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Found 11 papers, 3 papers with code
SIMAP: A simplicial-map layer for neural networks
In this paper, we present SIMAP, a novel layer integrated into deep learning models, aimed at enhancing the interpretability of the output.
A Topological Approach to Measuring Training Data Quality
Data quality is crucial for the successful training, generalization and performance of artificial intelligence models.
Trainable and Explainable Simplicial Map Neural Networks
In this paper, we overcome these issues by proposing an SMNN training procedure based on a support subset of the given dataset and replacing the construction of the convex polytope by a method based on projections to a hypersphere.
Emotion recognition in talking-face videos using persistent entropy and neural networks
The automatic recognition of a person's emotional state has become a very active research field that involves scientists specialized in different areas such as artificial intelligence, computer vision or psychology, among others.
Summary and Distance between Sets of Texts based on Topological Data Analysis
In this paper, we use topological data analysis (TDA) tools such as persistent homology, persistent entropy and bottleneck distance, to provide a {\it TDA-based summary} of any given set of texts and a general method for computing a distance between any two literary styles, authors or periods.
Two-hidden-layer Feedforward Neural Networks are Universal Approximators: A Constructive Approach
This approach is based on an approximation of continuous functions by simplicial maps.
Topological signature for periodic motion recognition
In this paper, we present an algorithm that computes the topological signature for a given periodic motion sequence.
Topology-based Representative Datasets to Reduce Neural Network Training Resources
We prove that the accuracy of the learning process of a neural network on a representative dataset is "similar" to the accuracy on the original dataset when the neural network architecture is a perceptron and the loss function is the mean squared error.
Topological Tracking of Connected Components in Image Sequences
In this paper, taking as input a time-varying sequence of two-dimensional (2D) binary digital images, we develop an algorithm for encoding, in the so-called {\it spatiotemporal barcode}, lifetime of connected components (of either the foreground or background) that are moving in the image sequence over time (this information may not coincide with the one provided by the persistence barcode).
Removal and Contraction Operations in $n$D Generalized Maps for Efficient Homology Computation
In this paper, we show that contraction operations preserve the homology of $n$D generalized maps, under some conditions.
3D Well-composed Polyhedral Complexes
A binary three-dimensional (3D) image $I$ is well-composed if the boundary surface of its continuous analog is a 2D manifold.
