PLLay: Efficient Topological Layer based on Persistence Landscapes
We propose PLLay, a novel topological layer for general deep learning models based on persistence landscapes, in which we can efficiently exploit the underlying topological features of the input data structure. In this work, we show differentiability with respect to layer inputs, for a general persistent homology with arbitrary filtration. Thus, our proposed layer can be placed anywhere in the network and feed critical information on the topological features of input data into subsequent layers to improve the learnability of the networks toward a given task. A task-optimal structure of PLLay is learned during training via backpropagation, without requiring any input featurization or data preprocessing. We provide a novel adaptation for the DTM function-based filtration, and show that the proposed layer is robust against noise and outliers through a stability analysis. We demonstrate the effectiveness of our approach by classification experiments on various datasets.
Code (2)
Tasks
Video-based Generative Performance Benchmarking (Contextual Understanding)Similar Papers 제목 키워드 기반
PLLay: Efficient Topological Layer based on Persistent Landscapes
We propose PLLay, a novel topological layer for general deep learning models based on persistence landscapes, in which we can efficiently exploit the underlying topological features of the input data structure. In this w…
Activation Landscapes as a Topological Summary of Neural Network Performance
We use topological data analysis (TDA) to study how data transforms as it passes through successive layers of a deep neural network (DNN). We compute the persistent homology of the activation data for each layer of the n…
Topological Data AnalysisTopological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia
We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI time series from each region. With these to…
ClusteringCommunity DetectionTime Series AnalysisTopological Data AnalysisImportance attribution in neural networks by means of persistence landscapes of time series
We propose and implement a method to analyze time series with a neural network using a matrix of area-normalized persistence landscapes obtained through topological data analysis. We include a gating layer in the network…
Time SeriesTime Series AnalysisTopological Data AnalysisTopoGCL: Topological Graph Contrastive Learning
Graph contrastive learning (GCL) has recently emerged as a new concept which allows for capitalizing on the strengths of graph neural networks (GNNs) to learn rich representations in a wide variety of applications which …
Contrastive LearningGraph Classification