Topological Data Analysis (tda) is a recent and fast growing eld providing a set of new topological and geometric tools to infer relevant features for possibly complex data. This paper is a brief introduction, through a few selected topics, to basic fundamental and practical aspects of tda for non experts. 1 Introduction and motivation Topological Data Analysis (tda) is a recent eld that emerged from various works in applied (algebraic) topology and computational geometry during the rst decade of the century. Although one can trace back geometric approaches for data analysis quite far in the past, tda really started as a eld with the pioneering works of Edelsbrunner et al. (2002) and Zomorodian and Carlsson (2005) in persistent homology and was popularized in a landmark paper in 2009 Carlsson (2009). tda is mainly motivated by the idea that topology and geometry provide a powerful approach to infer robust qualitative, and sometimes quantitative, information about the structure of data-see, e.g. Chazal (2017). tda aims at providing well-founded mathematical, statistical and algorithmic methods to infer, analyze and exploit the complex topological and geometric structures underlying data that are often represented as point clouds in Euclidean or more general metric spaces. During the last few years, a considerable eort has been made to provide robust and ecient data structures and algorithms for tda that are now implemented and available and easy to use through standard libraries such as the Gudhi library (C++ and Python) Maria et al. (2014) and its R software interface Fasy et al. (2014a). Although it is still rapidly evolving, tda now provides a set of mature and ecient tools that can be used in combination or complementary to other data sciences tools. The tdapipeline. tda has recently known developments in various directions and application elds. There now exist a large variety of methods inspired by topological and geometric approaches. Providing a complete overview of all these existing approaches is beyond the scope of this introductory survey. However, most of them rely on the following basic and standard pipeline that will serve as the backbone of this paper: 1. The input is assumed to be a nite set of points coming with a notion of distance-or similarity between them. This distance can be induced by the metric in the ambient space (e.g. the Euclidean metric when the data are embedded in R d) or come as an intrinsic metric dened by a pairwise distance matrix. The denition of the metric on the data is usually given as an input or guided by the application. It is however important to notice that the choice of the metric may be critical to reveal interesting topological and geometric features of the data.

Eric Sondheimer has been covering high school sports for the Los Angeles Times since 1997 and in Southern California since 1976. Get his latest from the field and follow all our prep sports coverage and analysis here. Soccer: Adidas West Coast Showcase set for Dec. 7-9 Bell Gardens, Downey, Paramount and Warren will be the sites for one of the top boys' soccer tournaments set for Dec. 7-9. The Adidas West Coast Showcase will bring together top teams from around Southern California. The West Division has Channel Islands, Clovis, Downey, Granada Hills, Long Beach Jordan, Moorpark, Palos Verdes and Warren.

Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological summaries, most noticeably the Persistence Diagram, are typically defined in complex spaces, we adopt a kernel approach to translate them into more familiar vector spaces. We define a topological exponential kernel, we characterize it, and we show that, despite not being positive semi-definite, it can be successfully used in regression and classification tasks.

Chicago Cubs manager Joe Maddon says he's looking forward to a two-game series at Tampa Bay. Maddon guided the Rays for nine seasons -- they were the Devil Rays when he started in 2006 -- and went 754-708, along with leading them to their only World Series appearance. The Cubs are visiting Tropicana Field for the first time since 2008, when Tampa Bay swept all three games and then-rookie Evan Longoria had an RBI in each victory. Maddon still has a lot of friends in the area, and his foundation recently donated $25,000 to those affected by Hurricane Irma.

We introduce an unsupervised discriminative model for the task of retrieving experts in online document collections. We exclusively employ textual evidence and avoid explicit feature engineering by learning distributed word representations in an unsupervised way. We compare our model to state-of-the-art unsupervised statistical vector space and probabilistic generative approaches. Our proposed log-linear model achieves the retrieval performance levels of state-of-the-art document-centric methods with the low inference cost of so-called profile-centric approaches. It yields a statistically significant improved ranking over vector space and generative models in most cases, matching the performance of supervised methods on various benchmarks. That is, by using solely text we can do as well as methods that work with external evidence and/or relevance feedback. A contrastive analysis of rankings produced by discriminative and generative approaches shows that they have complementary strengths due to the ability of the unsupervised discriminative model to perform semantic matching.

We address the problem of multi-class classification in the case where the number of classes is very large. We propose a double sampling strategy on top of a multi-class to binary reduction strategy, which transforms the original multi-class problem into a binary classification problem over pairs of examples. The aim of the sampling strategy is to overcome the curse of long-tailed class distributions exhibited in majority of large-scale multi-class classification problems and to reduce the number of pairs of examples in the expanded data. We show that this strategy does not alter the consistency of the empirical risk minimization principle defined over the double sample reduction. Experiments are carried out on DMOZ and Wikipedia collections with 10,000 to 100,000 classes where we show the efficiency of the proposed approach in terms of training and prediction time, memory consumption, and predictive performance with respect to state-of-the-art approaches.

Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier theory of natural language, due to Barwise and Cooper. The underlying setting is a compact closed category with bialgebras. We start from a generative grammar formalisation and develop an abstract categorical compositional semantics for it, then instantiate the abstract setting to sets and relations and to finite dimensional vector spaces and linear maps. We prove the equivalence of the relational instantiation to the truth theoretic semantics of generalised quantifiers. The vector space instantiation formalises the statistical usages of words and enables us to, for the first time, reason about quantified phrases and sentences compositionally in distributional semantics.

In this era of digitization, knowing the user's sociolect aspects have become essential features to build the user specific recommendation systems. These sociolect aspects could be found by mining the user's language sharing in the form of text in social media and reviews. This paper describes about the experiment that was performed in PAN Author Profiling 2017 shared task. The objective of the task is to find the sociolect aspects of the users from their tweets. The sociolect aspects considered in this experiment are user's gender and native language information. Here user's tweets written in a different language from their native language are represented as Document - Term Matrix with document frequency as the constraint. Further classification is done using the Support Vector Machine by taking gender and native language as target classes.

We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design learning algorithms using a surrogate loss approach and regularization techniques. We prove universal consistency and finite sample bounds characterizing the generalization properties of the proposed methods. Experimental results are provided to demonstrate the practical usefulness of the proposed approach.

Generating adversarial examples is a critical step for evaluating and improving the robustness of learning machines. So far, most existing methods only work for classification and are not designed to alter the true performance measure of the problem at hand. We introduce a novel flexible approach named Houdini for generating adversarial examples specifically tailored for the final performance measure of the task considered, be it combinatorial and non-decomposable. We successfully apply Houdini to a range of applications such as speech recognition, pose estimation and semantic segmentation. In all cases, the attacks based on Houdini achieve higher success rate than those based on the traditional surrogates used to train the models while using a less perceptible adversarial perturbation.