STAT 2984 Lecture Notes - Lecture 10: Multidimensional Scaling, Iris Flower Data Set, Euclidean Geometry
26 Feb 2018
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Document Summary
The dimension of graphs is limited by the human eye; therefore, the maximum number of dimensions for a graph is three. Observations in data are sometimes higher than three dimensions, so high-dimensional plots can be visualized using parallel plots and multidimensional scaling. Position on a vertical axis is relative to others. (+) can visualize many variables in a two-dimensional graph (-) can get overwhelming and messy. Mds maps high-dimensional observations an mds plot is similar to a shadow of the data. Mds plots are 2-dimensional but plot data from multiple dimensions. Distance points have meaning observations close to each other are. The distance in the graph approximates distance between data points more similar than observations far from each other. in their original high dimension. Distance is calculated using euclidean geometry such that: where each variable under the square root represents differences in measured variables between two observations.
