On Inversion-Free Mapping and Distortion Minimization

Naitsat, Alexander; Naitzat, Gregory; Zeevi, Yehoshua Y.

doi:10.1007/s10851-021-01038-y

Cited by 7 publications

(22 citation statements)

References 112 publications

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“…These methods are distinguished by the choice of variables, optimization objectives, type of constraints considered, guarantees these methods provide and initialization requirements. We briefly review most closely related work, and refer to recent surveys [Naitsat et al 2021] and [Fu et al 2021] for a more comprehensive review.…”

Section: Related Workmentioning

confidence: 99%

Metric Optimization in Penner Coordinates

Capouellez¹,

Zorin²

2022

Preprint

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Section: Related Workmentioning

confidence: 99%

Metric Optimization in Penner Coordinates

Capouellez¹,

Zorin²

2022

Preprint

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“…Surfaces and higher dimensional manifolds are endowed with intrinsic, well defined, geometric structures. Utilizing properties of surface geometry can be advantageous in the development of algorithms that involve mappings for the purpose of assessment of similarities by means of meaningful geometry-based distortion measures, and in their computations [1,2]. We have previously presented a complete framework of this approach, along with its practical applications in computer graphics and computer vision [1,3,4].…”

Section: Introductionmentioning

confidence: 99%

“…Utilizing properties of surface geometry can be advantageous in the development of algorithms that involve mappings for the purpose of assessment of similarities by means of meaningful geometry-based distortion measures, and in their computations [1,2]. We have previously presented a complete framework of this approach, along with its practical applications in computer graphics and computer vision [1,3,4]. The purpose of our present work is to adopt this powerful approach for the benefit of processing, similarity assessment, feature engineering and classification of one-dimensional signals, such as pulmonary sounds and speech.…”

Section: Introductionmentioning

confidence: 99%

“…signal segments represented by meshes, which are the discrete versions of the manifold surfaces, one can not practically estimate the required deformations and corresponding similarities by pairwise comparisons; this would not be computationally feasible. Instead, we map each one of the geometric objects into a reference, target, domain by a process known as surface flattening, or parametrization [1], and assess in doing so the transitive similarity. Such a target domain (actually a canonical domain [1]) may, for example, be a circle [15].…”

Section: Introductionmentioning

confidence: 99%

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Classification of audio signals using spectrogram surfaces and inherent distortion measures

Levy

Naitsat

Zeevi

2022

Preprint

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Representation of one-dimensional (1D) signals as surfaces and higher dimensional manifolds reveals geometric structures that can enhance assessment of signal similarity and classification of large sets of signals. We therefore represent 1D signals as surface objects embedded in higher dimensional Euclidean or other spaces. Specifically, since we are concerned with audio signals, the spectrogram is utilized for the representation of the 1D signals by surfaces, but a handful of other representations in combined spaces such as wavelets can be utilized for this purpose. A novel class of geometric features is then extracted by parameterizing the surfaces, and by utilizing distortion measures that are defined with reference to them. This yields a set of highly descriptive features that are instrumental in our approach to feature engineering, analysis and classification of audio or other 1D signals. Two examples of audio signals were selected to illustrate applications and the capabilities of the new approach: Lung sounds were chosen in view of the interest nowadays in respiratory pathologies caused by the Corona virus and environmental problems; Accent detection was selected as an example of a challenging speech problem. The proposed approach outperformed baseline models under all measured metrics. Our novel approach to 1D signal representation and processing can be further extended considering higher dimensional distortion measures.

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“…See[26],[27] for the survey of parametrization algorithms and for other related methods used in geometry processing.frequency time (seconds)…”

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Distortion measure of spectrograms for classification of respiratory diseases

Levy,

Naitsat,

Zeevi

2021

Preprint

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A new method for classification of respiratory diseases is presented. The method is based on a novel class of features, extracted from pulmonary sounds, by parameterizing their spectrograms that are represented as surfaces, and by utilizing geometrical distortions defined with reference to these surfaces. This method yields a set of highly descriptive features for analysis of pulmonary sound recordings. Furthermore, by combining these features with Mel-frequency cepstral coefficients, we introduce a powerful model for automatic diagnosis of common respiratory pathologies. Compared with baseline methods, our model achieves superior results for binary and multi-class classifications of common respiratory deceases. Our new approach to classification of one-dimensional signals is applicable to other signals in the context of their representations in combined spaces or manifolds.

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On Inversion-Free Mapping and Distortion Minimization

Cited by 7 publications

References 112 publications

Metric Optimization in Penner Coordinates

Metric Optimization in Penner Coordinates

Classification of audio signals using spectrogram surfaces and inherent distortion measures

Distortion measure of spectrograms for classification of respiratory diseases

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