Nielsen, Finn Årup

Online Research Database In Technology

Non-negative partial least squares formeta-analytic parcellation of the human brainFinn A˚rup Nielsenwith Daniela Balslev and Lars Kai HansenNeurobiology Research UnitCopenhagen University Hospital RigshospitaletandInformatics and Mathematical ModellingTechnical University of DenmarkSeptember 6, 2005Meta-analytic parcellation of the human brainParcellation of the human brainFigure 1: Parcellation of the dorsal surface of the human brain from(Kleist, 1934, figure 429).“Functional atlas”Complete atlas forthe entire human brainbased on brain le-sion and their asso-ciated change of be-havior (Kleist, 1934).“Manual” analysis ofbrain lesions.Finn A˚rup Nielsen 1 September 6, 2005Meta-analytic parcellation of the human brainComputer-based meta-analysisIs it now possible to automatically construct a functional atlas?Here:Brede Database + Multivariate analysis → Functional ParcellationExtension of some of our previous efforts to data mine for brain-functionassociations (Nielsen et al., 2004).Finn A˚rup Nielsen 2 September 6, 2005Meta-analytic parcellation of the human brainBrede DatabaseFigure 2: Web-page generated for the paper (Epstein andKanwisher, 1998) with abstract and Talairach coordinatesdisplayed in a corner cube environment (Rehm et al., 1998).Brede Database (Nielsen, 2003)inspired by the BrainMapdatabase (Fox and Lancaster,1994).Presently 183 papers and theinformation used is:Abstract of the article3D coordinates representingchange in brain activation orsite of lesion: so-called Ta-lairach coordinates (Talairachand Tournoux, 1988).Finn A˚rup Nielsen 3 September 6, 2005Meta-analytic parcellation of the human brainNon-negative matrix factorizationNon-negative matrix factorization (NMF) decomposes a non-negativedata matrix X(N × P ) (Lee and Seung, 1999)X =WH+U, (1)where W(N ×K) and H(K × P ) are also non-negative matrices.“Euclidean” cost function forE“eucl” = ||X−WH||2F (2)Iterative algorithm (Lee and Seung, 2001)Hkp ← Hkp(WTX)kp(WTWH)kp(3)Wnk ← Wnk(XHT)nk(WHHT)nk. (4)Finn A˚rup Nielsen 4 September 6, 2005Meta-analytic parcellation of the human brainPartial least squaresOne of the variations of partial least squares: Singular value decomposi-tion of a inner product matrix (McIntosh et al., 1996)ULVT = svd(XTY)(5)Probably most suitable for data that is symmetric, i.e., both positive andnegative.“Non-negative partial least squares”WH = nmf(XTY)(6)Should get two non-negative matrices (X and Y) as input.Finn A˚rup Nielsen 5 September 6, 2005Meta-analytic parcellation of the human brainFirst matrix: Bag-of-words matrix‘memory’ ‘visual’ ‘motor’ ‘time’ ‘retrieval’ . . .Fujii 6 0 1 0 4 . . .Maddock 5 0 0 0 0 . . .Tsukiura 0 0 4 0 0 . . .Belin 0 0 0 0 0 . . .Ellerman 0 0 0 5 0 . . .... ... ... ... ... ... . . .Representation of the abstracts of the papers in a bag-of-words matrix:(abstract × words)-matrix: Each element counts of the frequency of aword occurring in an abstract text (Salton et al., 1975).Exclusion of stop words: common words, brain anatomy, . . .Mostly wordsfor brain function left (Nielsen et al., 2005).Finn A˚rup Nielsen 6 September 6, 2005Meta-analytic parcellation of the human brainSecond matrix: Voxelization matrix−6 −4 −2 0 2 4 600.51Example locations−6 −4 −2 0 2 4 6012σ = 0.05 (Too small)−6 −4 −2 0 2 4 600.10.20.3σ = 3.00 (Too Large)−6 −4 −2 0 2 4 600.51σ = 0.49 (LOO CV optimal) ’Talairach coordinate’ in centimeter                                                           Probability density valueRegard the “locations” as being gen-erated from a distribution p(z), wherez is in 3D Talairach space (Fox et al.,1997).Kernel methods (N kernels centeredon each location: µn) with homoge-neous Gaussian kernel in 3D Talairachspace zpˆ(z) =(2piσ2)−3/2NN∑ne− 12σ2(z−µn)2σ2 fixed (σ = 1cm) or optimized withleave-one-out cross-validation (Nielsenand Hansen, 2002).Finn A˚rup Nielsen 7 September 6, 2005Meta-analytic parcellation of the human brainDetailsCoarse sampling of the volume with 8mm voxels: pˆ(z) ≡ YRestriction to gray matter regions using a anatomically labeled brain“AAL” (Tzourio-Mazoyer et al., 2002).Number of components in NMF: Using a rule of thumb we select K =√N/2 (Mardia et al., 1979): K = 10 ≈√183/2.10 runs of NMF with 1000 iterations each, with different initializationeach time.Exclusive assignment: Winner-takes-all function on W and H.Finn A˚rup Nielsen 8 September 6, 2005Meta-analytic parcellation of the human brainResulting NMF components 1: motor, movements, somatosensory, hand, finger 2: painful, perception, thermal, heat, warm 3: retrieval, neutral, words, encoding, episodic 4: faces, perceptual, face, recognition, category 5: visual, eye, time, attention, mental 6: pain, noxious, verbal, unpleasantness, hot 7: memory, alzheimer, autobiographical, rest, memories 8: auditory, spatial, neglect, awareness, language 9: emotion, emotions, disgust, sadness, happiness 10: semantic, phonological, cognitive, decision, judgmentLoadings on words in WW(K × P ) = W(10 × 466), i.e., 10components (“functions”) and 466words.Most dominant functions listed at thetop: motor, pain, retrieval, . . .5 most loaded words listed for eachfunction.Finn A˚rup Nielsen 9 September 6, 2005Meta-analytic parcellation of the human brainDorsolateral surface viewFigure 3: Labeled brain in corner cube environment (Rehmet al., 1998). Dorsolateral surface view seen from the left.H in Talairach space: H(K ×Q) = H(10 × 9975), i.e., 10components and 9975 voxels.Occipital and parietal lobe:“visual”, “eye”.Central sulcus: “Motor”,“movements”, “somatosen-sory”.Temporal cortex: “auditory”,“spatial”, “neglect”Finn A˚rup Nielsen 10 September 6, 2005Meta-analytic parcellation of the human brainMedial viewFigure 4: Medial surface view of the labeled right hemisphere.Seen from the left“Memory” in posterior cingu-late area. Probably due tothe many articles about mem-ory and the posterior cingu-late in the Brede database.Episodic memory retrieval isassociated with posterior cin-gulate (Cabeza and Nyberg,2000).“Emotion” in the medialfrontal area, e.g., amygdala.“Pain” in anterior cingulate,thalamus, insula. Previouslynoted: (Ingvar, 1999).Finn A˚rup Nielsen 11 September 6, 2005Meta-analytic parcellation of the human brainHow stable are the results?2 4 6 8 102468102 4 6 8 10246810The parcellation varies between runs of the NMF andwhen different parts of the data set are used.The different components are not matched betweenruns, e.g., the 2nd component in the first run mightmatch the 5rd component in the second run.It is possible to match the components, e.g., with thealgorithm suggested by (Meila˘, 2002).The “confusion matrices” (HHT) in the figure appearwith one instance of half-split resampling between the183 papers before and after sorting.Finn A˚rup Nielsen 12 September 6, 2005Meta-analytic parcellation of the human brainConsistent parcellationParcellation after masking thosevoxels that are consistently par-cellated.Consistent voxels determinedas those that fall in the samecomponent more than half thetime during half-split resam-pling.This results in 713 of the 9975voxels.Finn A˚rup Nielsen 13 September 6, 2005Meta-analytic parcellation of the human brainSummaryIt is possible to automatically perform a high-level coarse parcellation ofthe entire human brain.The results appear in accordance with general consensus in human brainmapping.We use the Brede Database and rely only on abstract and Talairachcoordinate information.We suggest “non-negative partial least squares” as a combination of non-negative matrix factorization and partial least squares.Finn A˚rup Nielsen 14 September 6, 2005ReferencesReferencesCabeza, R. and Nyberg, L. 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Kriegsverletzungen des Gehirns in ihrer Bedeutung fu¨r die Hirnlokalisation undHirnpathologie, volume IV, part 2 of Handbuch der A¨rztlichen Erfahrungen im Weltkriege 1914/1918.Johann Ambrosius Barth, Leipzig, Germany.Lee, D. D. and Seung, H. S. (1999). Learning the parts of objects by non-negative matrix factorization.Nature, 401(6755):788–791. PMID: 10548103.Lee, D. D. and Seung, H. S. (2001). Algorithms for non-negative matrix factorization. InLeen, T. K., Dietterich, T. G., and Tresp, V., editors, Advances in Neural Information Pro-cessing Systems 13: Proceedings of the 2000 Conference, pages 556–562, Cambridge, Mas-sachusetts. MIT Press. http://hebb.mit.edu/people/seung/papers/nmfconverge.pdf. CiteSeer:http://citeseer.ist.psu.com/lee00algorithms.html.Mardia, K. V., Kent, J. T., and Bibby, J. M. (1979). Multivariate Analysis. Probability and MathematicalStatistics. Academic Press, London. ISBN 0124712525.Finn A˚rup Nielsen 15 September 6, 2005ReferencesMcIntosh, A. R., Bookstein, F. L., Haxby, J. V., and Grady, C. L. (1996). Spatial pattern analysis offunctional brain images using Partial Least Square. NeuroImage, 3(3 part 1):143–157. PMID: 9345485.ftp://ftp.rotman-baycrest.on.ca/pub/Randy/PLS/pls article.pdf.Meila˘, M. (2002). Comparing clusterings. Technical Report 418, De-partment of Statistics, University of Washington, Seattle, Washington.http://www.stat.washington.edu/www/research/reports/2002/tr418.ps.Nielsen, F. A˚. (2003). The Brede database: a small database for functional neuroimaging. NeuroImage,19(2). http://208.164.121.55/hbm2003/abstract/abstract906.htm. Presented at the 9th InternationalConference on Functional Mapping of the Human Brain, June 19–22, 2003, New York, NY. Availableon CD-Rom.Nielsen, F. A˚., Balslev, D., and Hansen, L. K. (2005). Mining the posterior cin-gulate: Segregation between memory and pain component. NeuroImage, 27(3):520–532.DOI: 10.1016/j.neuroimage.2005.04.034.Nielsen, F. A˚. and Hansen, L. K. (2002). 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Commu-nication of the ACM, 18:613–620.Finn A˚rup Nielsen 16 September 6, 2005ReferencesTalairach, J. and Tournoux, P. (1988). Co-planar Stereotaxic Atlas of the Human Brain. Thieme MedicalPublisher Inc, New York. ISBN 0865772932.Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., Ma-zoyer, B., and Joliot, M. (2002). Automated anatomical labeling of activations in SPM using amacroscopic anatomical parcellation of the MNI MRI single-subject brain. NeuroImage, 15(1):273–289.DOI: 10.1006/nimg.2001.0978.Finn A˚rup Nielsen 17 September 6, 2005

Non-negative partial least squares for meta-analytic parcellation of the human brain

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Non-negative partial least squares for meta-analytic parcellation of the human brain

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