![]() ![]() These loading vectors are called p1 and p2. Such knowledge is given by the principal component loadings (graph below). In a PCA model with two components, that is, a plane in K-space, which variables (food provisions) are responsible for the patterns seen among the observations (countries)? We would like to know which variables are influential, and also how the variables are correlated. Colored by geographic location (latitude) of the respective capital city. The first component explains 32% of the variation, and the second component 19%. This provides a map of how the countries relate to each other. The PCA score plot of the first two PCs of a data set about food consumption profiles. A line or plane that is the least squares approximation of a set of data points makes the variance of the coordinates on the line or plane as large as possible. Statistically, PCA finds lines, planes and hyper-planes in the K-dimensional space that approximate the data as well as possible in the least squares sense. The goal is to extract the important information from the data and to express this information as a set of summary indices called principal components. PCA is a very flexible tool and allows analysis of datasets that may contain, for example, multicollinearity, missing values, categorical data, and imprecise measurements. PCA goes back to Cauchy but was first formulated in statistics by Pearson, who described the analysis as finding “ lines and planes of closest fit to systems of points in space”. This overview may uncover the relationships between observations and variables, and among the variables. The most important use of PCA is to represent a multivariate data table as smaller set of variables (summary indices) in order to observe trends, jumps, clusters and outliers. PCA forms the basis of multivariate data analysis based on projection methods. It has been widely used in the areas of pattern recognition and signal processing and is a statistical method under the broad title of factor analysis. ![]() Principal component analysis today is one of the most popular multivariate statistical techniques. Using PCA can help identify correlations between data points, such as whether there is a correlation between consumption of foods like frozen fish and crisp bread in Nordic countries. ![]() This article is posted on our Science Snippets Blog. The underlying data can be measurements describing properties of production samples, chemical compounds or reactions, process time points of a continuous process, batches from a batch process, biological individuals or trials of a DOE-protocol, for example. Principal component analysis, or PCA, is a statistical procedure that allows you to summarize the information content in large data tables by means of a smaller set of “summary indices” that can be more easily visualized and analyzed. ![]()
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