Persistent-Homology-Based Machine Learning and Its Applications -- A Survey

Pun, Chi Seng; Xia, Kelin; Lee, Si Xian

doi:10.2139/ssrn.3275996

Cited by 47 publications

(26 citation statements)

References 88 publications

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“…In this paper, we only consider topological features constructed using a binning approach [ 53 ]. More specifically, the filtration interval [0, F ] is divided into N bins of equal size f .…”

Section: Methodsmentioning

confidence: 99%

“…However, PH results are notorious for meaningful metric definition and statistic interface. Various methods are proposed [53] including barcode statistics, tropical coordinates, binning approach, persistent image, persistent landscapes and image representations to construct topological features. In this paper, we only consider topological features constructed using a binning approach [53].…”

Section: Topological Features Representation (Tfr)mentioning

confidence: 99%

“…Various methods are proposed [53] including barcode statistics, tropical coordinates, binning approach, persistent image, persistent landscapes and image representations to construct topological features. In this paper, we only consider topological features constructed using a binning approach [53]. More specifically, the filtration interval [0, F] is divided into N bins of equal size f. The number of barcodes which are located on each bin are then counted and used as feature vector [54,55].…”

Section: Topological Features Representation (Tfr)mentioning

confidence: 99%

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Weighted-persistent-homology-based machine learning for RNA flexibility analysis

2020

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With the great significance of biomolecular flexibility in biomolecular dynamics and functional analysis, various experimental and theoretical models are developed. Experimentally, Debye-Waller factor, also known as B-factor, measures atomic mean-square displacement and is usually considered as an important measurement for flexibility. Theoretically, elastic network models, Gaussian network model, flexibility-rigidity model, and other computational models have been proposed for flexibility analysis by shedding light on the biomolecular inner topological structures. Recently, a topology-based machine learning model has been proposed. By using the features from persistent homology, this model achieves a remarkable high Pearson correlation coefficient (PCC) in protein B-factor prediction. Motivated by its success, we propose weighted-persistent-homology (WPH)-based machine learning (WPHML) models for RNA flexibility analysis. Our WPH is a newly-proposed model, which incorporate physical, chemical and biological information into topological measurements using a weight function. In particular, we use local persistent homology (LPH) to focus on the topological information of local regions. Our WPHML model is validated on a well-established RNA dataset, and numerical experiments show that our model can achieve a PCC of up to 0.5822. The comparison with the previous sequence-information-based learning models shows that a consistent improvement in performance by at least 10% is achieved in our current model.

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Section: Methodsmentioning

confidence: 99%

Section: Topological Features Representation (Tfr)mentioning

confidence: 99%

Section: Topological Features Representation (Tfr)mentioning

confidence: 99%

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Weighted-persistent-homology-based machine learning for RNA flexibility analysis

2020

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“…We can, therefore, measure how close two images are topologically speaking by comparing signature real numbers extracted from their persistence diagrams. There are many ways to do so; see [10] for a survey of the different methods. In this work, we propose to use the amplitude of each persistence diagram or its entropy.…”

Section: A Topological Pipeline For Machine Learningmentioning

confidence: 99%

A Topological "Reading" Lesson: Classification of MNIST using TDA

Garin

Tauzin

2019

2019 18th IEEE International Conference on Machine Learning and Applications (ICMLA)

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We present a way to use Topological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological features using a point cloud obtained from an image, its natural grayscale filtration, and different filtrations defined on the binarized image. We show that this topological machine learning pipeline can be used as a highly relevant dimensionality reduction by applying it to the MNIST digits dataset. We conduct a feature selection and study their correlations while providing an intuitive interpretation of their importance, which is relevant in both machine learning and TDA. Finally, we show that we can classify digit images while reducing the size of the feature set by a factor 5 compared to the grayscale pixel value features and maintain similar accuracy.

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“…We believe that the formal foundation of our model is suitable to start a new theory of deep-learning engineering, and that novel research lines will stem from the synergy of machine learning and topology. This synergy is object of study by more and more researchers, focusing both on the treatment of data via TDA before applying classical machine learning [6,7], and the analysis of the topology of convolutional neural networks [8]. However, our approach differs from the previous ones in that it focuses on a new theoretical setting, based on the introduction of new topologies and metrics.…”

Section: Introductionmentioning

confidence: 99%

Towards a topological–geometrical theory of group equivariant non-expansive operators for data analysis and machine learning

et al. 2019

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The aim of this paper is to provide a general mathematical framework for group equivariance in the machine learning context. The framework builds on a synergy between persistent homology and the theory of group actions. We define group equivariant non-expansive operators (GENEOs), which are maps between function spaces associated with groups of transformations. We study the topological and metric properties of the space of GENEOs to evaluate their approximating power and set the basis for general strategies to initialise and compose operators. We begin by defining suitable pseudo-metrics for the function spaces, the equivariance groups, and the set of non-expansive operators. Basing on these pseudo-metrics, we prove that the space of GENEOs is compact and convex, under the assumption that the function spaces are compact and convex. These results provide fundamental guarantees in a machine learning perspective. We show examples on the MNIST and fashion-MNIST datasets. By considering isometry-equivariant non-expansive operators, we describe a simple strategy to select and sample operators, and show how the selected and sampled operators can be used to perform both classical metric learning and an effective initialisation of the kernels of a convolutional neural network.

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Persistent-Homology-Based Machine Learning and Its Applications -- A Survey

Cited by 47 publications

References 88 publications

Weighted-persistent-homology-based machine learning for RNA flexibility analysis

Weighted-persistent-homology-based machine learning for RNA flexibility analysis

A Topological "Reading" Lesson: Classification of MNIST using TDA

Towards a topological–geometrical theory of group equivariant non-expansive operators for data analysis and machine learning

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