{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:27:20Z","timestamp":1760239640469,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,12,8]],"date-time":"2020-12-08T00:00:00Z","timestamp":1607385600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MAKE"],"abstract":"<jats:p>Feature analysis is a fundamental research area in computer graphics; meanwhile, meaningful and part-aware feature bases are always demanding. This paper proposes a framework for conducting feature analysis on a three-dimensional (3D) model by introducing modified Non-negative Matrix Factorization (NMF) model into the graphical feature space and push forward further applications. By analyzing and utilizing the intrinsic ideas behind NMF, we propose conducting the factorization on feature matrices constructed based on descriptors or graphs, which provides a simple but effective way to raise compressed and scale-aware descriptors. In order to enable part-aware model analysis, we modify the NMF model to be sparse and constrained regarding to both bases and encodings, which gives rise to Sparse and Constrained Non-negative Matrix Factorization (SAC-NMF). Subsequently, by adapting the analytical components (including hidden variables, bases, and encodings) to design descriptors, several applications have been easily but effectively realized. The extensive experimental results demonstrate that the proposed framework has many attractive advantages, such as being efficient, extendable, and so forth.<\/jats:p>","DOI":"10.3390\/make2040034","type":"journal-article","created":{"date-parts":[[2020,12,8]],"date-time":"2020-12-08T09:17:04Z","timestamp":1607419024000},"page":"630-646","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["SAC-NMF-Driven Graphical Feature Analysis and Applications"],"prefix":"10.3390","volume":"2","author":[{"given":"Nannan","family":"Li","sequence":"first","affiliation":[{"name":"Department of Information Science and Technology, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengfa","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory for Ubiquitous Network and Service Software of Liaoning Province, DUT-RU International School of Information and Software Engineering, Dalian University of Technology, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haohao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Dalian University of Technology, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiyang","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Information Science and Technology, Dalian Maritime University, Dalian 116026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.cagd.2016.02.006","article-title":"Volumetric shape contexts for mesh co-segmentation","volume":"43","author":"Xie","year":"2016","journal-title":"Comput. Aided Geom. Des."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1125","DOI":"10.1109\/TVCG.2011.131","article-title":"Mesh Segmentation with Concavity-Aware Fields","volume":"18","author":"Zheng","year":"2012","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2530691","article-title":"Mesh Saliency via Spectral Processing","volume":"33","author":"Song","year":"2014","journal-title":"ACM Trans. Graph."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.cagd.2019.04.021","article-title":"EdgeNet: Deep metric learning for 3D shapes","volume":"72","author":"Chen","year":"2019","journal-title":"Comput. Aided Geom. Des."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2583","DOI":"10.1109\/TVCG.2018.2848628","article-title":"Detecting 3D Points of Interest Using Multiple Features and Stacked Auto-encoder","volume":"25","author":"Shu","year":"2019","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1002\/wics.101","article-title":"Principal Component Analysis","volume":"2","author":"Abdi","year":"2010","journal-title":"WIREs Comput. Stat."},{"key":"ref_7","unstructured":"Belyaev, A., and Garland, M. (2007). Laplace-Beltrami Eigenfunctions for Deformation Invariant Shape Representation. Geometry Processing, The Eurographics Association."},{"key":"ref_8","first-page":"433","article-title":"Independent Component Analysis","volume":"2","author":"Hyvarinen","year":"2001","journal-title":"Wiley Intersci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1016\/j.cagd.2015.03.003","article-title":"Multi-scale mesh saliency based on low-rank and sparse analysis in shape feature space","volume":"35\u201336","author":"Wang","year":"2015","journal-title":"Comput. Aided Geom. Des."},{"key":"ref_10","unstructured":"Burton, D., Shore, J., and Buck, J. (1983, January 14\u201316). A generalization of isolated word recognition using vector quantization. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Boston, MA, USA."},{"key":"ref_11","unstructured":"Liu, Z., Mitani, J., Fukui, Y., and Nishihara, S. (2007, January 13\u201315). A 3D Shape Retrieval Method Based on Continuous Spherical Wavelet Transform. Proceedings of the International Conference on Computer Graphics and Imaging, Innsbruck, Austria."},{"key":"ref_12","first-page":"261","article-title":"Shape matching of 3D contours using normalized Fourier descriptors","volume":"2002","author":"Zhang","year":"2002","journal-title":"Proc. SMI Shape Model. Int."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1038\/44565","article-title":"Learning the parts of objects with nonnegative matrix factorization","volume":"401","author":"Lee","year":"1999","journal-title":"Nature"},{"key":"ref_14","first-page":"1457","article-title":"Non-negative Matrix Factorization with Sparseness Constraints","volume":"5","author":"Hoyer","year":"2004","journal-title":"J. Mach. Learn. Res."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Cai, D., He, X., Wu, X., and Han, J. (2008, January 15\u201319). Non-negative Matrix Factorization on Manifold. Proceedings of the Eighth IEEE International Conference on Data Mining, Pisa, Italy.","DOI":"10.1109\/ICDM.2008.57"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1186\/1751-0473-8-10","article-title":"The non-negative matrix factorization toolbox for biological data mining","volume":"8","author":"Li","year":"2013","journal-title":"Source Code Biol. Med."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1650004","DOI":"10.1142\/S0219467816500042","article-title":"Sparse Non-Negative Matrix Factorization for Mesh Segmentation","volume":"16","author":"Mcgraw","year":"2016","journal-title":"Int. J. Image Graph."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","article-title":"A Global Geometric Framework for Nonlinear Dimensionality Reduction","volume":"290","author":"Tenenbaum","year":"2000","journal-title":"Science"},{"key":"ref_19","first-page":"585","article-title":"Laplacian eigenmaps and spectral techniques for embedding and clustering","volume":"14","author":"Belkin","year":"2001","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_20","unstructured":"Sheaves, M., Johnston, R., Johnson, A., Baker, R., and Connolly, R.M. (2014, January 13\u201318). Neighborhood preserving Nonnegative Matrix Factorization for spectral mixture analysis. Proceedings of the Geoscience and Remote Sensing Symposium, Quebec City, QC, Canada."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1016\/S0042-6989(01)00303-0","article-title":"Color categories revealed by non-negative matrix factorization of Munsell color spectra","volume":"42","author":"Buchsbaum","year":"2002","journal-title":"Vis. Res."},{"key":"ref_22","unstructured":"Guillamet, D., Bressan, M., and Vitri, J. (2001, January 8\u201314). A Weighted Non-Negative Matrix Factorization for Local Representations. Proceedings of the 2001 IEEE Computer Society Conference on CVPR 2001, Kauai, HI, USA."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Buciu, I., and Pitas, I. (2004, January 23\u201326). Application of non-Negative and Local non Negative Matrix Factorization to Facial Expression Recognition. Proceedings of the International Conference on Pattern Recognition, Cambridge, UK.","DOI":"10.1109\/ICPR.2004.1334109"},{"key":"ref_24","unstructured":"Li, S.Z., Hou, X.W., Zhang, H.J., and Cheng, Q. (2001, January 8\u201314). Learning spatially localized, parts-based representation. Proceedings of the 2001 IEEE Computer Society Conference on CVPR 2001, Kauai, HI, USA."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1016\/j.patrec.2004.02.002","article-title":"Non-negative matrix factorization based methods for object recognition","volume":"25","author":"Liu","year":"2004","journal-title":"Pattern Recognit. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2217","DOI":"10.1016\/j.patcog.2004.02.013","article-title":"Improving non-negative matrix factorizations through structured initialization","volume":"37","author":"Wild","year":"2004","journal-title":"Pattern Recognit."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Xu, W., Liu, X., and Gong, Y. (2003). Document clustering based on non-negative matrix factorization. Proc. Acm. Sigir., 267\u2013273.","DOI":"10.1145\/860435.860485"},{"key":"ref_28","unstructured":"Cai, D., He, X., Wang, X., Bao, H., and Han, J. (2009, January 11\u201317). Locality preserving nonnegative matrix factorization. Proceedings of the International Jont Conference on Artifical Intelligence, Pasadena, CA, USA."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1142\/S0218001405004198","article-title":"Non-negative Matrix Factorization framework for face recognition","volume":"19","author":"Yuang","year":"2005","journal-title":"Int. J. Pattern Recognit. Artif. Intell."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1109\/TNN.2006.873291","article-title":"Exploiting discriminant information in nonnegative matrix factorization with application to frontal face verification","volume":"17","author":"Zafeiriou","year":"2006","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_31","unstructured":"Kim, W.H., Pachauri, D., Hatt, C., Chung, M.K., Johnson, S., and Singh, V. (2012, January 3\u20136). Wavelet based multi-scale shape features on arbitrary surfaces for cortical thickness discrimination. Proceedings of the Advances in Neural Information Processing Systems, Lake Tahoe, NV, USA."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1383","DOI":"10.1111\/j.1467-8659.2009.01515.x","article-title":"A Concise and Provably Informative Multi-Scale Signature Based on Heat Diffusion","volume":"28","author":"Sun","year":"2009","journal-title":"Comput. Graph. Forum"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2094","DOI":"10.1109\/TVCG.2015.2498557","article-title":"Generalized Local-to-global Shape Feature Detection based on Graph Wavelets","volume":"22","author":"Li","year":"2016","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_34","first-page":"1","article-title":"Biharmonic Distance","volume":"29","author":"Lipman","year":"2010","journal-title":"ACM Trans. Graph."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Meyer, M., Desbrun, M., Schr\u00f6der, P., and Barr, A. (2003). Discrete Differential-Geometry Operators for Triangulated 2-Manifolds. Visualization and Mathematics III, Springer.","DOI":"10.1007\/978-3-662-05105-4_2"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Aubry, M., Schlickewei, U., and Cremers, D. (2011, January 6\u201313). The wave kernel signature: A quantum mechanical approach to shape analysis. Proceedings of the IEEE International Conference on Computer Vision Workshops, Barcelona, Spain.","DOI":"10.1109\/ICCVW.2011.6130444"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2975","DOI":"10.12733\/jics20103848","article-title":"Primary Correspondences between Intrinsically Symmetrical Shapes","volume":"11","author":"Wang","year":"2014","journal-title":"J. Inf. Comput. Sci."},{"key":"ref_38","unstructured":"Wang, H., Simari, P., Su, Z., and Zhang, H. (2014). Spectral global intrinsic symmetry invariant functions. Graphics Interface 2014, A K Peters\/CRC Press."},{"key":"ref_39","unstructured":"Liu, R., and Zhang, H. (2004, January 6\u20138). Segmentation of 3D meshes through spectral clustering. Proceedings of the 12th Pacific Conference on Computer Graphics and Applications, Seoul, Korea."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1145\/1073204.1073244","article-title":"Mesh saliency","volume":"24","author":"Lee","year":"2005","journal-title":"ACM Trans. Graph."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.gmod.2013.05.002","article-title":"Mesh Saliency with Global Rarity","volume":"75","author":"Wu","year":"2013","journal-title":"Graph. Models"}],"container-title":["Machine Learning and Knowledge Extraction"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2504-4990\/2\/4\/34\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:42:24Z","timestamp":1760179344000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2504-4990\/2\/4\/34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,8]]},"references-count":41,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["make2040034"],"URL":"https:\/\/doi.org\/10.3390\/make2040034","relation":{},"ISSN":["2504-4990"],"issn-type":[{"type":"electronic","value":"2504-4990"}],"subject":[],"published":{"date-parts":[[2020,12,8]]}}}