Efficient and interpretable spatial analysis is crucial in many fields such as geology, sports, and climate science. Large-scale spatial data often contains complex higher-order correlations across features and locations. While tensor latent factor models can describe higher-order correlations, they are inherently computationally expensive to train. Furthermore, for spatial analysis, these models should not only be predictive but also be spatially coherent. However, latent factor models are sensitive to initialization and can yield inexplicable results. We develop a novel Multi-resolution Tensor Learning (MRTL) algorithm for efficiently learning interpretable spatial patterns. MRTL initializes the latent factors from an approximate full-rank tensor model for improved interpretability and progressively learns from a coarse resolution to the fine resolution for an enormous computation speedup. We also prove the theoretical convergence and computational complexity of MRTL. When applied to two real-world datasets, MRTL demonstrates 4 ~ 5 times speedup compared to a fixed resolution while yielding accurate and interpretable models.

Unsupervised text encoding models have recently fueled substantial progress in NLP. The key idea is to use neural networks to convert words in texts to vector space representations based on word positions in a sentence and their contexts, which are suitable for end-to-end training of downstream tasks. We see a strikingly similar situation in spatial analysis, which focuses on incorporating both absolute positions and spatial contexts of geographic objects such as POIs into models. A general-purpose representation model for space is valuable for a multitude of tasks. However, no such general model exists to date beyond simply applying discretization or feed-forward nets to coordinates, and little effort has been put into jointly modeling distributions with vastly different characteristics, which commonly emerges from GIS data. Meanwhile, Nobel Prize-winning Neuroscience research shows that grid cells in mammals provide a multi-scale periodic representation that functions as a metric for location encoding and is critical for recognizing places and for path-integration. Therefore, we propose a representation learning model called Space2Vec to encode the absolute positions and spatial relationships of places. We conduct experiments on two real-world geographic data for two different tasks: 1) predicting types of POIs given their positions and context, 2) image classification leveraging their geo-locations. Results show that because of its multi-scale representations, Space2Vec outperforms well-established ML approaches such as RBF kernels, multi-layer feed-forward nets, and tile embedding approaches for location modeling and image classification tasks. Detailed analysis shows that all baselines can at most well handle distribution at one scale but show poor performances in other scales. In contrast, Space2Vec's multi-scale representation can handle distributions at different scales.

We present a novel method for learning densities with bounded support which enables us to incorporate hard' topological constraints. In particular, we show how emerging techniques from computational algebraic topology and the notion of Persistent Homology can be combined with kernel based methods from Machine Learning for the purpose of density estimation. The proposed formalism facilitates learning of models with bounded support in a principled way, and -- by incorporating Persistent Homology techniques in our approach -- we are able to encode algebraic-topological constraints which are not addressed in current state-of the art probabilistic models. We study the behaviour of our method on two synthetic examples for various sample sizes and exemplify the benefits of the proposed approach on a real-world data-set by learning a motion model for a racecar. We show how to learn a model which respects the underlying topological structure of the racetrack, constraining the trajectories of the car.

This paper presents a probabilistic-graphical model that can be used to infer characteristics of instantaneous brain activity by jointly analyzing spatial and temporal dependencies observed in electroencephalograms (EEG). Specifically, we describe a factor-graph-based model with customized factor-functions defined based on domain knowledge, to infer pathologic brain activity with the goal of identifying seizure-generating brain regions in epilepsy patients. We utilize an inference technique based on the graph-cut algorithm to exactly solve graph inference in polynomial time. We validate the model by using clinically collected intracranial EEG data from 29 epilepsy patients to show that the model correctly identifies seizure-generating brain regions. Our results indicate that our model outperforms two conventional approaches used for seizure-onset localization (5-7% better AUC: 0.72, 0.67, 0.65) and that the proposed inference technique provides 3-10% gain in AUC (0.72, 0.62, 0.69) compared to sampling-based alternatives. Papers published at the Neural Information Processing Systems Conference.

We present a unified representation for actionable spatial perception: 3D Dynamic Scene Graphs. Scene graphs are directed graphs where nodes represent entities in the scene (e.g. objects, walls, rooms), and edges represent relations (e.g. inclusion, adjacency) among nodes. Dynamic scene graphs (DSGs) extend this notion to represent dynamic scenes with moving agents (e.g. humans, robots), and to include actionable information that supports planning and decision-making (e.g. spatio-temporal relations, topology at different levels of abstraction). Our second contribution is to provide the first fully automatic Spatial PerceptIon eNgine(SPIN) to build a DSG from visual-inertial data. We integrate state-of-the-art techniques for object and human detection and pose estimation, and we describe how to robustly infer object, robot, and human nodes in crowded scenes. To the best of our knowledge, this is the first paper that reconciles visual-inertial SLAM and dense human mesh tracking. Moreover, we provide algorithms to obtain hierarchical representations of indoor environments (e.g. places, structures, rooms) and their relations. Our third contribution is to demonstrate the proposed spatial perception engine in a photo-realistic Unity-based simulator, where we assess its robustness and expressiveness. Finally, we discuss the implications of our proposal on modern robotics applications. 3D Dynamic Scene Graphs can have a profound impact on planning and decision-making, human-robot interaction, long-term autonomy, and scene prediction. A video abstract is available at https://youtu.be/SWbofjhyPzI

Landmarks are central to how people navigate, but most navigation technologies do not incorporate them into their representations. We propose the landmark graph generation task (creating landmark-based spatial representations from natural language) and introduce a fully end-to-end neural approach to generate these graphs. We evaluate our models on the SAIL route instruction dataset, as well as on a small set of real-world delivery instructions that we collected, and we show that our approach yields high quality results on both our task and the related robotic navigation task.

We present ShapeVis, a scalable visualization technique for point cloud data inspired from topological data analysis. Our method captures the underlying geometric and topological structure of the data in a compressed graphical representation. Much success has been reported by the data visualization technique Mapper, that discreetly approximates the Reeb graph of a filter function on the data. However, when using standard dimensionality reduction algorithms as the filter function, Mapper suffers from considerable computational cost. This makes it difficult to scale to high-dimensional data. Our proposed technique relies on finding a subset of points called landmarks along the data manifold to construct a weighted witness-graph over it. This graph captures the structural characteristics of the point cloud, and its weights are determined using a Finite Markov Chain. We further compress this graph by applying induced maps from standard community detection algorithms. Using techniques borrowed from manifold tearing, we prune and reinstate edges in the induced graph based on their modularity to summarize the shape of data. We empirically demonstrate how our technique captures the structural characteristics of real and synthetic data sets. Further, we compare our approach with Mapper using various filter functions like t-SNE, UMAP, LargeVis and show that our algorithm scales to millions of data points while preserving the quality of data visualization.

The US will impose new restrictions on the export of certain AI programs overseas, including to rival China. The ban, which comes into force on Monday, is the first to be applied under a 2018 law known as the Export Control Reform Act or ECRA. This requires the government to examine how it can restrict the export of "emerging" technologies "essential to the national security of the United States" -- including AI. News of the ban was first reported by Reuters. When ECRA was announced in 2018, some in the tech industry feared it would harm the field of artificial intelligence, which benefits greatly from the exchange of research and commercial programs across borders. Although the US is generally considered to be the world leader in AI, China is a strong second place and gaining fast.

Flow prediction (e.g., crowd flow, traffic flow) with features of spatial-temporal is increasingly investigated in AI research field. It is very challenging due to the complicated spatial dependencies between different locations and dynamic temporal dependencies among different time intervals. Although measurements of both dependencies are employed, existing methods suffer from the following two problems. First, the temporal dependencies are measured either uniformly or bias against long-term dependencies, which overlooks the distinctive impacts of short-term and long-term temporal dependencies. Second, the existing methods capture spatial and temporal dependencies independently, which wrongly assumes that the correlations between these dependencies are weak and ignores the complicated mutual influences between them. To address these issues, we propose a Spatial-Temporal Self-Attention Network (ST-SAN). As the path-length of attending long-term dependency is shorter in the self-attention mechanism, the vanishing of long-term temporal dependencies is prevented. In addition, since our model relies solely on attention mechanisms, the spatial and temporal dependencies can be simultaneously measured. Experimental results on real-world data demonstrate that, in comparison with state-of-the-art methods, our model reduces the root mean square errors by 9% in inflow prediction and 4% in outflow prediction on Taxi-NYC data, which is very significant compared to the previous improvement.

In this study the method of natural neighbours is used to interpolate data that has been drawn from a topological space with higher homology groups on its filtration. A particular difficulty with this algorithm are the boundary points. Its core is based on the Voronoi diagram, which induces a natural dual map to the Delaunay triangulation. Advantage is taken from this fact and the persistent homology is therefore calculated after each iteration to capture the changing topology of the data. The Bottleneck and Wasserstein distance serve as a measure of quality between the original data and the interpolation. If the norm of two distances exceeds a heuristically determined threshold, the algorithm terminates. The theoretical basis for this procedure is given and the validity of this approach is justified with numerical experiments.