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Persistent Homology-Based Classification of Chaotic Multi-variate Time Series: Application to Electroencephalograms
In this work, we present a combination of dimension reduction techniques and persistent homology for detection of epileptic events in...
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Image Classification Using Deep Neural Networks and Persistent Homology
Persistent Homology (PH), a key tool in Topological Data Analysis (TDA), has gained significant traction in Machine Learning and Data Science...
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The persistent homology of genealogical networks
Genealogical networks (i.e. family trees) are of growing interest, with the largest known data sets now including well over one billion individuals....
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Persistent-homology-based machine learning: a survey and a comparative study
A suitable feature representation that can both preserve the data intrinsic information and reduce data complexity and dimensionality is key to the...
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Persistent spectral theory-guided protein engineering
Although protein engineering, which iteratively optimizes protein fitness by screening the gigantic mutational space, is constrained by experimental...
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Persistent homology based Bottleneck distance in hypergraph products
In this paper, we extended the technique of measuring similarity between topological spaces using bottle neck distance between persistence diagrams...
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Topological measurement of deep neural networks using persistent homology
The inner representation of deep neural networks (DNNs) is indecipherable, which makes it difficult to tune DNN models, control their training...
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Lattice Paths for Persistent Diagrams
Persistent homology has undergone significant development in recent years. However, one outstanding challenge is to build a coherent statistical...
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Comparison of Word Embeddings of Unaligned Audio and Text Data Using Persistent Homology
We have performed preliminary work on topological analysis of audio and text data for unsupervised speech processing. The work is based on the...
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The Comparison of Diffeomorphic Images based on the Construction of Persistent Homology
AbstractAn object shape analysis is a problem that is related to such areas as geometry, topology, image processing and machine learning. For...
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Emotion recognition based on phase-locking value brain functional network and topological data analysis
Traditional threshold-based methods in brain functional network analysis have some drawbacks. First, the process of determining thresholds is often...
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A Persistent Homology-Based Topological Loss Function for Multi-class CNN Segmentation of Cardiac MRI
With respect to spatial overlap, CNN-based segmentation of short axis cardiovascular magnetic resonance (CMR) images has achieved a level of...
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Topological deep learning: a review of an emerging paradigm
Topological deep learning (TDL) is an emerging area that combines the principles of Topological data analysis (TDA) with deep learning techniques....
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Topological Analysis of Temporal Hypergraphs
In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is...
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Topology and Local Optima in Computer Vision
We present an application of persistent homology to the image correspondence problem, also known as image registration, which is used to produce 3D...
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Topological Analysis of Simple Segmentation Maps
In this paper, we propose a geometry-aware topological analysis of a segmentation of an image into regions which might correspond, for example, to a...
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Persistent Feature Analysis of Multimodal Brain Networks Using Generalized Fused Lasso for EMCI Identification
Early Mild Cognitive Impairment (EMCI) involves very subtle changes in brain pathological process, and thus identification of EMCI can be...
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Topological Analysis of Credit Data: Preliminary Findings
Intuitively, similar customers should have similar credit risk. Capturing this similarity is often attempted using Euclidean distances between...
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Fetal Cortex Segmentation with Topology and Thickness Loss Constraints
The segmentation of the fetal cerebral cortex from magnetic resonance imaging (MRI) is an important tool for neurobiological research about the...
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Persistence B-spline grids: stable vector representation of persistence diagrams based on data fitting
Many attempts have been made in recent decades to integrate machine learning (ML) and topological data analysis. A prominent problem in applying...
