When each data point is a large graph, graph statistics such as densities of certain subgraphs (motifs) can be used as feature vectors for machine learning. While intuitive, motif counts are expensive to compute and difficult to work with theoretically. Via graphon theory, we give an explicit quantitative bound for the ability of motif homomorphisms to distinguish large networks under both generative and sampling noise. Furthermore, we give similar bounds for the graph spectrum and connect it to homomorphism densities of cycles. This results in an easily computable classifier on graph data with theoretical performance guarantee. Our method yields competitive results on classification tasks for the autoimmune disease Lupus Erythematosus.

The characteristics (or numerical patterns) of a feature vector in the transform domain of a perturbation model differ significantly from those of its corresponding feature vector in the input domain. These differences - caused by the perturbation techniques used for the transformation of feature patterns - degrade the performance of machine learning techniques in the transform domain. In this paper, we proposed a nonlinear parametric perturbation model that transforms the input feature patterns to a set of elliptical patterns, and studied the performance degradation issues associated with random forest classification technique using both the input and transform domain features. Compared with the linear transformation such as Principal Component Analysis (PCA), the proposed method requires less statistical assumptions and is highly suitable for the applications such as data privacy and security due to the difficulty of inverting the elliptical patterns from the transform domain to the input domain. In addition, we adopted a flexible block-wise dimensionality reduction step in the proposed method to accommodate the possible high-dimensional data in modern applications. We evaluated the empirical performance of the proposed method on a network intrusion data set and a biological data set, and compared the results with PCA in terms of classification performance and data privacy protection (measured by the blind source separation attack and signal interference ratio). Both results confirmed the superior performance of the proposed elliptical transformation. 1 1. INTRODUCTION Feature vectors carry useful numerical patterns that characterize the original domain (or a sub original domain - input domain) formed by the feature vectors themselves. Machine learning algorithms generally utilize these patterns to generate classifiers, that can help make decisions from data, by using supervised or unsupervised learning techniques (Suthaharan, 2015).

This paper presents a general graph representation learning framework called DeepGL for learning deep node and edge representations from large (attributed) graphs. In particular, DeepGL begins by deriving a set of base features (e.g., graphlet features) and automatically learns a multi-layered hierarchical graph representation where each successive layer leverages the output from the previous layer to learn features of a higher-order. Contrary to previous work, DeepGL learns relational functions (each representing a feature) that generalize across-networks and therefore useful for graph-based transfer learning tasks. Moreover, DeepGL naturally supports attributed graphs, learns interpretable features, and is space-efficient (by learning sparse feature vectors). In addition, DeepGL is expressive, flexible with many interchangeable components, efficient with a time complexity of $\mathcal{O}(|E|)$, and scalable for large networks via an efficient parallel implementation. Compared with the state-of-the-art method, DeepGL is (1) effective for across-network transfer learning tasks and attributed graph representation learning, (2) space-efficient requiring up to 6x less memory, (3) fast with up to 182x speedup in runtime performance, and (4) accurate with an average improvement of 20% or more on many learning tasks.

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.

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.

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.

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.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

Generalized canonical correlation analysis (GCCA) aims at finding latent low-dimensional common structure from multiple views (feature vectors in different domains) of the same entities. Unlike principal component analysis (PCA) that handles a single view, (G)CCA is able to integrate information from different feature spaces. Here we focus on MAX-VAR GCCA, a popular formulation which has recently gained renewed interest in multilingual processing and speech modeling. The classic MAX-VAR GCCA problem can be solved optimally via eigen-decomposition of a matrix that compounds the (whitened) correlation matrices of the views; but this solution has serious scalability issues, and is not directly amenable to incorporating pertinent structural constraints such as non-negativity and sparsity on the canonical components. We posit regularized MAX-VAR GCCA as a non-convex optimization problem and propose an alternating optimization (AO)-based algorithm to handle it. Our algorithm alternates between {\em inexact} solutions of a regularized least squares subproblem and a manifold-constrained non-convex subproblem, thereby achieving substantial memory and computational savings. An important benefit of our design is that it can easily handle structure-promoting regularization. We show that the algorithm globally converges to a critical point at a sublinear rate, and approaches a global optimal solution at a linear rate when no regularization is considered. Judiciously designed simulations and large-scale word embedding tasks are employed to showcase the effectiveness of the proposed algorithm.