{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T10:47:58Z","timestamp":1761648478530,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,8,30]],"date-time":"2017-08-30T00:00:00Z","timestamp":1504051200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Data"],"abstract":"<jats:p>The Singular Value Decomposition (SVD) is a fundamental algorithm used to understand the structure of data by providing insight into the relationship between the row and column factors. SVD aims to approximate a rectangular data matrix, given some rank restriction, especially lower rank approximation. In practical data analysis, however, outliers and missing values maybe exist that restrict the performance of SVD, because SVD is a least squares method that is sensitive to errors in the data matrix. This paper proposes a robust SVD algorithm by applying an adjustable robust estimator. Through adjusting the tuning parameter in the algorithm, the method can be both robust and efficient. Moreover, a sequential robust SVD algorithm is proposed in order to decrease the computation volume in sequential and streaming data. The advantages of the proposed algorithms are proved with a financial application.<\/jats:p>","DOI":"10.3390\/data2030029","type":"journal-article","created":{"date-parts":[[2017,8,30]],"date-time":"2017-08-30T10:40:00Z","timestamp":1504089600000},"page":"29","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Adjustable Robust Singular Value Decomposition: Design, Analysis and Application to Finance"],"prefix":"10.3390","volume":"2","author":[{"given":"Deshen","family":"Wang","sequence":"first","affiliation":[{"name":"Institute for Financial Services Analytics, University of Delaware, Newark, DE 19716, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1080\/00401706.1978.10489617","article-title":"The Biplot as a Diagnostic Tool for Models of Two-Way Tables","volume":"20","author":"Bradu","year":"1978","journal-title":"Technometrics"},{"key":"ref_2","unstructured":"Greenacre, M.J. (1984). Theory and Applications of Correspondence Analysis, Academic Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1080\/00401706.1979.10489819","article-title":"Lower Rank Approximation of Matrices by Least Squares with Any Choice of Weights","volume":"21","author":"Gabriel","year":"1979","journal-title":"Technometrics"},{"key":"ref_4","unstructured":"Hawkins, D.M., Liu, L., and Young, S.S. (2001). Robust Singular Value Decomposition."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Arce, G.R. (2004). Nonlinear Signal Processing: A Statistical Approach, Wiley-Intersecience.","DOI":"10.1002\/0471691852"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1109\/78.902126","article-title":"Optimality of the myriad filter in practical impulsive-noise environments","volume":"2","author":"Gonzalez","year":"2001","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"363195","DOI":"10.1155\/S1110865702000483","article-title":"Statistically-Efficient Filtering in Impulsive Environments: Weighted Myriad Filters","volume":"2002","author":"Gonzalez","year":"2002","journal-title":"EURASIP J. Adv. Signal Proc."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1109\/LSP.2007.891323","article-title":"On the Optimal Alpha-k Curve of the Sample Myriad","volume":"8","author":"Lim","year":"2007","journal-title":"IEEE Signal Proc. Lett."},{"key":"ref_9","unstructured":"Gonzalez, J.G., Griffith, D.W., and Arce, G.R. Matched Myriad Filtering for Robust Communications. Proceedings of the 30th Annual Conference on Information Sciences and Systems (CISS), Princeton, NJ, USA."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1080\/01621459.1971.10482264","article-title":"Parameter Estimates for Symmetric Stable Distributions","volume":"334","author":"Fama","year":"1971","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"918","DOI":"10.1080\/01621459.1980.10477573","article-title":"Regression-Type Estimation of the Parameters of Stable Laws","volume":"372","author":"Koutrouvelis","year":"1980","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1080\/03610918608812563","article-title":"Simple consistent estimators of stable distribution parameters","volume":"4","author":"McCulloch","year":"1986","journal-title":"Commun. Stat. Simul. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1109\/78.815486","article-title":"Fast Algorithms for Weighted Myriad Computation by Fixed-Point Search","volume":"1","author":"Kalluri","year":"2000","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_14","first-page":"707","article-title":"Incremental Singular Value Decomposition of Uncertain Data with Missing Values","volume":"14","author":"Brand","year":"2002","journal-title":"Proc. 7th Eur. Conf. Comput. Vis. Part I"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Miyazaki, D., and Ikeuchi, K. (2010, January 26\u201329). Photometric Stereo Under Unknown Light Sources Using Robust SVD with Missing Data. Proceedings of the IEEE 17th International Conference on Imaging Processing, Hong Kong, China.","DOI":"10.1109\/ICIP.2010.5650067"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2368","DOI":"10.1109\/TASL.2013.2277929","article-title":"Robust SVD-Based Audio Watermaking Scheme With Differential Evolution Optimization","volume":"21","author":"Lei","year":"2013","journal-title":"IEEE Trans. Audio Speech Lang. Proc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"45","DOI":"10.2478\/s11772-014-0177-z","article-title":"A Robust SVD-Based Image Watermaking Using a Multi-objective Particle Swarm Optimization","volume":"22","author":"Loukhaoukha","year":"2014","journal-title":"Opto-Electron. Rev."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1016\/j.physa.2013.08.071","article-title":"The predictive power of singular value decomposition entropy for stock market dynamics","volume":"393","author":"Caraiani","year":"2014","journal-title":"Physica A"},{"key":"ref_19","first-page":"427","article-title":"The Cross-Section of Expected Stock Returns","volume":"47","author":"Fama","year":"1992","journal-title":"J. Financ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"42","DOI":"10.2469\/faj.v51.n3.1904","article-title":"The Three Types of Factor Models: A Comparison of Their Explanatory Power","volume":"51","author":"Connor","year":"1995","journal-title":"Financ. Anal. J."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Connor, G., and Korajczyk, R. (2009). Factor Models of Asset Returns. Encyclopedia of Quantitative Finance, Wiley.","DOI":"10.1002\/9780470061602.eqf19003"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1080\/14697680903124632","article-title":"Statistical arbitrage in the US equities market","volume":"10","author":"Avellaneda","year":"2010","journal-title":"Quant. Financ."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1142\/S0219024900000255","article-title":"Random Matrix Theory and Financial Correlations","volume":"3","author":"Laloux","year":"2000","journal-title":"Int. J. Theor. Appl. Financ."},{"key":"ref_24","unstructured":"Zivot, E. (2006). Factor Models for Asset Returns. Modeling Financial Time Series with S-PLUS\u00ae, Springer."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1086\/260061","article-title":"Risk, Return, and Equilibrium: Empirical Tests","volume":"81","author":"Fama","year":"1973","journal-title":"J. Political Econ."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1186\/s40008-016-0049-4","article-title":"A macroeconomic mathematical model for the national income of a union of countries with interaction and trade","volume":"5","author":"Dassios","year":"2016","journal-title":"J. Econ. Struct."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5402","DOI":"10.3390\/e17085402","article-title":"Fractional State Space Analysis of Economic Systems","volume":"17","author":"Machado","year":"2015","journal-title":"Entropy"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1186\/s40008-014-0007-y","article-title":"The Delay Effect in a Stochastic Multiplier\u2013Accelerator Model","volume":"3","author":"Dassios","year":"2014","journal-title":"J. Econ. Struct."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1734","DOI":"10.3390\/e17041734","article-title":"Research on the Stability of Open Financial System","volume":"17","author":"Yang","year":"2015","journal-title":"Entropy"}],"container-title":["Data"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2306-5729\/2\/3\/29\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:43:40Z","timestamp":1760208220000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2306-5729\/2\/3\/29"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,30]]},"references-count":29,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,9]]}},"alternative-id":["data2030029"],"URL":"https:\/\/doi.org\/10.3390\/data2030029","relation":{},"ISSN":["2306-5729"],"issn-type":[{"type":"electronic","value":"2306-5729"}],"subject":[],"published":{"date-parts":[[2017,8,30]]}}}