Vocabulary for Chapter 9
Chapter 9 covers multivariate methods for heterogenous data. It builds on methods covered in Chapter 7, like dimension reduction, by extending these ideas to more complex, heterogenous data.
The vocabulary words for Chapter 9 are:
| multidimensional scaling (MDS) | a linear dimension reduction method applied in cases where distances between observations are available |
| clusters | in the context of data analysis, data points that group together |
| robust | in the context of a statistical method, a ‘sturdy’ estimator that is not heavily influenced by outliers |
| outlier | a single data point with large distances to other data points, thus potentially dominating and skewing the analysis |
| breakdown point | a measure of the robustness of an estimator; larger values indicate more robust estimators |
| non-metric multidimensional scaling (NMDS) | a robust ordination method which attempts to embed data points in a new space while maintaining their respective order to one another |
| metadata | information, data, or descriptions that characterize other data |
| batch effects | hidden factors that affect the data but are not documented; e.g. running samples at the same time have a degree of similarity from being run in the same batch |
| confounded effects | a term describing when there is uncertainty in the source of variation impacting data |
| supplementary | in the context of variables for a statistical model, categorical variables added to continuous variables in heterogenous data |
| supplementary points | points created using the group-means of points in each of the groups |
| interactive | in the context of plots, data visualizations that can be manipulated in real time by the observer |
| contingency table | the result of counting the co-occurrence of any pair of categorical variables measured in a set of observations; for example, two phenotypes |
| chi-square distance | weighted Eucledian distance using relative counts and standardized by the mean, not the variance |
| biplots | a type of exploratory graph that displays information on both the observations and the variables of a data matrix |
| co-occurence matrix | a matrix that captures the extent to which variables are jointly observed in observations |
| correspondence analysis (CA) / dual scaling | a method for computing low dimensional projections that explain dependencies in categorical data |
| ordination method | a method which enables one to detect and interpret a hidden ordering, gradient or latent variable in the data |
| clustering | in the context of statistical methods, a way to detect and interpret a hidden factor/categorical variable |
| kernel | a linear algorithm designed to determine a non-linear decision boundary; used in pattern analysis to better understand general types of relations like clusters, rankings, principal components, or correlations |
| local linear embedding (LLE) | a nonlinear method for estimating nonlinear trajectories by points in the relevant state spaces |
| isomap | a nonlinear method for estimating nonlinear trajectories by points in the relevant state spaces |
| inertia | in the context of counts in a contingency table, the weighted sum of the squares of distances between observed and expected frequencies |
| covariance | measure of the joint variability of two random variables |
| matrix association | correlation of vectors derived from matrices based on dissimilarity |
| RV coefficient | the global measure of similarity of two data tables as opposed to two vectors; correlation coefficient for tables |
| penalty | a method to constrain the typical optimization algorithm, added to interpret correlation when there are too many degrees of freedom |
| sparsity penalty | an approach to maintain the number of non-zero coefficients to a minimum |
| heterogenous data | a mixture of many continuous and a few categorical variables |
| canonical correlation | a method for finding a few linear combinations of variables from each table that are as correlated as possible |
| nonlinear | a regression equation where the equation is not ‘linear in the parameters,’ meaning the relationship between parameters cannot be calulated by multiplying, exponentiating, or transforming independent variables |
| species tree | a simplified term for a diagram showing the relatedness of organisms based on biological, often genetic sequence, information |
| assay | an investigative (analytic) procedure in laboratory medicine, pharmacology, environmental biology and molecular biology for qualitatively assessing or quantitatively measuring the presence, amount, or functional activity of a target entity (the analyte) |
| protocol | a predefined written procedural method of conducting experiments |
| microarray | a ‘lab-on-a-chip’ method to assess many samples at once, often used in gene expression studies |
| taxon | a group of one or more populations of an organism making up a single unit, typically disected to the level of genus and species |
| mutation | an alteration in the nucleotide sequence of the genome of an organism or virus |
| phenotype | a visually observed genetic trait or characteristic |
| cell development | the process of a cell transitioning from one state to another, such as in the case of a cell transitioning from growth to division in mitosis |
| metabolite | an intermediate or end product of metabolism; typically a small, organic molecule |
Sources consulted or cited
Some of the definitions above are based in part or whole on listed definitions in the following sources.
- Holmes and Huber, 2019. Modern Statistics for Modern Biology. Cambridge University Press, Cambridge, United Kingdom.
- http://www.econ.upf.edu/~michael/stanford/maeb4.pdf
- https://statisticsbyjim.com/regression/difference-between-linear-nonlinear-regression-models/
- https://www.wikipedia.org
Practice
Sere Williams
Graduate Student in Cellular and Molecular Biology
Seré is interested in plant stress at the genetic level.