Rennes, CNRS, LETG F-35000 Rennes Optimal transport has recently gained a lot of interest in the machine learning community thanks to its ability to compare probability distributions while respecting the underlying space's geometry. Wasserstein distance deals with feature information through its metric or cost function, but fails in exploiting the structural information, i.e. the specific relations existing among the components of the distribution. Recently adapted to a machine learning context, the Gromov-Wasserstein distance defines a metric well suited for comparing distributions that live in different metric spaces by exploiting their inner structural information. In this paper we propose a new optimal transport distance, called the Fused Gromov-Wasserstein distance, capable of leveraging both structural and feature information by combining both views and prove its metric properties over very general manifolds. We also define the barycenter of structured objects as their Fréchet mean, leveraging both feature and structural information. We illustrate the versatility of the method for problems where structured objects are involved, computing barycenters in graph and time series contexts. We also use this new distance for graph classification where we obtain comparable or superior results than state-of-the-art graph kernel methods and end-to-end graph CNN approach.

Geography, enriched by information systems to form the Geographic Information System or GIS, is growing exponentially. A core geospatial technology, the GIS is used virtually in every field, adding value to practically every business segment and application areas. In text, the genesis of GIS platforms (solutions/software) lies in capturing, analyzing, and presenting spatial and non-spatial information as effective visualizations. In reality, the segment is much more! The segment includes fast-growth engineering, and construction project designs, 3D Modeling with spatial data.

We present ASP Modulo `Space-Time', a declarative representational and computational framework to perform commonsense reasoning about regions with both spatial and temporal components. Supported are capabilities for mixed qualitative-quantitative reasoning, consistency checking, and inferring compositions of space-time relations; these capabilities combine and synergise for applications in a range of AI application areas where the processing and interpretation of spatio-temporal data is crucial. The framework and resulting system is the only general KR-based method for declaratively reasoning about the dynamics of `space-time' regions as first-class objects. We present an empirical evaluation (with scalability and robustness results), and include diverse application examples involving interpretation and control tasks.

Hybrid manufacturing (HM) technologies combine additive and subtractive manufacturing (AM/SM) capabilities, leveraging AM's strengths in fabricating complex geometries and SM's precision and quality to produce finished parts. We present a systematic approach to automated computer-aided process planning (CAPP) for HM that can identify nontrivial, qualitatively distinct, and cost-optimal combinations of AM/SM modalities. A multimodal HM process plan is represented by a finite Boolean expression of AM and SM manufacturing primitives, such that the expression evaluates to an'as-manufactured' artifact. We show that primitives that respect spatial constraints such as accessibility and collision avoidance may be constructed by solving inverse configuration space problems on the'as-designed' artifact and manufacturing instruments. The primitives generate a finite Boolean algebra (FBA) that enumerates the entire search space for planning. The FBA's canonical intersection terms (i.e., 'atoms') provide the complete domain decomposition to reframe manufacturability analysis and process planning into purely symbolic reasoning, once a subcollection of atoms is found to be interchangeable with the design target. We demonstrate the practical potency of our framework and its computational efficiency when applied to process planning of complex 3D parts with dramatically different AM and SM instruments. Keywords: 1. Introduction Hybrid Manufacturing, Process Planning, Spatial Reasoning, Additive Manufacturing, Machining Hybrid manufacturing (HM), combining the capabilities of additive and subtractive manufacturing, is the new frontier of part fabrication. While additive manufacturing (AM) continues to enable unprecedented levels of structural complexity and customization, subtractive manufacturing (SM) remains indispensable for producing highprecision, mission-critical, and reliable mechanical components with functional interfaces. Versatile'multitasking' machines with simultaneous high-axis computer numerical control (CNC) of multiple AM and SM instruments (e.g., deposition heads and cutting tools) keep emerging on the market, enabling efficient use-cases for fabrication and repair (reviewed in Section 1.1).

We consider big spatial data, which is typically produced in scientific areas such as geological or seismic interpretation. The spatial data can be produced by observation (e.g. using sensors or soil instrument) or numerical simulation programs and correspond to points that represent a 3D soil cube area. However, errors in signal processing and modeling create some uncertainty, and thus a lack of accuracy in identifying geological or seismic phenomenons. Such uncertainty must be carefully analyzed. To analyze uncertainty, the main solution is to compute a Probability Density Function (PDF) of each point in the spatial cube area. However, computing PDFs on big spatial data can be very time consuming (from several hours to even months on a parallel computer). In this paper, we propose a new solution to efficiently compute such PDFs in parallel using Spark, with three methods: data grouping, machine learning prediction and sampling. We evaluate our solution by extensive experiments on different computer clusters using big data ranging from hundreds of GB to several TB. The experimental results show that our solution scales up very well and can reduce the execution time by a factor of 33 (in the order of seconds or minutes) compared with a baseline method.

We present a framework for the partitioning of a spatial trajectory in a sequence of segments based on spatial density and temporal criteria. The result is a set of temporally separated clusters interleaved by sub-sequences of unclustered points. A major novelty is the proposal of an outlier or noise model based on the distinction between intra-cluster (local noise) and inter-cluster noise (transition): the local noise models the temporary absence from a residence while the transition the definitive departure towards a next residence. We analyze in detail the properties of the model and present a comprehensive solution for the extraction of temporally ordered clusters. The effectiveness of the solution is evaluated first qualitatively and next quantitatively by contrasting the segmentation with ground truth. The ground truth consists of a set of trajectories of labeled points simulating animal movement. Moreover, we show that the approach can streamline the discovery of additional derived patterns, by presenting a novel technique for the analysis of periodic movement. From a methodological perspective, a valuable aspect of this research is that it combines the theoretical investigation with the application and external validation of the segmentation framework. This paves the way to an effective deployment of the solution in broad and challenging fields such as e-science.

Journal of Parallel and Distributed Computing 104, 19-35.

Spatial information is often expressed using qualitative terms such as natural language expressions instead of coordinates; reasoning over such terms has several practical applications, such as bus routes planning. Representing and reasoning on trajectories is a specific case of qualitative spatial reasoning that focuses on moving objects and their paths. In this work, we propose two versions of a trajectory calculus based on the allowed properties over trajectories, where trajectories are defined as a sequence of non-overlapping regions of a partitioned map. More specifically, if a given trajectory is allowed to start and finish at the same region, 6 base relations are defined (TC-6). If a given trajectory should have different start and finish regions but cycles are allowed within, 10 base relations are defined (TC-10). Both versions of the calculus are implemented as ASP programs; we propose several different encodings, including a generalised program capable of encoding any qualitative calculus in ASP. All proposed encodings are experimentally evaluated using a real-world dataset. Experiment results show that the best performing implementation can scale up to an input of 250 trajectories for TC-6 and 150 trajectories for TC-10 for the problem of discovering a consistent configuration, a significant improvement compared to previous ASP implementations for similar qualitative spatial and temporal calculi. This manuscript is under consideration for acceptance in TPLP.

About this course: Spatial (map) is considered as a core infrastructure of modern IT world, which is substantiated by business transactions of major IT companies such as Apple, Google, Microsoft, Amazon, Intel, and Uber, and even motor companies such as Audi, BMW, and Mercedes. Consequently, they are bound to hire more and more spatial data scientists. Based on such business trend, this course is designed to present a firm understanding of spatial data science to the learners, who would have a basic knowledge of data science and data analysis, and eventually to make their expertise differentiated from other nominal data scientists and data analysts. Additionally, this course could make learners realize the value of spatial big data and the power of open source software's to deal with spatial data science problems. This course will start with defining spatial data science and answering why spatial is special from three different perspectives - business, technology, and data in the first week.

Semantic segmentation is an established while rapidly evolving field in medical imaging. In this paper we focus on the segmentation of brain Magnetic Resonance Images (MRI) into cerebral structures using convolutional neural networks (CNN). CNNs achieve good performance by finding effective high dimensional image features describing the patch content only. In this work, we propose different ways to introduce spatial constraints into the network to further reduce prediction inconsistencies. A patch based CNN architecture was trained, making use of multiple scales to gather contextual information. Spatial constraints were introduced within the CNN through a distance to landmarks feature or through the integration of a probability atlas. We demonstrate experimentally that using spatial information helps to reduce segmentation inconsistencies.