Computing the proximal operator of the $\ell_\infty$ norm, $\textbf{prox}_{\alpha ||\cdot||_\infty}(\mathbf{x})$, generally requires a sort of the input data, or at least a partial sort similar to quicksort. In order to avoid using a sort, we present an $O(m)$ approximation of $\textbf{prox}_{\alpha ||\cdot||_\infty}(\mathbf{x})$ using a neural network. A novel aspect of the network is that it is able to accept vectors of varying lengths due to a feature selection process that uses moments of the input data. We present results on the accuracy of the approximation, feature importance, and computational efficiency of the approach. We show that the network outperforms a "vanilla neural network" that does not use feature selection. We also present an algorithm with corresponding theory to calculate $\textbf{prox}_{\alpha ||\cdot||_\infty}(\mathbf{x})$ exactly, relate it to the Moreau decomposition, and compare its computational efficiency to that of the approximation.

This course is about statistical analysis of vector data and machine learning using vector data. In this course I demonstrate open source python packages for the analysis of vector-based geospatial data. I use Jupyter Notebooks as an interactive Python environment. GeoPandas is used for reading and storing geospatial data, exploratory data analysis, preparing data for use in statistical models (feature engineering, dealing with outlier and missing data, etc.), and simple plotting. Statsmodels is used for statistical inference as it provides more detail on the explanatory power of individual explanatory variables and a framework for model selection.

Recent wildfires in the United States have resulted in loss of life and billions of dollars, destroying countless structures and forests. Fighting wildfires is extremely complex. It is difficult to observe the true state of fires due to smoke and risk associated with ground surveillance. There are limited resources to be deployed over a massive area and the spread of the fire is challenging to predict. This paper proposes a decision-theoretic approach to combat wildfires. We model the resource allocation problem as a partially-observable Markov decision process. We also present a data-driven model that lets us simulate how fires spread as a function of relevant covariates. A major problem in using data-driven models to combat wildfires is the lack of comprehensive data sources that relate fires with relevant covariates. We present an algorithmic approach based on large-scale raster and vector analysis that can be used to create such a dataset. Our data with over 2 million data points is the first open-source dataset that combines existing fire databases with covariates extracted from satellite imagery. Through experiments using real-world wildfire data, we demonstrate that our forecasting model can accurately model the spread of wildfires. Finally, we use simulations to demonstrate that our response strategy can significantly reduce response times compared to baseline methods.

Today we will focus on vector data and linear algebra handling when building this type of model. Note that data preprocessing may be ignored due to the things we are focusing on is not there this time. Vector data, also known as 2D tensors. If we say a single data is a vector, then 2D vector data is just when we handle more than one single data at a time. Suppose we are implementing a 3-layers multilayer perceptron for the Iris dataset for classification on TensorFlow 1.X.

Graph learning methods, especially graph convolutional networks, have been investigated for their potential applicability in many fields of study based on topological data. Their topological data processing capabilities have proven to be powerful. However, the relationships among separate entities include not only topological adjacency, but also correlation in vision, for example, the spatial vector data of buildings. In this study, we propose a spatial adaptive algorithm framework with a data-driven design to accomplish building group division and building group pattern recognition tasks, which is not sensitive to the difference in the spatial distribution of the buildings in various geographical regions. In addition, the algorithm framework has a multi-stage design, and processes the building group data from whole to parts, since the objective is closely related to multi-object detection on topological data.

Recent innovations in agile aerospace have created unique offerings in high cadence satellite imagery. While this is of immense interest to imagery analysts, a significant portion of GIS professionals and geo-data scientists work less with raster data (AKA imagery) and more with point and vector data. Planet operates the world's largest constellation of earth observation satellites providing near-daily coverage of the entirety of Earth's landmass. Over the past couple of years, we have been working on bringing computer vision and spatiotemporal analysis to market to enable access and data transformations on this rich imagery archive. We recently announced the general availability of our analytic feeds and the launch of our building change detection analytics in private beta (sign up for info here).

So I wanted to create a seamless tutorial for taking OpenStreetMap (OSM) vector data and converting it for use with machine learning (ML) models. In particular, I am really interested in creating a tight, clean pipeline for disaster relief applications, where we can use something like crowd sourced building polygons from OSM to train a supervised object detector to discover buildings in an unmapped location. The recipe for building a basic deep learning object detector is to have two components: (1) training data (raster image vector label pairs) and (2) model framework. The deep learning model itself will be a Single Shot Detector (SSD) object detector. We will use OSM polygons as the basis of our label data and Digital Globe imagery for the raster data. We won't go into the details of an SSD here, as there are plenty sources available.

Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper, we give an introduction to some methods relying on graphs for learning. This includes both unsupervised and supervised methods. Unsupervised learning algorithms usually aim at visualising graphs in latent spaces and/or clustering the nodes. Both focus on extracting knowledge from graph topologies. While most existing techniques are only applicable to static graphs, where edges do not evolve through time, recent developments have shown that they could be extended to deal with evolving networks. In a supervised context, one generally aims at inferring labels or numerical values attached to nodes using both the graph and, when they are available, node characteristics. Balancing the two sources of information can be challenging, especially as they can disagree locally or globally. In both contexts, supervised and un-supervised, data can be relational (augmented with one or several global graphs) as described above, or graph valued. In this latter case, each object of interest is given as a full graph (possibly completed by other characteristics). In this context, natural tasks include graph clustering (as in producing clusters of graphs rather than clusters of nodes in a single graph), graph classification, etc. 1 Real networks One of the first practical studies on graphs can be dated back to the original work of Moreno [51] in the 30s. Since then, there has been a growing interest in graph analysis associated with strong developments in the modelling and the processing of these data. Graphs are now used in many scientific fields. In Biology [54, 2, 7], for instance, metabolic networks can describe pathways of biochemical reactions [41], while in social sciences networks are used to represent relation ties between actors [66, 56, 36, 34]. Other examples include powergrids [71] and the web [75]. Recently, networks have also been considered in other areas such as geography [22] and history [59, 39]. In machine learning, networks are seen as powerful tools to model problems in order to extract information from data and for prediction purposes. This is the object of this paper. For more complete surveys, we refer to [28, 62, 49, 45]. In this section, we introduce notations and highlight properties shared by most real networks. In Section 2, we then consider methods aiming at extracting information from a unique network. We will particularly focus on clustering methods where the goal is to find clusters of vertices. Finally, in Section 3, techniques that take a series of networks into account, where each network is

KI - Künstliche Intelligenz manuscript No. (will be inserted by the editor) Abstract Artificial neural networks are simple and efficient machine learning tools. Defined originally in the traditional setting of simple vector data, neural network models have evolved to address more and more difficulties of complex real world problems, ranging from time evolving data to sophisticated data structures such as graphs and functions. This paper summarizes advances on those themes from the last decade, with a focus on results obtained by members of the SAMM team of Université Paris 1. 1 Introduction In many real world applications of machine learning and related techniques, the raw data are not anymore in a standard and simple tabular format in which each object is described by a common and fixed set of numerical attributes. This standard vector model, while useful and efficient, has some obvious limitations: it is limited to numerical attributes, it cannot handle objects with non uniform descriptions (e.g., situations in which some objects have a richer description than others), relations between objects (e.g., persons involved in a social network), etc. In addition, it is quite common for real world applications to have some dynamic aspect in the sense that the data under study are the results of a temporal process. Then, the traditional hypothesis of statistical independence between observations does not hold anymore: new hypothesis and theoretical analysis are needed to justify the mathematical soundness of the machine learning methods in this context.

Dimensionality reduction plays a vital role in pattern recognition. However, for normalized vector data, existing methods do not utilize the fact that the data is normalized. In this paper, we propose to employ an Angular Decomposition of the normalized vector data which corresponds to embedding them on a unit surface. On graph data for similarity/kernel matrices with constant diagonal elements, we propose the Angular Decomposition of the similarity matrices which corresponds to embedding objects on a unit sphere. In these angular embeddings, the Euclidean distance is equivalent to the cosine similarity. Thus data structures best described in the cosine similarity and data structures best captured by the Euclidean distance can both be effectively detected in our angular embedding. We provide the theoretical analysis, derive the computational algorithm, and evaluate the angular embedding on several datasets. Experiments on data clustering demonstrate that our method can provide a more discriminative subspace.