Analysis of a data matrix and a graph: Metagenomic data and the phylogenetic tree

Annals of Applied Statistics - Tập 5 Số 4 - 2011
Elizabeth Purdom1
1University of California, Berkeley

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Felsenstein, J. (1981). Evolutionary trees from gene frequencies and quantitative characters: Finding maximum likelihood estimates. <i>Evolution</i> <b>35</b> 1229–1242.

Hansen, T. F. and Martins, E. P. (1996). Translating between microevolutionary process and macroevolutionary patterns: The correlation structure of interspecific data. <i>Evolution</i> <b>50</b> 1404–1417.

Bach, F. R. and Jordan, M. I. (2002). Kernel independent component analysis. <i>J. Mach. Learn. Res.</i> <b>3</b> 1–48.

Aluja-Ganet, T. and Nonell-Torrent, R. (1991). Local principal components analysis. <i>Questiio</i> <b>15</b> 267–278.

Bapat, R., Kirkland, S. J. and Neumann, M. (2005). On distance matrices and Laplacians. <i>Linear Algebra Appl.</i> <b>401</b> 193–209.

Biyikoğlu, T., Leydold, J. and Stadler, P. F. (2007). <i>Laplacian Eigenvectors of Graphs. Lecture Notes in Mathematics</i> <b>1915</b>. Springer, Berlin.

Cavalli-Sforza, L. L. and Piazza, A. (1975). Analysis of evolution: Evolutionary rates, independence and treeness. <i>Theoretical Population Biology</i> <b>8</b> 127–165.

D’Ambra, L. and Lauro, N. C. (1992). Non-symmetrical exploratory data analysis. <i>Statist. Appl.</i> <b>4</b> 511–529.

di Bella, G. and Jona-Lasinio, G. (1996). Including spatial contiguity information in the analysis of multispecific patterns. <i>Environmental and Ecological Statistics</i> <b>3</b> 260–280.

Diestel, R. (2005). <i>Graph Theory</i>, 3rd ed. <i>Graduate Texts in Mathematics</i> <b>173</b>. Springer, New York.

Dray, S. and Dufour, A.-B. (2007). The ade4 package: Implementing the duality diagram for ecologists. <i>J. Statist. Softw.</i> <b>22</b>.

Dray, S., Saïd, S. and Debias, F. (2008). Spatial ordination of vegetation data using a generalization of Wartenberg’s multivariate spatial correlation. <i>Journal of Vegetation Science</i> <b>19</b> 45–56.

Eckburg, P. B., Bik, E. M., Bernstein, C. N., Purdom, E., Dethlefsen, L., Sargent, M., Gill, S. R., Nelson, K. E. and Relman, D. A. (2005). Diversity of the human intestinal microbial flora. <i>Science</i> <b>308</b> 1635–1638.

Escoufier, Y. (1987). The duality diagram: A means for better practical applications. In <i>Developments in Numerical Ecology</i> (P. Legendre and L. Legendre, eds.). <i>NATO ASI Series</i> <b>G14</b> 139–156. Springer, Berlin.

Excoffier, L., Smouse, P. and Quattro, J. (1992). Analysis of molecular variance inferred from metric distances among DNA haplotypes: Application to human mitochondrial DNA restriction data. <i>Genetics</i> <b>131</b> 479–491.

Gimaret-Carpentier, C., Chessel, D. and Pascal, J. P. (1998). Non-symmetric correspondence analysis: An alternative for community analysis with species occurrences data. <i>Plant Ecology</i> <b>138</b> 97–112.

Holmes, S. (2008). Multivariate analysis: The French way. In <i>Probability and Statistics: Essays in Honor of David A. Freedman</i> (D. Nolan and T. Speed, eds.). <i>IMS Lecture Notes</i> <b>2</b> 219–233. IMS, Beachwood, OH.

Legendre, P. and Legendre, L. (1998). <i>Numerical Ecology</i>, 2nd English ed. <i>Developments in Environmental Modeling</i> <b>20</b>. Elsevier, New York.

Maesschalck, R. D., Jouan-Rimbaud, D. and Massart, D. (2000). The Mahalanobis distance. <i>Chemometrics and Intelligent Laboratory Systems</i> <b>50</b> 1–18.

Martin, A. (2002). Phylogenetic approaches for describing and comparing the diversity of microbial communities. <i>Applied and Environmental Microbiology</i> <b>68</b> 3673–3682.

Martins, E. P. and Housworth, E. A. (2002). Phylogeny shape and the phylogenetic comparative method. <i>Syst. Biol.</i> <b>51</b> 873–880.

Pavoine, S., Dufour, A.-B. and Chessel, D. (2004). From dissimilarities among species to dissimilarities among sites: A double principal coordinate analysis. <i>J. Theoret. Biol.</i> <b>228</b> 523–537.

Pavoine, S., Ollier, S., Pontier, D. and Chessel, D. (2008). Testing for phylogenetic signal in phenotypic traits: New matrices of phylogenetic proximities. <i>Theoretical Population Biology</i> <b>73</b> 79–91.

Pélissier, R., Couteron, P., Dray, S. and Sabatier, D. (2003). Consistency between ordination techniques and diversity measurements: Two strategies for species occurrence data. <i>Ecology</i> <b>84</b> 242–251.

Rao, C. R. (1982). Diversity and dissimilarity coefficients: A unified approach. <i>Theoretical Population Biology</i> <b>21</b> 24–43.

Rapaport, F., Zinovyev, A., Dutreix, M., Barillot, E. and Vert, J.-P. (2007). Classification of microarray data using gene networks. <i>BMC Bioinformatics</i> <b>8</b>.

Rohlf, F. J. (2001). Comparative methods for the analysis of continuous variables: Geometric interpretations. <i>Evolution</i> <b>55</b> 2143–2160.

Thioulouse, J., Chessel, D. and Champely, S. (1995). Multivariate analysis of spatial patterns: A unified approach to local and global structures. <i>Environmental and Ecological Statistics</i> <b>2</b> 1–14.

Golub, G. H. and Van Loan, C. F. (1996). <i>Matrix Computations</i>, 3rd ed. Johns Hopkins Univ. Press, Baltimore.

Greenacre, M. J. (1984). <i>Theory and Applications of Correspondence Analysis</i>. Academic Press, London.

Chessel, D., Dufour, A.-B., Dray, S., with contributions from Jean R. Lobry, Ollier, S., Pavoine, S. and Thioulouse., J. (2005). ade4: Analysis of environmental data: Exploratory and Euclidean methods in environmental sciences. R package Version 1.4-1.

Jolliffe, I. T. (2002). <i>Principal Components Analysis</i>, 2nd ed. Springer, New York.

Kondor, R. I. and Lafferty, J. (2002). Diffusion kernels on graphs and other discrete input spaces. In <i>Proceedings of ICML</i> 315–322.

Purdom, E. (2006). Multivariate kernel methods in the analysis of graphical structures. Ph.D. thesis, Stanford Univ.

R Development Core Team (2008). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0.

Schölkopf, B. and Smola, A. J. (2002). <i>Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond</i>. MIT Press, Cambridge, MA.