Related papers: Learning Topology-Preserving Data Representations

Comparison of data representations is a complex multi-aspect problem that has not enjoyed a complete solution yet. We propose a method for comparing two data representations. We introduce the Representation Topology Divergence (RTD),…

Dimensionality reduction is an integral part of data visualization. It is a process that obtains a structure preserving low-dimensional representation of the high-dimensional data. Two common criteria can be used to achieve a dimensionality…

Unsupervised dimensionality reduction is one of the commonly used techniques in the field of high dimensional data recognition problems. The deep autoencoder network which constrains the weights to be non-negative, can learn a low…

The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…

Auto-encoder models that preserve similarities in the data are a popular tool in representation learning. In this paper we introduce several auto-encoder models that preserve local distances when mapping from the data space to the latent…

Manifold learning aims to discover and represent low-dimensional structures underlying high-dimensional data while preserving critical topological and geometric properties. Existing methods often fail to capture local details with global…

We propose TopDis (Topological Disentanglement), a method for learning disentangled representations via adding a multi-scale topological loss term. Disentanglement is a crucial property of data representations substantial for the…

In this paper, we explore how to use topological tools to compare dimension reduction methods. We first make a brief overview of some of the methods often used dimension reduction such as Isometric Feature Mapping, Laplacian Eigenmaps, Fast…

Dimensionality reduction techniques are powerful tools for data preprocessing and visualization which typically come with few guarantees concerning the topological correctness of an embedding. The interleaving distance between the…

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of…

We explore the use of a topological manifold, represented as a collection of charts, as the target space of neural network based representation learning tasks. This is achieved by a simple adjustment to the output of an encoder's network…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

Topological Data Analysis (TDA) provides tools to describe the shape of data, but integrating topological features into deep learning pipelines remains challenging, especially when preserving local geometric structure rather than…

We propose a novel algorithm for supervised dimensionality reduction named Manifold Partition Discriminant Analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is…

Manifold learning techniques, such as Locally linear embedding (LLE), are designed to preserve the local neighborhood structures of high-dimensional data during dimensionality reduction. Traditional LLE employs Euclidean distance to define…

A new dimension reduction (DR) method for data sets is proposed by autonomous deforming of data manifolds. The deformation is guided by the proposed deforming vector field, which is defined by two kinds of virtual interactions between data…

Dimensionality reduction techniques map data represented on higher dimensions onto lower dimensions with varying degrees of information loss. Graph dimensionality reduction techniques adopt the same principle of providing latent…

Representation learning seeks to expose certain aspects of observed data in a learned representation that's amenable to downstream tasks like classification. For instance, a good representation for 2D images might be one that describes only…

One of the main drawbacks of the practical use of neural networks is the long time required in the training process. Such a training process consists of an iterative change of parameters trying to minimize a loss function. These changes are…

Topological Data Analysis (TDA) is an approach to handle with big data by studying its shape. A main tool of TDA is the persistence diagram, and one can use it to compare data sets. One approach to learn on the similarity between two…