Related papers: Persistence Diagrams with Linear Machine Learning …

Early diagnosis of interstitial lung diseases is crucial for their treatment, but even experienced physicians find it difficult, as their clinical manifestations are similar. In order to assist with the diagnosis, computer-aided diagnosis…

Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying…

Data association is at the core of many computer vision tasks, e.g., multiple object tracking, image matching, and point cloud registration. however, current data association solutions have some defects: they mostly ignore the intra-view…

Persistence diagrams are important tools in the field of topological data analysis that describe the presence and magnitude of features in a filtered topological space. However, current approaches for comparing a persistence diagram to a…

Inverse problems exist in many domains such as phase imaging, image processing, and computer vision. These problems are often solved with application-specific algorithms, even though their nature remains the same: mapping input image(s) to…

There is strong interest in developing mathematical methods that can be used to understand complex neural networks used in image analysis. In this paper, we introduce techniques from Linear Algebra to model neural network layers as maps…

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…

Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of networks flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and…

Feature learning on point clouds has shown great promise, with the introduction of effective and generalizable deep learning frameworks such as pointnet++. Thus far, however, point features have been abstracted in an independent and…

Many topological data analysis (TDA) pipelines compute large collections of persistence diagrams, yet vectorizations and kernel methods discard the rank-induced implication relations among persistence intervals that are essential for…

This overview article makes the case for how topological concepts can enrich research in machine learning. Using the Euler Characteristic Transform (ECT), a geometrical-topological invariant, as a running example, I present different use…

In this paper we derive an efficient algorithm to learn the parameters of structured predictors in general graphical models. This algorithm blends the learning and inference tasks, which results in a significant speedup over traditional…

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to…

In topological data analysis, we want to discern topological and geometric structure of data, and to understand whether or not certain features of data are significant as opposed to simply random noise. While progress has been made on…

Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…

Graph representation learning is fundamental for analyzing graph-structured data. Exploring invariant graph representations remains a challenge for most existing graph representation learning methods. In this paper, we propose a cross-view…

The rapid advancements in machine learning have made its application to anomalous diffusion analysis both essential and inevitable. This review systematically introduces the integration of machine learning techniques for enhanced analysis…

We present a simple and general framework for feature learning from point clouds. The key to the success of CNNs is the convolution operator that is capable of leveraging spatially-local correlation in data represented densely in grids…