Principal component analysis
Principal Component Analysis (pronunciation: prin-si-puhl kuhm-puh-nuhnt uh-nal-uh-sis) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. This transformation is defined in such a way that the first principal component has the largest possible variance, and each succeeding component in turn has the highest variance possible under the constraint that it is orthogonal to the preceding components. The resulting vectors are an uncorrelated orthogonal basis set.
Etymology
The term "Principal Component Analysis" is derived from the mathematical term "principal component", which refers to the first component in a data set that explains the most variance. The word "analysis" is used to denote the process of examining something in detail in order to understand its nature or to determine its essential features.
Related Terms
- Eigenvalue: In linear algebra, an eigenvalue is a scalar associated with a linear system of equations, which is a number such that a given matrix minus that number times the identity matrix has zero determinant.
- Eigenvector: An eigenvector of a square matrix is a non-zero vector that changes by a scalar factor when that matrix is multiplied by the vector.
- Variance: In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.
- Correlation: In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data.
- Orthogonal: In mathematics, orthogonality is the relation of two lines at right angles to one another, and the generalization of this relation into n dimensions.
- Linear Algebra: Linear algebra is the branch of mathematics concerning linear equations and linear functions and their representations through matrices and vector spaces.
External links
- Medical encyclopedia article on Principal component analysis
- Wikipedia's article - Principal component analysis
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