Vocabulary for Chapter 7
Chapter 7 covers multivariate analysis, with a focus on principal component analysis and dimension reduction in general.
| principal component analysis (PCA) | an unsupervised ordination method used to reduce the dimensionality of data by creating scores that maximize the explained variation in the data |
| matrix | a two dimensional arrangement of rows and columns used to store data |
| mass spectroscopy | a measurement procedure based on the mass-to-charge ratio of ions, often used to measure metabolite abundance |
| correlation coefficient | a measure of how two variables co-vary, reported as a single summary value |
| centering | subtracting the mean of the data so the new mean is 0 |
| scaling / standardizing | dividing data values by the data’s standard deviation so the new standard deviation is 1 |
| data simplification | a broadly applicable term referring to the process of summarizing or reducing the dimensions of multivariate data |
| dimension reduction | summarizing data to reduce the number of variables for downstream analyses |
| principal scores | a normally distributed z-score assigned to each subject that corresponds with the specific ordering and weighting of original variables within a given principal component |
| unsupervised learning | a machine learning method used to find patterns in the data without a priori variable ranking or labeling |
| status | in the context of variables in a statistical learning algorithm, a ranking or labeling of variables (e.g., to consider one variable as the outcome or goal and the rest as potential predictive variables) |
| projection | a representation of data from a higher dimensional space to a lower dimensional space |
| linear | in the context of a statistical technique, a description that describes the search for relationships between variables that can be expressed as a linear combination of predictors |
| regression line | a linear function of the form y = mx + b which is used to project two-dimensional data onto a 1 dimensional line |
| linear regression | a supervised method that models the relationship between explanatory and response variables by minimizing the residual sum of squares with respect to the response variable |
| supervised learning | in the context of a statistical learning technique, a machine learning method that uses specified, user defined inputs to map patterns (input/output associations) in data |
| predictor | an independent, explanatory, or ‘x’ variable in a model |
| response | an outcome or ‘y’ variable in a model that is thought to be affected by a predictor |
| principal components | uncorrelated latent variables created by the PCA procedure, of which there are as many as there are original variables entered into the procedure |
| inertia | in the context of variability of points, the total variance of a point cloud based on the sum of squares of the projection of points |
| linear combination | mathematical expression in which terms are scaled by constants and then added together |
| loadings | in the context of principal components, these values quantify the weight of each original variable in a principal component |
| singular value decomposition (SVD) | a way to decompose a rectangular matrix by factoring it into three different matrices in a way that has some useful mathematical applications |
| rank | in the context of a matrix, the maximum number of linearly independent column or row vectors |
| norm | in the context of a vector, a positive scalar quantity reflecting its size/magnitude |
| singular value | a non-negative, normalizing value from a singular value decomposition quantifying the relative importance of the corresponding singular vectors |
| orthonormal | the characteristic of a set of vectors that are both orthogonal (uncorrelated) and normalized |
| principal plane | a 2-dimensional space across which the data are most spread out or variable |
| trace | in the context of matrices, the sum of the diagonal elements of a square matrix |
| supplementary information | extra information or instruction to help clarify research question, procedure or results |
| metadata | information, data, or descriptions that characterize other data |
| biplot | a type of exploratory graph that displays information on both the observations and the variables of a data matrix |
| biometric characteristics | physical, physiological, demographic, or behavioral features of an organism that can be measured and quantified |
| proliferation rate | speed at which the number of cells increase through the process of cellular division |
| gene expression profile | a snapshot measure of the level of activity/expression (transcription) of a collection (thousands) of genes, representing a global measure of gene function |
| T-cell populations | groups of differentiated white blood cells that function in immune response |
| operational taxonomic units (OTUs) | clusters of closely related species of bacteria based on sequence similarity |
| transcriptome data | the complete set of all RNA molecules measured from a biological sample generated from genome-wide sequencing methods, like RNA-seq |
| sequence read | an inferred sequence of base pairs, or fragments of the genome, generated from one of many genomics methods |
| proteomic profile | a snapshot measure of the levels of all proteins measured in a biological sample |
| molecule | two or more chemically bond atoms that lack a charge |
| m/z ratio | mass to charge ratio used in mass spectrometry to differentiation molecules |
| wild-type | a normal allele or phenotype that occurs under natural conditions |
Source Consulted or Cited
Some of the definitons above are based in part or whole on listed definitions in the following source:
- Holmes and Huber, 2019. Modern Statistics for Modern Biology. Cambridge University Press, Cambridge, United Kingdom.
- Wikipedia: The Free Encyclopedia. http://en.wikipedia.org/wiki/Main_Page
Practice
Zach Laubach
Morris Animal Foundation Postdoc Fellow
My research interests are behavioral ecology and evolutionary biology, with an emphasis on deveopmental plasticity.