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.

Mastering unsupervised learning opens up a broad range of avenues for a data scientist. There is so much scope in the vast expanse of unsupervised learning and yet a lot of beginners in machine learning tend to shy away from it. In fact, I'm sure most newcomers will stick to basic clustering algorithms like K-Means clustering and hierarchical clustering. While there's nothing wrong with that approach, it does limit what you can do when faced with clustering projects. And why limit yourself when you can expand your learning, knowledge, and skillset by learning the powerful DBSCAN clustering algorithm?

Dimension reduction plays a pivotal role in analysing high-dimensional data. However, observations with missing values present serious difficulties in directly applying standard dimension reduction techniques. As a large number of dimension reduction approaches are based on the Gram matrix, we first investigate the effects of missingness on dimension reduction by studying the statistical properties of the Gram matrix with or without missingness, and then we present a bias-corrected Gram matrix with nice statistical properties under heterogeneous missingness. Extensive empirical results, on both simulated and publicly available real datasets, show that the proposed unbiased Gram matrix can significantly improve a broad spectrum of representative dimension reduction approaches.

Knowledge graphs have emerged as a widely adopted medium for storing relational data, making methods for automatically reasoning with them highly desirable. In this paper, we present a novel approach for inducing a hierarchy of subject clusters, building upon our earlier work done in taxonomy induction. Our method first constructs a tag hierarchy before assigning subjects to clusters on this hierarchy. We quantitatively demonstrate our method's ability to induce a coherent cluster hierarchy on three real-world datasets.