- Introduction
- Background
- Motivation and Overview
- Approach
- Description and the Approach used
- Explanation of the concepts used
- Covariance Matrix
- Eigen vectors
- Power simulation
- Coding and Simulation
- Approach of coding strategy
- Simulations and outputs
- Conclusion
The idea behind the project is to implement Principle Component Analysis (PCA) to a medical data (of liver patients)and give the key variables with the help of eigen value decomposition and covariance relations.
“Principal components are the key to PCA; they represent what's underneath the hood of your data.” Principal Component Analysis or PCA is a dimensionality reduction technique. Many non-linear dimensionality reduction techniques exist out there (Sammons Mapping) but linear methods are more mature, if more limited.
PCA minimizes low-dimensional reconstruction error, but another sensible objective is to maximize the scatter of the projection, under the rationale that doing so would yield the most informative projection (this choice is sometimes called classical scaling). There are other methods too for linear dimensionality reduction. We have included Multidimensional scaling as it is connected with PCA. This project focuses on obtaining the principal components of a matrix. The Principal Component Analysis helps find the component of the matrix that contribute most significantly. It is used for compression of data without losing any significant information. This project uses many concepts of linear algebra thus increasing our grasp and understanding of the concepts. It also helps us in seeing how these concepts are used in the real life and how it changes our lives in ways we can’t imagine. Our group has tried to reduce the dimensions of a medical data set thus focusing on the components that really matter and even combining different components to form one singular variable.
• PCA (Principal Component Analysis) and data reduction • Eigen vectors and Eigen values