Principal Component Analysis Computation Research Articles

DivBrowse-interactive visualization and exploratory data analysis of variant call matrices.

The sequencing of whole genomes is becoming increasingly affordable. In this context, large-scale sequencing projects are generating ever larger datasets of species-specific genomic diversity. As a consequence, more and more genomic data need to be made easily accessible and analyzable to the scientific community. We present DivBrowse, a web application for interactive visualization and exploratory analysis of genomic diversity data stored in Variant Call Format (VCF) files of any size. By seamlessly combining BLAST as an entry point together with interactive data analysis features such as principal component analysis in one graphical user interface, DivBrowse provides a novel and unique set of exploratory data analysis capabilities for genomic biodiversity datasets. The capability to integrate DivBrowse into existing web applications supports interoperability between different web applications. Built-in interactive computation of principal component analysis allows users to perform ad hoc analysis of the population structure based on specific genetic elements such as genes and exons. Data interoperability is supported by the ability to export genomic diversity data in VCF and General Feature Format 3 files. DivBrowse offers a novel approach for interactive visualization and analysis of genomic diversity data and optionally also gene annotation data by including features like interactive calculation of variant frequencies and principal component analysis. The use of established standard file formats for data input supports interoperability and seamless deployment of application instances based on the data output of established bioinformatics pipelines.

<p><strong>Variability and Traits Association Analyses in Bacterial Wilt Resistant Genotypes of Tomato </strong><strong>(<em>Solanum lycopersicum </em>L.) under Mid-Hill Conditions of Himachal Pradesh </strong></p>

18 bacterial wilt resistant F4 progenies of tomato were evaluated along with two bacterial wilt resistant checks at the Vegetable Research Farm of the Department of Vegetable Science and Floriculture, Chaudhary Sarwan Kumar Himachal Pradesh Krishi Vishvavidyalaya, Palampur during summer-rainy season’2016 to identify the most promising progenies on the basis of nature and extent of genetic variability and heritability coupled with genetic gain. To ascertain the variability source structure, computation of principal component analysis (PCA) was also done. Estimates for phenotypic coefficient of variation (PCV), genotypic coefficient of variation (GCV), heritability and genetic gain were found to be high for average fruit weight, total fruits per plant, marketable fruits per plant, marketable yield per plant, gross yield per plant and lycopene content. High PCV and GCV indicated the presence of sufficient variability ensuring ample scope for improvement through selection. High heritability allied with high genetic gain suggested the presence of additive gene action and thereby these traits could be considered as reliable indices for selection. For PCA studies, eigen values were calculated for 16 morphological traits of tomato. The results of PCA revealed that out of these 16 traits, initial eight traits exhibited more than 0.5 eigen values and showed more than 95 per cent of genetic variability. Among all, PC1 (days to 50 per cent flowering) has highest eigen value (4.927) and accounts for 30.793 per cent of genetic variability. As a result, these traits might be taken into consideration for effective selection to develop elite bacterial wilt resistant lines in tomato.

Randomized algorithms for distributed computation of principal component analysis and singular value decomposition.

Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a low-rank approximation (in the form of a singular value decomposition) to an arbitrary matrix. Carefully honed algorithms yield results that are uniformly superior to those of the stock, deterministic implementations in Spark (the popular platform for distributed computation); in particular, whereas the stock software will without warning return left singular vectors that are far from numerically orthonormal, a significantly burnished randomized implementation generates left singular vectors that are numerically orthonormal to nearly the machine precision.

Memory Efficient Principal Component Analysis for the Dimensionality Reduction of Large Mass Spectrometry Imaging Data Sets

A memory efficient algorithm for the computation of principal component analysis (PCA) of large mass spectrometry imaging data sets is presented. Mass spectrometry imaging (MSI) enables two- and three-dimensional overviews of hundreds of unlabeled molecular species in complex samples such as intact tissue. PCA, in combination with data binning or other reduction algorithms, has been widely used in the unsupervised processing of MSI data and as a dimentionality reduction method prior to clustering and spatial segmentation. Standard implementations of PCA require the data to be stored in random access memory. This imposes an upper limit on the amount of data that can be processed, necessitating a compromise between the number of pixels and the number of peaks to include. With increasing interest in multivariate analysis of large 3D multislice data sets and ongoing improvements in instrumentation, the ability to retain all pixels and many more peaks is increasingly important. We present a new method which has no limitation on the number of pixels and allows an increased number of peaks to be retained. The new technique was validated against the MATLAB (The MathWorks Inc., Natick, Massachusetts) implementation of PCA (princomp) and then used to reduce, without discarding peaks or pixels, multiple serial sections acquired from a single mouse brain which was too large to be analyzed with princomp. Then, k-means clustering was performed on the reduced data set. We further demonstrate with simulated data of 83 slices, comprising 20,535 pixels per slice and equaling 44 GB of data, that the new method can be used in combination with existing tools to process an entire organ. MATLAB code implementing the memory efficient PCA algorithm is provided.