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Found 12 papers, 3 papers with code
Convolutional Persistence Transforms
In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filters before computing persistence.
Topological Simplification of Signals for Inference and Approximate Reconstruction
As Internet of Things (IoT) devices become both cheaper and more powerful, researchers are increasingly finding solutions to their scientific curiosities both financially and computationally feasible.
Improving Metric Dimensionality Reduction with Distributed Topology
We propose a novel approach to dimensionality reduction combining techniques of metric geometry and distributed persistent homology, in the form of a gradient-descent based method called DIPOLE.
From Geometry to Topology: Inverse Theorems for Distributed Persistence
Moreover, the quasi-isometry bounds depend on the size of the subsets taken, so that as the size of these subsets goes from small to large, the invariant interpolates between a purely geometric one and a topological one.
A Fast and Robust Method for Global Topological Functional Optimization
Topological statistics, in the form of persistence diagrams, are a class of shape descriptors that capture global structural information in data.
Geometric Fusion via Joint Delay Embeddings
We introduce geometric and topological methods to develop a new framework for fusing multi-sensor time series.
Graph Spectral Embedding for Parsimonious Transmission of Multivariate Time Series
This representation, which we call Laplacian Events Signal Segmentation (LESS), can be computed on time series of arbitrary dimension and originating from sensors of arbitrary type.
Multi-scale Geometric Summaries for Similarity-based Sensor Fusion
A fused similarity template is then derived from the modality-specific SSMs using a technique called similarity network fusion (SNF).
Geometric Cross-Modal Comparison of Heterogeneous Sensor Data
The information represented by the two modalities is compared using self-similarity matrices (SSMs) corresponding to time-ordered point clouds in feature spaces of each of these data sources; we note that these feature spaces can be of entirely different scale and dimensionality.
Supervised Learning of Labeled Pointcloud Differences via Cover-Tree Entropy Reduction
We introduce a new algorithm, called CDER, for supervised machine learning that merges the multi-scale geometric properties of Cover Trees with the information-theoretic properties of entropy.
Multi-Scale Local Shape Analysis and Feature Selection in Machine Learning Applications
We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset.
Topological and Statistical Behavior Classifiers for Tracking Applications
We introduce the first unified theory for target tracking using Multiple Hypothesis Tracking, Topological Data Analysis, and machine learning.
