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Algorithms
Special Issues
Algorithms for Manifold Learning and Its Applications
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Algorithms for Manifold Learning and Its Applications

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (30 April 2019) | Viewed by 8874

Special Issue Editor

Dr. Varun Chandola

E-Mail Website
Guest Editor
Computer Science and Engineering Department, University at Buffalo, New York, NY 14260, USA
Interests: scalable anomaly detection; data mining for big graphs; temporal and spatial data

Special Issue Information

Dear Colleagues,

We invite you to submit your latest research in the area of manifold learning to this Special Issue, “Algorithms for Manifold Learning and Its Applications”. The progress in science and engineering depends more than ever on our ability to analyze huge amounts of sensor and simulation data. The vast majority of this data, coming from, for example, high performance high fidelity numerical simulations, high resolution scientific instruments (microscopes, DNA sequencers, etc.) or Internet of Things streams and feeds, is a result of complex non-linear processes. While these non-linear processes can be characterized by low dimensional sub-manifolds, the actual observable data they generate is high dimensional. Revealing the low-dimensional representation of such high-dimensional data sets not only leads to a more compact description of the data, but also enhances our understanding of the system. Manifold learning-based dimensionality reduction algorithms are an important class of solutions presented for this problem. Such algorithms assume that the observed data lies on a low-dimensional manifold, embedded in a high-dimensional space. Manifold-learning algorithms attempt to recover the original low-dimensional domain structure in different ways.

We are looking for new and innovative approaches for solving the problem of manifold learning, with an emphasis on handling the big data challenges encountered in real-world applications. High-quality papers are solicited that address theoretical foundations, computational and other algorithmic challenges and present novel applications. Potential topics include, but are not limited to, real-time manifold learning, handling potential dependencies in the observed data, dealing with data from multiple manifolds, and accelerating manifold learning on upcoming computational architectures.

Dr. Varun Chandola
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Theoretical guarantees for convergence
  • Quantitative measures for measuring quality
  • Complexity issues with manifold learning
  • Learning from high throughput streams
  • Deployment on new architectures, e.g., mobile supercomputers
  • Handling non-traditional data, images, etc.
  • Big data analytics
  • Novel applications

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Published Papers (2 papers)

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Research

16 pages, 7286 KiB  
Article
Learning Manifolds from Dynamic Process Data
by Frank Schoeneman, Varun Chandola, Nils Napp, Olga Wodo and Jaroslaw Zola
Algorithms 2020, 13(2), 30; https://doi.org/10.3390/a13020030 - 21 Jan 2020
Cited by 3 | Viewed by 3964
Abstract
Scientific data, generated by computational models or from experiments, are typically results of nonlinear interactions among several latent processes. Such datasets are typically high-dimensional and exhibit strong temporal correlations. Better understanding of the underlying processes requires mapping such data to a low-dimensional manifold [...] Read more.
Scientific data, generated by computational models or from experiments, are typically results of nonlinear interactions among several latent processes. Such datasets are typically high-dimensional and exhibit strong temporal correlations. Better understanding of the underlying processes requires mapping such data to a low-dimensional manifold where the dynamics of the latent processes are evident. While nonlinear spectral dimensionality reduction methods, e.g., Isomap, and their scalable variants, are conceptually fit candidates for obtaining such a mapping, the presence of the strong temporal correlation in the data can significantly impact these methods. In this paper, we first show why such methods fail when dealing with dynamic process data. A novel method, Entropy-Isomap, is proposed to handle this shortcoming. We demonstrate the effectiveness of the proposed method in the context of understanding the fabrication process of organic materials. The resulting low-dimensional representation correctly characterizes the process control variables and allows for informative visualization of the material morphology evolution. Full article
(This article belongs to the Special Issue Algorithms for Manifold Learning and Its Applications)
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21 pages, 1336 KiB  
Article
An Application of Manifold Learning in Global Shape Descriptors
by Fereshteh S. Bashiri, Reihaneh Rostami, Peggy Peissig, Roshan M. D’Souza and Zeyun Yu
Algorithms 2019, 12(8), 171; https://doi.org/10.3390/a12080171 - 16 Aug 2019
Cited by 3 | Viewed by 4070
Abstract
With the rapid expansion of applied 3D computational vision, shape descriptors have become increasingly important for a wide variety of applications and objects from molecules to planets. Appropriate shape descriptors are critical for accurate (and efficient) shape retrieval and 3D model classification. Several [...] Read more.
With the rapid expansion of applied 3D computational vision, shape descriptors have become increasingly important for a wide variety of applications and objects from molecules to planets. Appropriate shape descriptors are critical for accurate (and efficient) shape retrieval and 3D model classification. Several spectral-based shape descriptors have been introduced by solving various physical equations over a 3D surface model. In this paper, for the first time, we incorporate a specific manifold learning technique, introduced in statistics and machine learning, to develop a global, spectral-based shape descriptor in the computer graphics domain. The proposed descriptor utilizes the Laplacian Eigenmap technique in which the Laplacian eigenvalue problem is discretized using an exponential weighting scheme. As a result, our descriptor eliminates the limitations tied to the existing spectral descriptors, namely dependency on triangular mesh representation and high intra-class quality of 3D models. We also present a straightforward normalization method to obtain a scale-invariant and noise-resistant descriptor. The extensive experiments performed in this study using two standard 3D shape benchmarks—high-resolution TOSCA and McGill datasets—demonstrate that the present contribution provides a highly discriminative and robust shape descriptor under the presence of a high level of noise, random scale variations, and low sampling rate, in addition to the known isometric-invariance property of the Laplace–Beltrami operator. The proposed method significantly outperforms state-of-the-art spectral descriptors in shape retrieval and classification. The proposed descriptor is limited to closed manifolds due to its inherited inability to accurately handle manifolds with boundaries. Full article
(This article belongs to the Special Issue Algorithms for Manifold Learning and Its Applications)
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