Discriminant Analysis

BackgroundThe dramatic progress in sequencing technologies offers unprecedented prospects for deciphering the organization of natural populations in space and time. However, the size of the datasets generated also poses some daunting challenges. In particular, Bayesian clustering algorithms based on pre-defined population genetics models such as the STRUCTURE or BAPS software may not be able to cope with this unprecedented amount of data. Thus, there is a need for less computer-intensive approaches. Multivariate analyses seem particularly appealing as they are specifically devoted to extracting information from large datasets. Unfortunately, currently available multivariate methods still lack some essential features needed to study the genetic structure of natural populations.ResultsWe introduce the Discriminant Analysis of Principal Components (DAPC), a multivariate method designed to identify and describe clusters of genetically related individuals. When group priors are lacking, DAPC uses sequential K-means and model selection to infer genetic clusters. Our approach allows extracting rich information from genetic data, providing assignment of individuals to groups, a visual assessment of between-population differentiation, and contribution of individual alleles to population structuring. We evaluate the performance of our method using simulated data, which were also analyzed using STRUCTURE as a benchmark. Additionally, we illustrate the method by analyzing microsatellite polymorphism in worldwide human populations and hemagglutinin gene sequence variation in seasonal influenza.ConclusionsAnalysis of simulated data revealed that our approach performs generally better than STRUCTURE at characterizing population subdivision. The tools implemented in DAPC for the identification of clusters and graphical representation of between-group structures allow to unravel complex population structures. Our approach is also faster than Bayesian clustering algorithms by several orders of magnitude, and may be applicable to a wider range of datasets.

BackgroundVariable selection on high throughput biological data, such as gene expression or single nucleotide polymorphisms (SNPs), becomes inevitable to select relevant information and, therefore, to better characterize diseases or assess genetic structure. There are different ways to perform variable selection in large data sets. Statistical tests are commonly used to identify differentially expressed features for explanatory purposes, whereas Machine Learning wrapper approaches can be used for predictive purposes. In the case of multiple highly correlated variables, another option is to use multivariate exploratory approaches to give more insight into cell biology, biological pathways or complex traits.ResultsA simple extension of a sparse PLS exploratory approach is proposed to perform variable selection in a multiclass classification framework.ConclusionssPLS-DA has a classification performance similar to other wrapper or sparse discriminant analysis approaches on public microarray and SNP data sets. More importantly, sPLS-DA is clearly competitive in terms of computational efficiency and superior in terms of interpretability of the results via valuable graphical outputs. sPLS-DA is available in the R package mixOmics, which is dedicated to the analysis of large biological data sets.

BackgroundPartial Least-Squares Discriminant Analysis (PLS-DA) is a popular machine learning tool that is gaining increasing attention as a useful feature selector and classifier. In an effort to understand its strengths and weaknesses, we performed a series of experiments with synthetic data and compared its performance to its close relative from which it was initially invented, namely Principal Component Analysis (PCA).ResultsWe demonstrate that even though PCA ignores the information regarding the class labels of the samples, this unsupervised tool can be remarkably effective as a feature selector. In some cases, it outperforms PLS-DA, which is made aware of the class labels in its input. Our experiments range from looking at the signal-to-noise ratio in the feature selection task, to considering many practical distributions and models encountered when analyzing bioinformatics and clinical data. Other methods were also evaluated. Finally, we analyzed an interesting data set from 396 vaginal microbiome samples where the ground truth for the feature selection was available. All the 3D figures shown in this paper as well as the supplementary ones can be viewed interactively at http://biorg.cs.fiu.edu/plsda CONCLUSIONS: Our results highlighted the strengths and weaknesses of PLS-DA in comparison with PCA for different underlying data models.

This investigation aimed to assess the effectiveness of different classification models in diagnosing prostate cancer using a screening dataset obtained from the National Cancer Institute's Cancer Data Access System. The dataset was first reduced using the PCLDA method, which combines Principal Component Analysis and Linear Discriminant Analysis. Two classifiers, Support Vector Machine (SVM) and k-Nearest Neighbour (KNN), were then applied to compare their performance. The results showed that the PCLDA-SVM model achieved an impressive accuracy rate of 97.99%, with a precision of 0.92, sensitivity of 92.83%, specificity of 97.65%, and F1 score of 0.93. Additionally, it demonstrated a low error rate of 0.016 and a Matthews Correlation Coefficient (MCC) and Kappa coefficient of 0.946. On the other hand, the PCLDA-KNN model also performed well, achieving an accuracy of 97.8%, precision of 0.93, sensitivity of 93.39%, specificity of 97.86%, an F1 score of 0.92, a high MCC and Kappa coefficient of 0.98, and an error rate of 0.006. In conclusion, the PCLDA-SVM method exhibited improved efficacy in diagnosing prostate cancer compared to the PCLDA-KNN model. Both models, however, showed promising results, suggesting the potential of these classifiers in prostate cancer diagnosis.