Related papers: The Rough Topology for Numerical Data

In this paper we presented a novel constructive approach for training deep neural networks using geometric approaches. We show that a topological covering can be used to define a class of distributed linear matrix inequalities, which in…

We introduce a meta-learning algorithm for adversarially robust classification. The proposed method tries to be as model agnostic as possible and optimizes a dataset prior to its deployment in a machine learning system, aiming to…

Deep learning is one of the new and important branches in machine learning. Deep learning refers to a set of algorithms that solve various problems such as images and texts by using various machine learning algorithms in multi-layer neural…

The study of topology is strictly speaking, a topic in pure mathematics. However in only a few years, Topological Data Analysis (TDA), which refers to methods of utilizing topological features in data (such as connected components, tunnels,…

Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…

Passive network tomography uses end-to-end observations of network communication to characterize the network, for instance to estimate the network topology and to localize random or adversarial glitches. Under the setting of linear network…

Many real world network problems often concern multivariate nodal attributes such as image, textual, and multi-view feature vectors on nodes, rather than simple univariate nodal attributes. The existing graph estimation methods built on…

The value proposition of a dataset often resides in the implicit interconnections or explicit relationships (patterns) among individual entities, and is often modeled as a graph. Effective visualization of such graphs can lead to key…

Texture is a visual attribute largely used in many problems of image analysis. Currently, many methods that use learning techniques have been proposed for texture discrimination, achieving improved performance over previous handcrafted…

Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing…

Despite encouraging recent progresses in ensemble approaches, classification methods seem to have reached a plateau in development. Further advances depend on a better understanding of geometrical and topological characteristics of point…

We provide a short introduction to the field of topological data analysis and discuss its possible relevance for the study of complex systems. Topological data analysis provides a set of tools to characterise the shape of data, in terms of…

The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most…

Machine learning and deep learning have been used extensively to classify physical surfaces through images and time-series contact data. However, these methods rely on human expertise and entail the time-consuming processes of data and…

A graph-based classification method is proposed for semi-supervised learning in the case of Euclidean data and for classification in the case of graph data. Our manifold learning technique is based on a convex optimization problem involving…

Robust topological information commonly comes in the form of a set of persistence diagrams, finite measures that are in nature uneasy to affix to generic machine learning frameworks. We introduce a fast, learnt, unsupervised vectorization…

Feature weighting algorithms try to solve a problem of great importance nowadays in machine learning: The search of a relevance measure for the features of a given domain. This relevance is primarily used for feature selection as feature…

Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…

This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…

Dimensionality reduction (DR) of image features plays an important role in image retrieval and classification tasks. Recently, two types of methods have been proposed to improve the both the accuracy and efficiency for the dimensionality…