Large datasets are increasingly common and are often difficult to interpret. Principal component analysis (PCA) is a technique for reducing the dimensionality of such datasets, increasing interpretability but at the same time minimizing information loss. It does so by creating new uncorrelated variables that successively maximize variance. Finding such new variables, the principal components, reduces to solving an eigenvalue/eigenvector problem, and the new variables are defined by the dataset at hand, not a priori , hence making PCA an adaptive data analysis technique. It is adaptive in another sense too, since variants of the technique have been developed that are tailored to various different data types and structures. This article will begin by introducing the basic ideas of PCA, discussing what it can and cannot do. It will then describe some variants of PCA and their application.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2015.0202

Principal component analysis: a review and recent developments

Introduction.- Data management and software.- Advice for teachers.- Exploration.- Linear regression.- Generalised linear modelling.- Additive and generalised additive modelling.- Introduction to mixed modelling.- Univariate tree models.- Measures of association.- Ordination--first encounter.- Principal component analysis and redundancy analysis.- Correspondence analysis and canonical correspondence analysis.- Introduction to discriminant analysis.- Principal coordinate analysis and non-metric multidimensional scaling.- Time series analysis--Introduction.- Common trends and sudden changes.- Analysis and modelling lattice data.- Spatially continuous data analysis and modelling.- Univariate methods to analyse abundance of decapod larvae.- Analysing presence and absence data for flatfish distribution in the Tagus estuary, Portugual.- Crop pollination by honeybees in an Argentinean pampas system using additive mixed modelling.- Investigating the effects of rice farming on aquatic birds with mixed modelling.- Classification trees and radar detection of birds for North Sea wind farms.- Fish stock identification through neural network analysis of parasite fauna.- Monitoring for change: using generalised least squares, nonmetric multidimensional scaling, and the Mantel test on western Montana grasslands.- Univariate and multivariate analysis applied on a Dutch sandy beach community.- Multivariate analyses of South-American zoobenthic species--spoilt for choice.- Principal component analysis applied to harbour porpoise fatty acid data.- Multivariate analysis of morphometric turtle data--size and shape.- Redundancy analysis and additive modelling applied on savanna tree data.- Canonical correspondence analysis of lowland pasture vegetation in the humid tropics of Mexico.- Estimating common trends in Portuguese fisheries landings.- Common trends in demersal communities on the Newfoundland-Labrador Shelf.- Sea level change and salt marshes in the Wadden Sea: a time series analysis.- Time series analysis of Hawaiian waterbirds.- Spatial modelling of forest community features in the Volzhsko-Kamsky reserve.

Analysing Ecological Data

We introduce glmulti, an R package for automated model selection and multi-model inference with glm and related functions. From a list of explanatory variables, the provided function glmulti builds all possible unique models involving these variables and, optionally, their pairwise interactions. Restrictions can be specified for candidate models, by excluding specific terms, enforcing marginality, or controlling model complexity. Models are fitted with standard R functions like glm. The n best models and their support (e.g., (Q)AIC, (Q)AICc, or BIC) are returned, allowing model selection and multi-model inference through standard R functions. The package is optimized for large candidate sets by avoiding memory limitation, facilitating parallelization and providing, in addition to exhaustive screening, a compiled genetic algorithm method. This article briefly presents the statistical framework and introduces the package, with applications to simulated and real data.

glmulti: An R Package for Easy Automated Model Selection with (Generalized) Linear Models

In many multivariate statistical techniques, a set of linear functions of the original p variables is produced. One of the more difficult aspects of these techniques is the interpretation of the linear functions, as these functions usually have nonzero coefficients on all p variables. A common approach is to effectively ignore (treat as zero) any coefficients less than some threshold value, so that the function becomes simple and the interpretation becomes easier for the users. Such a procedure can be misleading. There are alternatives to principal component analysis which restrict the coefficients to a smaller number of possible values in the derivation of the linear functions, or replace the principal components by “principal variables.” This article introduces a new technique, borrowing an idea proposed by Tibshirani in the context of multiple regression where similar problems arise in interpreting regression equations. This approach is the so-called LASSO, the “least absolute shrinkage and selection o...

/pdf/a-modified-principal-component-technique-based-on-the-lasso-5gjjknb261.pdf

A Modified Principal Component Technique Based on the LASSO

In recent years, there has been an exponential growth in the number of complex documents and texts that require a deeper understanding of machine learning methods to be able to accurately classify texts in many applications. Many machine learning approaches have achieved surpassing results in natural language processing. The success of these learning algorithms relies on their capacity to understand complex models and non-linear relationships within data. However, finding suitable structures, architectures, and techniques for text classification is a challenge for researchers. In this paper, a brief overview of text classification algorithms is discussed. This overview covers different text feature extractions, dimensionality reduction methods, existing algorithms and techniques, and evaluations methods. Finally, the limitations of each technique and their application in real-world problems are discussed.

Text Classification Algorithms: A Survey

BACKGROUND: Dry matter degradability (DMD) parameters (a, b and c in the Orskov and McDonald model) are usually determined by the nylon bag technique. The aim of this study was to estimate DMD parameters of ruminant mixed diets, which are in general unavailable, through multiple linear regressions on their chemical composition (ash, crude protein, neutral detergent fibre (NDF), acid detergent fibre (ADF) and acid detergent lignin (ADL)). The regressions were based on data from 77 feeds.



RESULTS: The prediction model for a was reduced to a simple linear regression on NDF (adjusted R2 = 0.727, F test P < 0.001). A regression model for b was obtained with ADL as the sole predictor (adjusted R2 = 0.691, P < 0.001). The model's upper asymptote (a + b) was predicted from ADL, NDF and ash (adjusted R2 = 0.908, P < 0.001). Modelling c proved more difficult (adjusted R2 with all five predictors = 0.481, P < 0.001).



CONCLUSION: Regressing model parameters on feed chemical composition is a promising method for estimating the degradability of mixed diets, providing an alternative to invasive and expensive laboratory techniques. Copyright © 2010 Society of Chemical Industry

Predicting degradability parameters of diets for ruminants using regressions on chemical components.

Selecting Variable Subsets [R package subselect version 0.15.2]

Minimizing the dispersion of germination across time allows greater uniformity during crop development. The aim of this paper was to model the spread of germination, under non-limiting wate...

/pdf/modeling-the-spread-of-germination-of-four-mediterranean-38rjv0v571.pdf

Modeling the spread of germination of four Mediterranean crops at different temperatures

Selecting variables in multivariate linear models with subselect

Crop establishment is a major factor determining crop productivity. Successful crop establishment requires generalized, fast and concentrated germination. Final germination counts (size), s...

Jorge Cadima

Papers

Predicting degradability parameters of diets for ruminants using regressions on chemical components.

Selecting Variable Subsets [R package subselect version 0.15.2]

Modeling the spread of germination of four Mediterranean crops at different temperatures

Selecting variables in multivariate linear models with subselect

Optimizing germination of seven Mediterranean crops