Partial Wasserstein helps overcoming some of the limitations of Optimal Transport when the distributions at stake differ in mass, contain noise or outliers or exhibit mass mismatches across distribution modes. We introduce PAWL, a novel algorithm designed to efficiently compute exact PArtial Wasserstein distances on the Line. PAWL not only solves the partial transportation problem for a specified amount of mass to be transported, but _for all_ admissible mass amounts. This flexibility is valuable for machine learning tasks where the level of noise is uncertain and needs to be determined through cross-validation, for example. By achieving $O(n \log n)$ time complexity for the partial 1-Wasserstein problem on the line, it enables practical applications with large scale datasets. Additionally, we introduce a novel slicing strategy tailored to Partial Wasserstein, which does not permit transporting mass between outliers or noisy data points. We demonstrate the advantages of PAWL in terms of computational efficiency and performance in downstream tasks, outperforming existing (sliced) Partial Optimal Transport techniques.

Optimal Transport (OT) has attracted significant interest in the machine learning community, not only for its ability to define meaningful distances between probability distributions -- such as the Wasserstein distance -- but also for its formulation of OT plans. Its computational complexity remains a bottleneck, though, and slicing techniques have been developed to scale OT to large datasets. Recently, a novel slicing scheme, dubbed min-SWGG, lifts a single one-dimensional plan back to the original multidimensional space, finally selecting the slice that yields the lowest Wasserstein distance as an approximation of the full OT plan. Despite its computational and theoretical advantages, min-SWGG inherits typical limitations of slicing methods: (i) the number of required slices grows exponentially with the data dimension, and (ii) it is constrained to linear projections. Here, we reformulate min-SWGG as a bilevel optimization problem and propose a differentiable approximation scheme to efficiently identify the optimal slice, even in high-dimensional settings. We furthermore define its generalized extension for accommodating data living on manifolds. Finally, we demonstrate the practical value of our approach in various applications, including gradient flows on manifolds and high-dimensional spaces, as well as a novel sliced OT-based conditional flow matching for image generation -- where fast computation of transport plans is essential.

Kaligo-based Intelligent Handwriting Teacher (KIHT) is a bi-nationally funded research project. The aim of this joint project is to develop an intelligent learning device for automated handwriting, composed of existing components, which can be made available to as many students as possible. With KIHT, we specifically address the challenging task of using inertial sensors to retrace the trajectory of a pen without relying on external reference systems. The nearly unlimited freedom to let the pen glide over the paper has not yet provided a satisfactory solution to this challenge in the state-of-the-art methods, even with sophisticated algorithms and AI approaches. The final phase of the project is now being launched and together with partners from industry and academia, we are taking a holistic approach by considering the entire chain of components, from the pen to the embedded processing system, the algorithms and the app.

Optimal transport has recently been reintroduced to the machine learning community thanks in part to novel efficient optimization procedures allowing for medium to large scale applications. We propose a Python toolbox that implements several key optimal transport ideas for the machine learning community. The toolbox contains implementations of a number of founding works of OT for machine learning such as Sinkhorn algorithm and Wasserstein barycenters, but also provides generic solvers that can be used for conducting novel fundamental research. This toolbox, named POT for Python Optimal Transport, is open source with an MIT license.

Times series classification can be successfully tackled by jointly learning a shapelet-based representation of the series in the dataset and classifying the series according to this representation. This shapelet-based classification is both accurate and explainable since the shapelets are time series themselves and thus can be visualized and be provided as a classification explanation. In this paper, we claim that not all shapelets are good visual explanations and we propose a simple, yet also accurate, adversarily regularized EXplainable Convolutional Neural Network, XCNN, that can learn shapelets that are, by design, suited for explanations. We validate our method on the usual univariate time series benchmarks of the UCR repository.

tslearn is a general-purpose Python machine learning library for time series that offers tools for pre-processing and feature extraction as well as dedicated models for clustering, classification and regression. It follows scikit-learn's Application Programming Interface for transformers and estimators, allowing the use of standard pipelines and model selection tools on top of tslearn objects. It is distributed under the BSD-2-Clause license, and its source code is available at https://github.com/tslearn-team/tslearn.

This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance ( i.e. that minimizes a total cost of transporting probability masses) that unveils the geometric nature of the structured objects space. Unlike Wasserstein or Gromov-Wasserstein metrics that focus solely and respectively on features (by considering a metric in the feature space) or structure (by seeing structure as a metric space), our new distance exploits jointly both information, and is consequently called Fused Gromov-Wasserstein (FGW). After discussing its properties and computational aspects, we show results on a graph classification task, where our method outperforms both graph kernels and deep graph convolutional networks. Exploiting further on the metric properties of FGW, interesting geometric objects such as Fr{é}chet means or barycenters of graphs are illustrated and discussed in a clustering context.

Recently used in various machine learning contexts, the Gromov-Wasserstein distance (GW) allows for comparing distributions whose supports do not necessarily lie in the same metric space. However, this Optimal Transport (OT) distance requires solving a complex non convex quadratic program which is most of the time very costly both in time and memory. Contrary to GW, the Wasserstein distance (W) enjoys several properties ({\em e.g.} duality) that permit large scale optimization. Among those, the solution of W on the real line, that only requires sorting discrete samples in 1D, allows defining the Sliced Wasserstein (SW) distance. This paper proposes a new divergence based on GW akin to SW. We first derive a closed form for GW when dealing with 1D distributions, based on a new result for the related quadratic assignment problem. We then define a novel OT discrepancy that can deal with large scale distributions via a slicing approach and we show how it relates to the GW distance while being $O(n\log(n))$ to compute. We illustrate the behavior of this so called Sliced Gromov-Wasserstein (SGW) discrepancy in experiments where we demonstrate its ability to tackle similar problems as GW while being several order of magnitudes faster to compute.

A family of algorithms for time series classification (TSC) involve running a sliding window across each series, discretising the window to form a word, forming a histogram of word counts over the dictionary, then constructing a classifier on the histograms. A recent evaluation of two of this type of algorithm, Bag of Patterns (BOP) and Bag of Symbolic Fourier Approximation Symbols (BOSS) found a significant difference in accuracy between these seemingly similar algorithms. We investigate this phenomenon by deconstructing the classifiers and measuring the relative importance of the four key components between BOP and BOSS. We find that whilst ensembling is a key component for both algorithms, the effect of the other components is mixed and more complex. We conclude that BOSS represents the state of the art for dictionary-based TSC. Both BOP and BOSS can be classed as bag of words approaches. These are particularly popular in Computer Vision for tasks such as image classification. We adapt three techniques used in Computer Vision for TSC: Scale Invariant Feature Transform; Spatial Pyramids; and Histogram Intersection. We find that using Spatial Pyramids in conjunction with BOSS (SP) produces a significantly more accurate classifier. SP is significantly more accurate than standard benchmarks and the original BOSS algorithm. It is not significantly worse than the best shapelet-based or deep learning approaches, and is only outperformed by an ensemble that includes BOSS as a constituent module.

Kernel based feature extraction method overcomes the curse of dimensionality and captures the non-linearities present in the data. However, these methods are not scalable with large number of pixels found with hyperspectral images. Thus, a small subset of pixels are randomly selected to make the solution of kernel based methods tractable. In this paper, we propose scalable nonlinear component analysis for dimensionality reduction of hyperspectral images. The proposed method relies on the randomized feature maps to capture the non-linearities between the variables in the hyperspectral data. Experiments conducted with three hyperspectral datasets show that our proposed method has provided better quality components and outperformed the state-of-the-art in terms of classification performance.

Automatic land cover classification from satellite image time series is of paramount relevance to assess vegetation and crop status, with important implications in agriculture, biofuels, and food. However, due to the high cost and human resources needed to characterize and classify land cover through field campaigns, a recurrent limiting factor is the lack of available labeled data. On top of this, the biophysical-geophysical variables exhibit particular temporal structures that need to be exploited. Land cover classification based on image time series is very complex because of the data manifold distortions through time. We propose the use of the kernel manifold alignment (KEMA) method for domain adaptation of remote sensing time series before classification. KEMA is nonlinear and semisupervised and reduces to solve a simple generalized eigenproblem. We give empirical evidence of performance through classification of biophysical (leaf area index, fraction of absorbed photosynthetically active radiation, fractional vegetation cover, and normalized difference vegetation index) time series on a global scale.

Mapping croplands is a challenging problem in a context of climate change and evolving agricultural calendars. Classification based on MODIS vegetation index time series is performed in order to map crop types in the Brazilian state of Mato Grosso. We used the recently developed Dense Bag-of-Temporal-SIFT-Words algorithm, which is able to capture temporal locality of the data. It allows the accurate detection of around 70% of the agricultural areas. It leads to better classification rates than a baseline algorithm, discriminating more accurately classes with similar profiles.

In this paper, we postulate that temporal information is important for action recognition in videos. Keeping temporal information, videos are represented as word×time documents. We propose to use time-sensitive probabilistic topic models and we extend them for the context of supervised learning. Our time-sensitive approach is compared to both PLSA and Bag-of-Words. Our approach is shown to both capture semantics from data and yield classification performance comparable to other methods, outperforming them when the amount of training data is low.

Recent indexing techniques inspired by source coding have been shown successful to index billions of high-dimensional vectors in memory. In this paper, we propose an approach that re-ranks the neighbor hypotheses obtained by these compressed-domain indexing methods. In contrast to the usual post-verification scheme, which performs exact distance calculation on the short-list of hypotheses, the estimated distances are refined based on short quantization codes, to avoid reading the full vectors from disk. We have released a new public dataset of one billion 128 dimensional vectors and proposed an experimental setup to evaluate high dimensional indexing algorithms on a realistic scale. Experiments show that our method accurately and efficiently re-ranks the neighbor hypotheses using little memory compared to the full vectors representation.

Due to rapid advances in networking and sensing technology we are witnessing a growing interest in sensor networks, in which a variety of sensors are connected to each other and to computational devices capable of multimodal signal processing and data analysis. Such networks are seen to play an increasingly important role as key enablers in emerging pervasive computing technologies. In the first part of this paper we give an overview of recent developments in the area of multimodal sensor networks, paying special attention to ambient intelligence applications. In the second part, we discuss how the time series generated by data streams emanating from the sensors can be mined for temporal patterns, indicating cross-sensor signal correlations.