional forecasting methods. In some cases, it may be possible to further improve Amazon Forecast accuracy by training the models with similarly behaving subsets of the time series dataset.

One of the key challenges to deep reinforcement learning (deep RL) is to ensure safety at both training and testing phases. In this work, we propose a novel technique of unsupervised action planning to improve the safety of on-policy reinforcement learning algorithms, such as trust region policy optimization (TRPO) or proximal policy optimization (PPO). We design our safety-aware reinforcement learning by storing all the history of "recovery" actions that rescue the agent from dangerous situations into a separate "safety" buffer and finding the best recovery action when the agent encounters similar states. Because this functionality requires the algorithm to query similar states, we implement the proposed safety mechanism using an unsupervised learning algorithm, k-means clustering. We evaluate the proposed algorithm on six robotic control tasks that cover navigation and manipulation. Our results show that the proposed safety RL algorithm can achieve higher rewards compared with multiple baselines in both discrete and continuous control problems. The supplemental video can be found at: https://youtu.be/AFTeWSohILo.

This paper introduces kdiff, a novel kernel-based measure for estimating distances between instances of time series, random fields and other forms of structured data. This measure is based on the idea of matching distributions that only overlap over a portion of their region of support. Our proposed measure is inspired by MPdist which has been previously proposed for such datasets and is constructed using Euclidean metrics, whereas kdiff is constructed using non-linear kernel distances. Also, kdiff accounts for both self and cross similarities across the instances and is defined using a lower quantile of the distance distribution. Comparing the cross similarity to self similarity allows for measures of similarity that are more robust to noise and partial occlusions of the relevant signals. Our proposed measure kdiff is a more general form of the well known kernel-based Maximum Mean Discrepancy (MMD) distance estimated over the embeddings. Some theoretical results are provided for separability conditions using kdiff as a distance measure for clustering and classification problems where the embedding distributions can be modeled as two component mixtures. Applications are demonstrated for clustering of synthetic and real-life time series and image data, and the performance of kdiff is compared to competing distance measures for clustering.

Cloud-based software has many advantages. When services are divided into many independent components, they are easier to update. Also, during peak demand, it is easier to scale cloud services (just hire more CPUs). Hence, many organizations are partitioning their monolithic enterprise applications into cloud-based microservices. Recently there has been much work using machine learning to simplify this partitioning task. Despite much research, no single partitioning method can be recommended as generally useful. More specifically, those prior solutions are "brittle''; i.e. if they work well for one kind of goal in one dataset, then they can be sub-optimal if applied to many datasets and multiple goals. In order to find a generally useful partitioning method, we propose DEEPLY. This new algorithm extends the CO-GCN deep learning partition generator with (a) a novel loss function and (b) some hyper-parameter optimization. As shown by our experiments, DEEPLY generally outperforms prior work (including CO-GCN, and others) across multiple datasets and goals. To the best of our knowledge, this is the first report in SE of such stable hyper-parameter optimization. To aid reuse of this work, DEEPLY is available on-line at https://bit.ly/2WhfFlB.

Accurate, long-term forecasting of human pedestrian trajectories in highly dynamic and interactive scenes is a long-standing challenge. Recent advances in using data-driven approaches have achieved significant improvements in terms of prediction accuracy. However, the lack of group-aware analysis has limited the performance of forecasting models. This is especially apparent in highly populated scenes, where pedestrians are moving in groups and the interactions between groups are extremely complex and dynamic. In this paper, we present Grouptron, a multi-scale dynamic forecasting framework that leverages pedestrian group detection and utilizes individual-level, group-level, and scene-level information for better understanding and representation of the scenes. Our approach employs spatio-temporal clustering algorithms to identify pedestrian groups, creates spatio-temporal graphs at the individual, group, and scene levels. It then uses graph neural networks to encode dynamics at different scales and incorporates encoding across different scales for trajectory prediction. We carried out extensive comparisons and ablation experiments to demonstrate the effectiveness of our approach. Our method achieves 9.3% decrease in final displacement error (FDE) compared with state-of-the-art methods on ETH/UCY benchmark datasets, and 16.1% decrease in FDE in more crowded scenes where extensive human group interactions are more frequently present.

Intelligent data-driven fault diagnosis methods have been widely applied, but most of these methods need a large number of high-quality labeled samples. It costs a lot of labor and time to label data in actual industrial processes, which challenges the application of intelligent fault diagnosis methods. To solve this problem, a multi-stage semi-supervised improved deep embedded clustering (MS-SSIDEC) method is proposed for the bearing fault diagnosis under the insufficient labeled samples situation. This method includes three stages: pre-training, deep clustering and enhanced supervised learning. In the first stage, a skip-connection based convolutional auto-encoder (SCCAE) is proposed and pre-trained to automatically learn low-dimensional representations. In the second stage, a semi-supervised improved deep embedded clustering (SSIDEC) model that integrates the pre-trained auto-encoder with a clustering layer is proposed for deep clustering. Additionally, virtual adversarial training (VAT) is introduced as a regularization term to overcome the overfitting in the model's training. In the third stage, high-quality clustering results obtained in the second stage are assigned to unlabeled samples as pseudo labels. The labeled dataset is augmented by those pseudo-labeled samples and used to train a bearing fault discriminative model. The effectiveness of the method is evaluated on the Case Western Reserve University (CWRU) bearing dataset. The results show that the method can not only satisfy the semi-supervised learning under a small number of labeled samples, but also solve the problem of unsupervised learning, and has achieved better results than traditional diagnosis methods. This method provides a new research idea for fault diagnosis with limited labeled samples by effectively using unsupervised data.