Data dimensional reduction and principal components analysis

EUREKA: Physics and Engineering

The recent trends in collecting huge datasets have posed a great challenge that is brought by the high dimensionality and aggravated by the presence of irrelevant dimensions. Machine learning models for regression is recognized as a convenient way of improving the estimation for empirical models. Popular machine learning models is support vector regression (SVR). However, the usage of principal component analysis (PCA) as a variable reduction method along with SVR is suggested. The principal component analysis helps in building a predictive model that is simple as it contains the smallest number of variables and efficient. In this paper, we investigate the competence of SVR with PCA to explore its performance for a more accurate estimation. Simulation study and Renal Failure (RF) data of SVR optimized by four different kernel functions; linear, polynomial, radial basis, and sigmoid functions using R software, version (R x64 3.2.5) to compare the behavior of ε SVR and v-SVR models fo...

Zenodo (CERN European Organization for Nuclear Research), 2023

Anomaly detection has become a crucial technology in several application fields, mostly for network security. The classification challenge of anomaly detection using machine learning techniques on network data has been described here. Using the KDD99 dataset for network IDS, dimensionality reduction and classification techniques are investigated and assessed. For the application on network data, Principal Component Analysis for dimensionality reduction and Support Vector Machine for classification have been taken into consideration, and the results are examined.. The result shows the decrease in execution time for the classification as we reduce the dimension of the input data and also the precision and recall parameter values of the classification algorithm shows that the SVM with PCA method is more accurate as the number of misclassification decreases. Enormous data in health research is extremely interesting since data-based studies may move more quickly than hypothesis-based research, despite the fact that enormous databases are becoming common and hence challenging to interpret. Using Principal Component Analysis (PCA), one may make some datasets less dimensional. enhances interpretability while retaining most of the information. It does this by introducing fresh variables that are unrelated to one another.

Generally, today data analysts and researchers are often faced with a daunting task of reducing high dimensional datasets as large volume of data can be easily generated given the explosive activities of the internet. The most widely used tools for data reduction is the principal component analysis. Merely in some cases, the singular value decomposition method is applied. The study examined the application and theoretical framework of these methods in terms of its linear algebra foundation. The study discovered that the SVD method is a more robust and general method for a change of basis and low rank approximations. But.in terms of application, the PCA method is easy to interpret as illustrated in the work.

International Research Journal of Modernization in Engineering Technology and Science , 2020

In this paper, we have assessed a calculation utilizing Principal Component Analysis (PCA) for its application in information analysis. In the examination field, it is hard to comprehend the enormous measure of information and is very tedious as well. This way, to maintain a strategic distance from wastage of time and for the simplicity in understanding, we have investigated a PCA calculation that can diminish the immense element of the information into 2-dimensional. The technique for PCA is utilized to pack the most extreme measure of data into initial two segments of the changed network known as the principal components by dismissing the other vectors that convey the insignificant data or repetitive information. The primary target of the paper is to isolate two mixes state A and B having various focuses for every one of the four sensors also, distinguishes which sensors have the comparative or unique focus with the assistance of different plots that clarifies the connection between's the various factors.

1998

Principal Component Analysis (PCA) is a useful technique for reducing the dimensionality of datasets for compression or recognition purposes. Many different methods have been proposed for performing PCA. This study aims to compare these methods by analysing the solutions which these methods find. We have estimated the correlation between these solutions and produced the errors using bootstrap resampling.

Principal component analysis (PCA) is a multivariate technique that analyzes a data table in which observations are described by several inter-correlated quantitative dependent variables. Its goal is to extract the important information from the table, to represent it as a set of new orthogonal variables called principal components, and to display the pattern of similarity of the observations and of the variables as points in maps. The quality of the PCA model can be evaluated using cross-validation techniques such as the bootstrap and the jackknife. PCA can be generalized as correspondence analysis (CA) in order to handle qualitative variables and as multiple factor analysis (MFA) in order to handle heterogeneous sets of variables. Mathematically, PCA depends upon the eigen-decomposition of positive semidefinite matrices and upon the singular value decomposition (SVD) of rectangular matrices.

2004

This note is intended as a brief introduction to singular value decomposition (SVD) and principal component analysis (PCA). These are very useful techniques in data analysis and visualization. Further information can found for example in Numerical Recipes, section 2.6, available free online: http://www. nr. com/http://www. library. cornell. edu/nr/bookcpdf. html and in C. Bishop, Neural Networks for Pattern Recognition, Chapter 8.

International Statistical Review, 2017

PCA is a statistical method, which is directly related to EVD and SVD. Neural networks-based PCA method estimates PC online from the input data sequences, which especially suits for high-dimensional data due to the avoidance of the computation of large covariance matrix, and for the tracking of nonstationary data, where the covariance matrix changes slowly over time. Neural networks and algorithms for PCA will be described in this chapter, and algorithms given in this chapter are typically unsupervised learning methods. PCA has been widely used in engineering and scientific disciplines, such as pattern recognition, data compression and coding, image processing, high-resolution spectrum analysis, and adaptive beamforming. PCA is based on the spectral analysis of the second moment matrix that statistically characterizes a random vector. PCA is directly related to SVD, and the most common way to perform PCA is via the SVD of a data matrix. However, the capability of SVD is limited for very large data sets. It is well known that preprocessing usually maps a high-dimensional space to a low-dimensional space with the least information loss, which is known as feature extraction. PCA is a well-known feature extraction method, and it allows the removal of the second-order correlation among given random processes. By calculating the eigenvectors of the covariance matrix of the input vector, PCA linearly transforms a high-dimensional input vector into a low-dimensional one whose components are uncorrelated.

International Journal of Engineering Sciences & Research Technology, 2014

This paper presents the results of a comparative study of Pca and Ica in the field of data reduction. In particular, we compare the two feature extraction techniques- independent component analysis (ICA) and Principal component analysis (PCA) to project microarray data into statistically independent components and genes are clustered according to their mean distances from the calculated centroid. We test the statistical significance of enrichment of gene annotations within clusters. Result shows PCA outperforms ICA in constructing functionally coherent clusters on microarray Breast Cancer Wisconsin, Primary Tumours,, Parkinson’s tele monitoring and ecoli data and hepatitis data set.

Journal of Autonomous Intelligence

Feature extraction plays an important role in accurate preprocessing and real-world applications. High-dimensional features in the data have a significant impact on the machine learning classification system. Relevant feature extraction is a fundamental step not only to reduce the dimensionality but also to improve the performance of the classifier. In this paper, the author proposes a hybrid dimensionality reduction technique using principal component analysis (PCA) and singular value decomposition (SVD) in a machine classification system with a support vector classifier (SVC). To evaluate the performance of PCSVD, the results are compared without using feature extraction techniques or with existing methods of independent component analysis (ICA), PCA, linear discriminant analysis (LDA), and SVD. In addition, the efficiency of the PCSVD method is measured on an increased scale of 1.54% accuracy, 2.70% sensitivity, 3.71% specificity, and 3.58% precision. In addition, reduce the 15% ...