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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\u2014high-resolution TOSCA and McGill datasets\u2014demonstrate 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\u2013Beltrami 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.<\/jats:p>","DOI":"10.3390\/a12080171","type":"journal-article","created":{"date-parts":[[2019,8,19]],"date-time":"2019-08-19T06:10:14Z","timestamp":1566195014000},"page":"171","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["An Application of Manifold Learning in Global Shape Descriptors"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0153-4958","authenticated-orcid":false,"given":"Fereshteh S.","family":"Bashiri","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA"},{"name":"Marshfield Clinic Research Institute, Marshfield, WI 54449, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Reihaneh","family":"Rostami","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4156-0189","authenticated-orcid":false,"given":"Peggy","family":"Peissig","sequence":"additional","affiliation":[{"name":"Marshfield Clinic Research Institute, Marshfield, WI 54449, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roshan M.","family":"D\u2019Souza","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zeyun","family":"Yu","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA"},{"name":"Department of Computer Science, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/j.triboint.2016.07.001","article-title":"Tribological study in microscale using 3D SEM surface reconstruction","volume":"103","author":"Omrani","year":"2016","journal-title":"Tribol. 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