{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T07:03:54Z","timestamp":1761894234495},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Bioinformatics"],"published-print":{"date-parts":[[2006,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:sec>\n            <jats:title>Background<\/jats:title>\n            <jats:p>Accurate methods for extraction of meaningful patterns in high dimensional data have become increasingly important with the recent generation of data types containing measurements across thousands of variables. Principal components analysis (PCA) is a linear dimensionality reduction (DR) method that is unsupervised in that it relies only on the data; projections are calculated in Euclidean or a similar linear space and do not use tuning parameters for optimizing the fit to the data. However, relationships within sets of nonlinear data types, such as biological networks or images, are frequently mis-rendered into a low dimensional space by linear methods. Nonlinear methods, in contrast, attempt to model important aspects of the underlying data structure, often requiring parameter(s) fitting to the data type of interest. In many cases, the optimal parameter values vary when different classification algorithms are applied on the same rendered subspace, making the results of such methods highly dependent upon the type of classifier implemented.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Results<\/jats:title>\n            <jats:p>We present the results of applying the spectral method of Lafon, a nonlinear DR method based on the weighted graph Laplacian, that minimizes the requirements for such parameter optimization for two biological data types. We demonstrate that it is successful in determining implicit ordering of brain slice image data and in classifying separate species in microarray data, as compared to two conventional linear methods and three nonlinear methods (one of which is an alternative spectral method). This spectral implementation is shown to provide more meaningful information, by preserving important relationships, than the methods of DR presented for comparison.<\/jats:p>\n            <jats:p>Tuning parameter fitting is simple and is a general, rather than data type or experiment specific approach, for the two datasets analyzed here. Tuning parameter optimization is minimized in the DR step to each subsequent classification method, enabling the possibility of valid cross-experiment comparisons.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Conclusion<\/jats:title>\n            <jats:p>Results from the spectral method presented here exhibit the desirable properties of preserving meaningful nonlinear relationships in lower dimensional space and requiring minimal parameter fitting, providing a useful algorithm for purposes of visualization and classification across diverse datasets, a common challenge in systems biology.<\/jats:p>\n          <\/jats:sec>","DOI":"10.1186\/1471-2105-7-74","type":"journal-article","created":{"date-parts":[[2006,2,17]],"date-time":"2006-02-17T07:48:35Z","timestamp":1140162515000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Spectral embedding finds meaningful (relevant) structure in image and microarray data"],"prefix":"10.1186","volume":"7","author":[{"given":"Brandon W","family":"Higgs","sequence":"first","affiliation":[]},{"given":"Jennifer","family":"Weller","sequence":"additional","affiliation":[]},{"given":"Jeffrey L","family":"Solka","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2006,2,16]]},"reference":[{"key":"813_CR1","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1016\/0031-3203(73)90025-3","volume":"5","author":"JV Kittler","year":"1973","unstructured":"Kittler JV, Young PC: A new approach to feature selection based on the Karhunen-Loeve expansion. Pattern Recognition 1973, 5: 335\u2013352. 10.1016\/0031-3203(73)90025-3","journal-title":"Pattern Recognition"},{"key":"813_CR2","volume-title":"Multidimensional Scaling","author":"TF Cox","year":"1994","unstructured":"Cox TF, Cox MAA: Multidimensional Scaling. Second edition. London: Chapman and Hall; 1994.","edition":"Second"},{"key":"813_CR3","volume-title":"PhD thesis","author":"S Lafon","year":"2004","unstructured":"Lafon S: Diffusion Maps and Geometric Harmonics. PhD thesis. Yale University, Mathematics Department; 2004."},{"issue":"21","key":"813_CR4","doi-asserted-by":"publisher","first-page":"7426","DOI":"10.1073\/pnas.0500334102","volume":"102","author":"RR Coifman","year":"2005","unstructured":"Coifman RR, Lafon S, Lee AB, Maggioni M, Nadler B, Warner F, Zucker SW: Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion Maps. PNAS 2005, 102(21):7426\u20137431. 10.1073\/pnas.0500334102","journal-title":"PNAS"},{"key":"813_CR5","volume-title":"PhD thesis","author":"B Higgs","year":"2005","unstructured":"Higgs B: Deriving Meaningful Structure from Spectral Embedding. PhD thesis. George Mason University, School of Computational Sciences; 2005."},{"key":"813_CR6","volume-title":"Microsoft Research Technical Report No. MSR-TR-2004-55","author":"CJC Burges","year":"2004","unstructured":"Burges CJC: Geometric Method for Feature Extraction and Dimensional Reduction: A Guided Tour. Microsoft Research Technical Report No. MSR-TR-2004\u201355 2004."},{"key":"813_CR7","volume-title":"Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92)","author":"FRK Chung","year":"1997","unstructured":"Chung FRK: Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92). Providence: American Mathematical Society; 1997."},{"key":"813_CR8","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1023\/B:MACH.0000033120.25363.1e","volume":"56","author":"M Belkin","year":"2004","unstructured":"Belkin M, Niyogi P: Semi-Supervised Learning on Riemannian Manifolds. Machine Learning 2004, 56: 209\u2013239. 10.1023\/B:MACH.0000033120.25363.1e","journal-title":"Machine Learning"},{"issue":"6","key":"813_CR9","doi-asserted-by":"publisher","first-page":"1373","DOI":"10.1162\/089976603321780317","volume":"15","author":"M Belkin","year":"2003","unstructured":"Belkin M, Niyogi P: Laplacian Eigenmaps for dimensionality reduction and data representation. Neural Computation 2003, 15(6):1373\u20131396. 10.1162\/089976603321780317","journal-title":"Neural Computation"},{"issue":"21","key":"813_CR10","doi-asserted-by":"publisher","first-page":"7432","DOI":"10.1073\/pnas.0500896102","volume":"102","author":"RR Coifman","year":"2005","unstructured":"Coifman RR, Lafon S, Lee AB, Maggioni M, Nadler B, Warner F, Zucker SW: Geometric diffusions as a tool for harmonic analysis and structure definition of data: Multiscale Methods. PNAS 2005, 102(21):7432\u20137437. 10.1073\/pnas.0500896102","journal-title":"PNAS"},{"key":"813_CR11","first-page":"14","volume-title":"NIPS","author":"AY Ng","year":"2001","unstructured":"Ng AY, Jordan MI, Weiss Y: On Spectral Clustering: Analysis and an Algorithm. NIPS 2001, 14."},{"key":"813_CR12","volume-title":"Max Planck Technical Report No. TR-110","author":"J Ham","year":"2003","unstructured":"Ham J, Lee DD, Mika M, Scholkopf B: A kernel view of the dimensionality reduction of manifolds. Max Planck Technical Report No. TR-110 2003."},{"key":"813_CR13","first-page":"975","volume-title":"IEEE International Conference on Computer Vision","author":"Y Weiss","year":"1999","unstructured":"Weiss Y: Segmentation using eigenvectors: A unifying view. IEEE International Conference on Computer Vision 1999, 975\u2013982."},{"key":"813_CR14","first-page":"14","volume-title":"NIPS","author":"N Cristianini","year":"2002","unstructured":"Cristianini N, Shawe-Taylor J, Kandola J: Spectral Kernel Methods for Clustering. NIPS 2002, 14."},{"key":"813_CR15","first-page":"11","volume-title":"NIPS","author":"S Mika","year":"1999","unstructured":"Mika S, Scholkopf B, Smola AJ, Muller KR, Scholz M, Ratsch G: Kernel PCA and de-noising in feature spaces. NIPS 1999, 11."},{"issue":"8","key":"813_CR16","first-page":"731","volume":"22","author":"J Shi","year":"2000","unstructured":"Shi J, Malik J: Normalized cuts and image segmentation. Proc IEEE Transactions on Pattern Analysis and Machine Intelligence 2000, 22(8):731\u2013737.","journal-title":"Proc IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"813_CR17","first-page":"655","volume-title":"Proc 5th ECCV","author":"P Perona","year":"1998","unstructured":"Perona P, Freeman WT: A factorization approach to grouping. In Proc 5th ECCV Edited by: Burkardt H, Neumann B. 1998, 655\u2013670."},{"key":"813_CR18","doi-asserted-by":"publisher","first-page":"14863","DOI":"10.1073\/pnas.95.25.14863","volume":"95","author":"MB Eisen","year":"1998","unstructured":"Eisen MB, Spellman PT, Brown PO, Botstein D: Cluster analysis and display of genome-wide expression patterns. PNAS 1998, 95: 14863\u201314868. 10.1073\/pnas.95.25.14863","journal-title":"PNAS"},{"key":"813_CR19","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/S1097-2765(00)80114-8","volume":"2","author":"RJ Cho","year":"1998","unstructured":"Cho RJ, Campbell MJ, Winzeler EA, Steinmetz L, Conway A, Wodicka L, Wolfsberg TG, Gabrielian AE, Landsman D, Lockhart DJ, Davis RW: A genome-wide transcriptional analysis of the mitotic cell cycle. Mol Cell 1998, 2: 65\u201373. 10.1016\/S1097-2765(00)80114-8","journal-title":"Mol Cell"},{"issue":"12","key":"813_CR20","doi-asserted-by":"publisher","first-page":"3273","DOI":"10.1091\/mbc.9.12.3273","volume":"9","author":"P Spellman","year":"1998","unstructured":"Spellman P, Sherlock G, Zhang MQ, Iyer VR, Anders K, Eisen MB, Brown PO, Botstein D, Futcher B: Comprehensive Identification of Cell Cycle-regulated Genes of the Yeast Saccharomyces cerevisiae by Microarray Hybridization. Molecular Biology of the Cell 1998, 9(12):3273\u20133297.","journal-title":"Molecular Biology of the Cell"},{"key":"813_CR21","doi-asserted-by":"publisher","first-page":"874","DOI":"10.1093\/bioinformatics\/btg496","volume":"20","author":"J Nilsson","year":"2004","unstructured":"Nilsson J, Fioretos T, Hoglund M, Fontes M: Approximate geodesic distances reveal biologically relevant structures in microarray data. Bioinformatics 2004, 20: 874\u2013880. 10.1093\/bioinformatics\/btg496","journal-title":"Bioinformatics"},{"key":"813_CR22","doi-asserted-by":"publisher","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","volume":"290","author":"JB Tenenbaum","year":"2000","unstructured":"Tenenbaum JB, Silva V, Langford JC: A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science 2000, 290: 2319\u20132322. 10.1126\/science.290.5500.2319","journal-title":"Science"},{"key":"813_CR23","doi-asserted-by":"publisher","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","volume":"290","author":"ST Roweis","year":"2000","unstructured":"Roweis ST, Saul LK: Nonlinear Dimensionality Reduction by Local Linear Embedding. Science 2000, 290: 2323\u20132326. 10.1126\/science.290.5500.2323","journal-title":"Science"},{"issue":"1\u20132","key":"813_CR24","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1023\/A:1007515423169","volume":"36","author":"E Bauer","year":"1999","unstructured":"Bauer E, Kohavi R: An empirical comparison of voting classification algorithms: Bagging, boosting, and variants. Machine Learning 1999, 36(1\u20132):105\u2013139. 10.1023\/A:1007515423169","journal-title":"Machine Learning"},{"key":"813_CR25","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1016\/j.jbi.2004.07.005","volume":"37","author":"RL Somorjai","year":"2004","unstructured":"Somorjai RL, Dolenko B, Demko A, Mandelzweig M, Nikulin AE, Baumgartner R, Pizzi NJ: Mapping high dimensional data onto a relative distance plane-an exact method for visualizing and characterizing high-dimensional patterns. Journal of Biomedical Informatics 2004, 37: 366\u2013379. 10.1016\/j.jbi.2004.07.005","journal-title":"Journal of Biomedical Informatics"},{"key":"813_CR26","unstructured":"University of Massachusetts at Amherst CATSCAN images; [http:\/\/vis-www.cs.umass.edu\/files.html]"},{"key":"813_CR27","doi-asserted-by":"publisher","first-page":"1619","DOI":"10.1101\/gr.1289803","volume":"13","author":"MW Karaman","year":"2003","unstructured":"Karaman MW, Houck ML, Chemnick LG, Nagpal S, Chawannakul D, Sudano D, Pike BL, Ho VV, Ryder OA, Hacia JG: Comparative Analysis of Gene-Expression Patterns in Human and African Great Ape Cultured Fibroblasts. Genome Research 2003, 13: 1619\u20131630. 10.1101\/gr.1289803","journal-title":"Genome Research"},{"key":"813_CR28","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1038\/ng0298-155","volume":"18","author":"JG Hacia","year":"1998","unstructured":"Hacia JG, Makalowski W, Edgemon K, Erdos MR, Robbins CM, Fodor SP, Brody LC, Collins FS: Evolutionary sequence comparisons using high-density oligonucleotide arrays. Nature Genetics 1998, 18: 155\u2013158. 10.1038\/ng0298-155","journal-title":"Nature Genetics"},{"key":"813_CR29","volume-title":"R: A Language and Environment for Statistical Computing","author":"R Development Core Team","year":"2004","unstructured":"R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria; 2004."},{"key":"813_CR30","first-page":"871","volume-title":"Graph Theory, Combinatorics, and Applications","author":"B Mohar","year":"1991","unstructured":"Mohar B: The Laplacian spectrum of graphs. In Graph Theory, Combinatorics, and Applications. Volume 2. Edited by: Alavi Y, Schwenk A. Wiley; 1991:871\u2013898."},{"key":"813_CR31","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1007\/BF02289694","volume":"29","author":"JB Kruskal","year":"1964","unstructured":"Kruskal JB: Nonmetric multidimensional scaling: a numerical method. Psychometrika 1964, 29: 115\u2013129. 10.1007\/BF02289694","journal-title":"Psychometrika"}],"container-title":["BMC Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1471-2105-7-74.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T03:12:39Z","timestamp":1630465959000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcbioinformatics.biomedcentral.com\/articles\/10.1186\/1471-2105-7-74"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,2,16]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,12]]}},"alternative-id":["813"],"URL":"https:\/\/doi.org\/10.1186\/1471-2105-7-74","relation":{},"ISSN":["1471-2105"],"issn-type":[{"value":"1471-2105","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,2,16]]},"assertion":[{"value":"7 September 2005","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 February 2006","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 February 2006","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"74"}}