{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T09:35:10Z","timestamp":1761989710545,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,29]],"date-time":"2023-01-29T00:00:00Z","timestamp":1674950400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, the concept of ultrametric structure is intertwined with the SLAM procedure. A set of pre-existing transformations has been used to create a new simultaneous localization and mapping (SLAM) algorithm. We have developed two new parallel algorithms that implement the time-consuming Boolean transformations of the space dissimilarity matrix. The resulting matrix is an important input to the vector quantization (VQ) step in SLAM processes. These algorithms, written in Compute Unified Device Architecture (CUDA) and Open Multi-Processing (OpenMP) pseudo-codes, make the Boolean transformation computationally feasible on a real-world-size dataset. We expect our newly introduced SLAM algorithm, ultrametric Fast Appearance Based Mapping (FABMAP), to outperform regular FABMAP2 since ultrametric spaces are more clusterable than regular Euclidean spaces. Another scope of the presented research is the development of a novel measure of ultrametricity, along with creation of Ultrametric-PAM clustering algorithm. Since current measures have computational time complexity order, O(n3) a new measure with lower time complexity, O(n2), has a potential significance.<\/jats:p>","DOI":"10.3390\/a16020074","type":"journal-article","created":{"date-parts":[[2023,1,30]],"date-time":"2023-01-30T10:19:28Z","timestamp":1675073968000},"page":"74","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["CUDA and OpenMp Implementation of Boolean Matrix Product with Applications in Visual SLAM"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6223-2013","authenticated-orcid":false,"given":"Amir","family":"Zarringhalam","sequence":"first","affiliation":[{"name":"Computer Science and Mathematics Department, Amirkabir University of Technology, 424 Hafez Ave, Tehran 15916634311, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9019-3947","authenticated-orcid":false,"given":"Saeed","family":"Shiry Ghidary","sequence":"additional","affiliation":[{"name":"Computer Science and Mathematics Department, Amirkabir University of Technology, 424 Hafez Ave, Tehran 15916634311, Iran"},{"name":"Department of Computing, Staffordshire University, Stoke-on-Trent ST4 2DE, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6118-2245","authenticated-orcid":false,"given":"Ali","family":"Mohades","sequence":"additional","affiliation":[{"name":"Computer Science and Mathematics Department, Amirkabir University of Technology, 424 Hafez Ave, Tehran 15916634311, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6197-3410","authenticated-orcid":false,"given":"Seyed-Ali","family":"Sadegh-Zadeh","sequence":"additional","affiliation":[{"name":"Department of Computing, Staffordshire University, Stoke-on-Trent ST4 2DE, UK"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"012002","DOI":"10.1088\/1742-6596\/1334\/1\/012002","article-title":"Data Ultrametricity and Clusterability","volume":"1334","author":"Simovici","year":"2020","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0024-3795(00)00168-3","article-title":"On the powers of matrices over a distributive lattice","volume":"336","author":"Tan","year":"2001","journal-title":"Linear Algebra Its Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.laa.2004.11.016","article-title":"On the transitive matrices over distributive lattices","volume":"400","author":"Tan","year":"2005","journal-title":"Linear Algebra Its Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1134\/S2070046616030055","article-title":"Sparse p-adic data coding for computationally efficient and effective big data analytics","volume":"8","author":"Murtagh","year":"2016","journal-title":"P-Adic Numbers Ultrametric Anal. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Bradley, P.E., Keller, S., and Weinmann, M. (2018). Unsupervised Feature Selection Based on Ultrametricity and Sparse Training Data: A Case Study for the Classification of High-Dimensional Hyperspectral Data. Remote Sens., 10.","DOI":"10.3390\/rs10101564"},{"key":"ref_6","unstructured":"Decker, R., and Lenz, H. (2006). Proceedings of the Advances in Data Analysis, Proceedings of the 30th Annual Conference of the Gesellschaft f\u00fcr Klassifikation e.V., Freie Universit\u00e4t Berlin, 8\u201310 March 2006, Springer."},{"key":"ref_7","unstructured":"Murtagh, F., and Contreras, P. (2012). The Future of Search and Discovery in Big Data Analytics: Ultrametric Information Spaces. arXiv."},{"key":"ref_8","unstructured":"Kaufman, L., and Rousseeuw, P. (2009). Finding Groups in Data: An Introduction to Cluster Analysis, John Wiley."},{"key":"ref_9","unstructured":"(2022, December 10). K-Medoids. Available online: https:\/\/en.wikipedia.org\/wiki\/K-medoids."},{"key":"ref_10","unstructured":"(2022, December 10). K-Medoids Clustering with Solved Example. Available online: https:\/\/www.geeksforgeeks.org\/ml-k-medoids-clustering-with-example\/."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1177\/0278364908090961","article-title":"FAB-MAP: Probabilistic Localization and Mapping in the Space of Appearance","volume":"27","author":"Cummins","year":"2008","journal-title":"Int. J. Robot. Res."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Glover, A., Maddern, W., Warren, M., Reid, S., Milford, M., and Wyeth, G. (2012, January 14\u201318). OpenFABMAP: An Open Source Toolbox for Appearance-based Loop Closure Detection. Proceedings of the International Conference on Robotics and Automation, Saint Paul, MN, USA.","DOI":"10.1109\/ICRA.2012.6224843"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1051\/jphyslet:019850046020094500","article-title":"On the degree of ultrametricity","volume":"46","author":"Rammal","year":"1985","journal-title":"J. Phys. Lett."},{"key":"ref_14","unstructured":"Cattaneo, D., Vaghi, M., and Valada, A. (2021). LCDNet: Deep Loop Closure Detection for LiDAR SLAM based on Unbalanced Optimal Transport. arXiv."},{"key":"ref_15","unstructured":"Lu, S., Xu, X., Tang, L., Xiong, R., and Wang, Y. (2022). DeepRING: Learning Roto-translation Invariant Representation for LiDAR based Place Recognition. arXiv."},{"key":"ref_16","unstructured":"Zarringhalam, A., Ghidary, S.S., and Khorasani, A.M. (2022). Self-supervised Vector-Quantization in Visual SLAM using Deep Convolutional Autoencoders. arXiv."},{"key":"ref_17","unstructured":"Zarringhalam, A., Ghidary, S.S., and Khorasani, A.M. (2022). Semi-supervised Vector-Quantization in Visual SLAM using HGCN. arXiv."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1137\/060676532","article-title":"Hierarchical Clustering of Massive, High Dimensional Data Sets by Exploiting Ultrametric Embedding","volume":"30","author":"Murtagh","year":"2008","journal-title":"SIAM J. Sci. Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1093\/comjnl\/41.8.547","article-title":"Similarity and Dissimilarity Methods for Processing Chemical Structure Databases","volume":"41","author":"Gillet","year":"1998","journal-title":"Comput. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"572","DOI":"10.1021\/ci9501047","article-title":"Use of Structure\u2013Activity Data To Compare Structure-Based Clustering Methods and Descriptors for Use in Compound Selection","volume":"36","author":"Brown","year":"1996","journal-title":"J. Chem. Inf. Comput. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1094","DOI":"10.1021\/ci00021a011","article-title":"Similarity Searching and Clustering of Chemical-Structure Databases Using Molecular Property Data","volume":"34","author":"Downs","year":"1994","journal-title":"J. Chem. Inf. Comput. Sci."},{"key":"ref_22","first-page":"155","article-title":"Several Remarks on Dissimilarities and Ultrametrics","volume":"25","author":"Rammal","year":"2015","journal-title":"Sci. Ann. Comput. Sci."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/2\/74\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:19:02Z","timestamp":1760120342000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/16\/2\/74"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,29]]},"references-count":22,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["a16020074"],"URL":"https:\/\/doi.org\/10.3390\/a16020074","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2023,1,29]]}}}