Principal component analysis (PCA) to analyze data
- 1. Rajiv Gandhi University Rono hills, Doimukh (A.P) Assignment on Principal component Analysis (PCA) in biological studies. Paper code: ZOOC-511 Paper title: Biostatistics and bioinformatics. Submitted to: Dr. M. Stelin singh By: Bethel Modi Roll no: 23/ZOO/PG/00-004 Class: 4th semester HP
- 2. Contents: 1. Introduction 2. PCA in biological researches 3. PCA in gene expression analysis 4. Advantages of PCA 5. Disadvantages of PCA 6. Conclusion references
- 3. INTRODUCTION Principal component analysis (PCA) is a standard tool in multivariate data analysis to reduce the number of dimensions, while retaining as much as possible of the data’s variation. It is a dimensionality reduction technique used in machine learning and statistics to simplify complex sets while retaining as much information as possible. It transforms a set of correlated variables into a smaller set of uncorrelated variables called principal components. Principal components are a few linear combinations of the original variables that maximally explain the variance of all the variables. In the process, the method provides an approximation of the original data table using o In principal component analysis often reveals the relationship that were not previously suspected and thereby allows interpretations that would not ordinarily result. The visualization and statistical analysis of these new variables, the principal components, can help to find similarities and differences
- 4. between samples. Important original variables that are major contributors to the first component can be discovered as well. The main graphical result is often in the form of a biplot, using the major components to map the cases and adding the original variables to support the distance interpretation of the case’s positions. Variants of the method are also treated, such as the analysis of grouped data, as well as the analysis of categorical data, known as correspondence analysis. The advantage of using PCA is Reduces computational complexity. Removes noise and redundancy. Improves visualization for high dimensional data. Help reduce multicollinearity in models.
- 5. The goal of PCA is to identify a reduced set of features that represent the original data in a lower dimensional subspace with minimal loss of information. PCA and related methods provide means to summarize the data and extract information about individual differences. This makes these methods particularly useful in the era of big data and personalized medicine. (Ferath kherif, Adeliya latypova) There is a neat distinction between the general purpose statistical techniques and quantitative models developed for specific problems. Principal Component analysis (PCA) blurs this distinction: while being a general purpose statistical technique, it implies a peculiar style of reasoning. PCA is a hypothesis generating tool creating a statistical mechanics frame for biological systems modeling without the need for strong a prioritheoretical assumptions. This makes PCA of utmost importance for approaching drug discovery by a systematic perspective overcoming too narrow reductionist approach.
- 6. PCA in biological researches. The application of PCA ranges across all the main themes of pharmacology and biomedical sciences as well, going from quantitative structure activity relationship to data mining and different omics approaches. Here’s how PCA is applied in different biological fields. 1. Genomics and transcriptomics Gene expression analysis: PCA helps reduce the complexity of RNA sequenced and microarray data by identifying patterns in gene expression across different conditions (eg. Healthy vs. diseased state). Population Genetics: it is used to detect population structure ancestry relationship in genome wide association studies (GWAS). 2. Proteomics and Metabolomics. Biomarker Discovery: PCA is used to identify key proteins or metabolites that differentiate disease and control samples.
- 7. Spectroscopy Data analysis: Helps in processing and interpreting mass spectrometry (MS) and nuclear magnetic resonance (NMR) data 3. Microbiology and Ecology Microbial community analysis: PCA is applied to 16S rRNA sequencing data to visualize microbiome differences across samples. Ecological Studies: Helps in analyzing species distribution patterns based on environmental factors. 4. Medical and clinal research Disease classification: PCA assists in clustering patients based on clinical and genetic features. Drug response analysis: Used to analyze how different individuals respond to treatment based on multi- omics data. 5. Structural Biology and imaging. Protein structural analysis: Helps identify structural variations in protein dynamics simulations.
- 8. Medical Imaging: PCA is used for dimensionality reduction in MRI, CT and histopathological image analysis. PCA is a fundamental tool in computational biology, enabling researchers to make sense of large, complex datasets efficiently. PCA in Gene Expression Analysis. Karl pearson synthetically defined the main goal of PCA: ‘In many physical, statistical and biological investigations is desirable to represent a system of points in plane, three or higher dimensioned spaced by the best fitting straight line or plane’. Pearson continues: ‘In nearly all the cases dealt with in the text books of least squares, the variables on the right of our equaions are treated as independent, those on the left as independent variables.’ This implies that the minimization of the sum of squared distances only deals with the dependent (y) variable. The variance along independent
- 9. (x) variable, being the consequence of the choice of the scientist (eg. Dose, time of observation.) is supposed to be strictly controlled and thus does not enter in least squares computation. The novelty of PCA lies in a different look at reality: in many cases of physics and biology, however the ‘independent’ variable is a subject to just as much deviation of error as a ‘ dependent’ variable , we don’t for Example, know x accurately and then proceed to find y, but both x and y are found by experiment or observation. The axes represent the directions with maximum variability and provide a simple and parsimonious descriptions of the covariance structure.
- 10. There are different type of cells, unfortunately we can observe the differences from outside, so we sequence mRNA in each cell to identify which genes are active, this tells us what the cell is doing. Cell 1 Cell 2 Cell 3 Cell 4 Gene 1 3 0.25 2.8 0.1 Gene 2 2.9 0.8 2.2 1.8 Gene 3 2.2 1 1.5 3.2 Gene 4 2 1.4 2 0.3 Gene 5 1.3 1.6 1.6 0
- 11. Gene 6 1.5 2 2.1 3 Gene 7 1.1 2.2 0.9 2.8 Gene 8 1 2.7 0.9 0.3 Gene 9 0.4 3 0.6 0.1 Each cell show how much gene is transcribed in each cell. The gene 1 is transcribed lowly in cell 1 and it is transcribed highly in cell 2. In general the cell 1 and cell 2 have inverse correlation. This means that they are probably 2 different types of cells, since they are using different genes. Alternatively, we could try to plot all three cells at once on a 3 Dimensional graph. We can see how these cells are related to each other. When these cells are more than 3 plots, instead we use Principle component analysis plot.
- 12. The axes are ranked in order of importance, differences along the first Principal component axis PC1 are more important than differences along the second Principle component axis PC2. A PCA plot converts the correlations ( or lack there of) among all of the cells into a 2 dimensional graph. Cells that highly closer are correlated. Once identified the clusters in the PCA plot we go back to original cells and see they represent 3 different types of cells doing 3 different things with their genes. Advantages of PCA 1. Useful for Noise reduction- PCA can filter out noise by capturing only the most significant variations in the data.
- 13. 2. Improves intrepretibility- By transforming data into principle components, it can reveal hidden structures and patterns that were not obvious in the original features. 3. Removes Redundancy- PCA eliminates correlated and redundant features, improving model efficiency. 4. Enhances Computational Efficiency- By reducing the no. of dimension, PCA helps in visualizing patterns by projecting data into 2D or 3D space. 5. Removes Dimensionality – It simplifies complex datasets by reducing the number of features while preserving important patterns, making data easier to visualize and analyze. However PCA should be used carefully, as it can lead to information loss if too many components are removed. Disadvantages of PCA While PCA has many advantages, it also has a several disadvantage that should be considered:
- 14. 1. Difficulty in choosing the number of components- Depending how many principal components to retain require careful analysis, such as using the explained variance ratio. 2. May not work for categorical Data: PCA is designed for continuous numerical data and may not perform well with categorical variables unless properly encoded. 3. Computational Cost: For every large datasets, computing the covariance matrix and eigenvectors can be computationally expensive. 4. Assumes Linearity- PCA assumes that relationship between variables are linear, which may not be true for real world data. 5. Risk of Information loss- If too many Principal components are removed, important data variations may be lost, leading to reduced model performance. Conclusion: Principle component analysis is a powerful dimensionality reduction technique widely used in data analysis and machine
- 15. learning. It helps simplify complex data sets by transforming correlated variables into a smaller set of uncorrelated principal components while preserving the most significant variance. However, it also has limitations, such as potential information loss, difficulty in interpretability and sensitivity to data scaling. Despite this drawbacks, PCA remains a valuable tool for feature extraction, noise reduction and improving model performance when applied appropriately. REFERENCES: 1. Andrzej mackliewicz, Waldemar Ratajczak (1993), Principal component analysis.
- 16. 2. Andreas Daffertshofer, Claudine J.C lamoth, Onno G Meijer, Peter J. Beek (2004). PCA in studying coordination and variability: a tutorial. Elsevier publications. 3. K.Y. Yeung, W.L. Ruzzo (2001). Principal component publication analysis for clustering gene expression data. 4. Herve Abdi, Lynne J. Williams (2010). Principal component analysis. WIREs computational statistics. Wiley publications. 5. Yang chen (2016). Reference- related component analysis: A new method inheriting the advantages of PLS and PCA for separating interesting information and reducing data dimension. Elsevier publications. 6. Kelly J. Egan, L. Brian Ready (1994). Patient satisfaction with intravenous PCA or Epidural morphine. Canadian journal of Anesthesia. 7. Vincent Barra (2004). Analysis of gene expression data using functional principal components.