Upper and Lower Bounds on the Quality of the PCA Bounding Boxes
نویسندگان
چکیده
Principle component analysis (PCA) is commonly used to compute a bounding box of a point set in Rd . The popularity of this heuristic lies in its speed, easy implementation and in the fact that usually, PCA bounding boxes quite well approximate the minimum-volume bounding boxes. In this paper we give a lower bound on the approximation factor of PCA bounding boxes of convex polytopes in arbitrary dimension, and an upper bound on the approximation factor of PCA bounding boxes of convex polygons in R2.
منابع مشابه
Bounds on the quality of the PCA bounding boxes
Principal component analysis (PCA) is commonly used to compute a bounding box of a point set in R. The popularity of this heuristic lies in its speed, easy implementation and in the fact that usually, PCA bounding boxes quite well approximate the minimumvolume bounding boxes. We present examples of discrete points sets in the plane, showing that the worst case ratio of the volume of the PCA bou...
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