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Upper and lower bounds on the quality of the PCA bounding boxes
 In International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision  WSCG 2007
, 2007
"... Principle component analysis (PCA) is commonly used to compute a bounding box of a point set in R d. 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. In this paper we giv ..."
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Principle component analysis (PCA) is commonly used to compute a bounding box of a point set in R d. 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. 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 R 2.
On the Bounding Boxes Obtained by Principal Component Analysis
"... Principle component analysis (PCA) is a commonly used to compute a bounding box of a point set in R d. In this paper we give bounds on the approximation factor of PCA bounding boxes of convex polygons in R² (lower and upper bounds) and convex polyhedra in R³ (lower bound). ..."
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Principle component analysis (PCA) is a commonly used to compute a bounding box of a point set in R d. In this paper we give bounds on the approximation factor of PCA bounding boxes of convex polygons in R² (lower and upper bounds) and convex polyhedra in R³ (lower bound).
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 d. 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 o ..."
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Principal component analysis (PCA) is commonly used to compute a bounding box of a point set in R d. 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 bounding box and the volume of the minimumvolume bounding box tends to infinity. Thus, we concentrate our attention on PCA bounding boxes for continuous sets, especially for the convex hull of a point set. Here, we contribute lower bounds on the approximation factor of PCA bounding boxes of convex sets in arbitrary dimension, and upper bounds in R² and R³.
19.1 Some Geometry
, 2008
"... Isn’t it an artificial, sterilized, didactically pruned world, a mere sham world in which you cravenly vegetate, a world without vices, without passions without hunger, without sap and salt, a world without family, without mothers, without children, almost without women? The instinctual life is tame ..."
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Isn’t it an artificial, sterilized, didactically pruned world, a mere sham world in which you cravenly vegetate, a world without vices, without passions without hunger, without sap and salt, a world without family, without mothers, without children, almost without women? The instinctual life is tamed by meditation. For generations you have left to others dangerous, daring, and responsible things like economics, law, and politics. Cowardly and wellprotected, fed by others, and having few burdensome duties, you lead your drones ’ lives, and so that they won’t be too boring you busy yourselves with all these erudite specialties, count syllables and letters, make music, and play the Glass Bead Game, while outside in the filth of the world poor harried people live real lives and do real work.
Laboratoire de l'Informatique du Paralllisme
, 1998
"... This paper discusses some algorithmic issues when computing with a heterogeneous network of workstations (the typical poor man's parallel computer). Dealing with processors of dioeerent speeds requires to use more involved strategies than blockcyclic data distributions ..."
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This paper discusses some algorithmic issues when computing with a heterogeneous network of workstations (the typical poor man's parallel computer). Dealing with processors of dioeerent speeds requires to use more involved strategies than blockcyclic data distributions
Minimal enclosing parallelepiped in 3D
"... We investigate the problem of nding a minimal volume parallelepiped enclosing a given set of n threedimensional points. We give two mathematical properties of these parallelepipeds, from which we derive two algorithms of theoretical complexity O(n ). Experiments show that in practice our quickes ..."
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We investigate the problem of nding a minimal volume parallelepiped enclosing a given set of n threedimensional points. We give two mathematical properties of these parallelepipeds, from which we derive two algorithms of theoretical complexity O(n ). Experiments show that in practice our quickest algorithm runs in O(n ) (at least for n 10 ). We also present our application in structural biology.
Minimal enclosing parallelepiped in 3d
 Computational Geometry: Theory and Applications
"... We investigate the problem of nding a minimal volume parallelepiped enclosing a given set of n threedimensional points. We give two mathematical properties of these parallelepipeds, from which we derive two algorithms of theoretical complexity O(n ). Experiments show that in practice our quickes ..."
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We investigate the problem of nding a minimal volume parallelepiped enclosing a given set of n threedimensional points. We give two mathematical properties of these parallelepipeds, from which we derive two algorithms of theoretical complexity O(n ). Experiments show that in practice our quickest algorithm runs in O(n ) (at least for n 10 ). We also present our application in structural biology.
20.1 Some Geometry
, 2009
"... Isn’t it an artificial, sterilized, didactically pruned world, a mere sham world in which you cravenly vegetate, a world without vices, without passions without hunger, without sap and salt, a world without family, without mothers, without children, almost without women? The instinctual life is tame ..."
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Isn’t it an artificial, sterilized, didactically pruned world, a mere sham world in which you cravenly vegetate, a world without vices, without passions without hunger, without sap and salt, a world without family, without mothers, without children, almost without women? The instinctual life is tamed by meditation. For generations you have left to others dangerous, daring, and responsible things like economics, law, and politics. Cowardly and wellprotected, fed by others, and having few burdensome duties, you lead your drones ’ lives, and so that they won’t be too boring you busy yourselves with all these erudite specialties, count syllables and letters, make music, and play the Glass Bead Game, while outside in the filth of the world poor harried people live real lives and do real work.
Bounding Boxes
"... Abstract. Principle component analysis (PCA) is commonly used to compute a bounding box of a point set in R d. 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. In this pap ..."
Abstract
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Abstract. Principle component analysis (PCA) is commonly used to compute a bounding box of a point set in R d. 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. 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 R 2.
22.1 Some Geometry
, 2010
"... Isn’t it an artificial, sterilized, didactically pruned world, a mere sham world in which you cravenly vegetate, a world without vices, without passions without hunger, without sap and salt, a world without family, without mothers, without children, almost without women? The instinctual life is tame ..."
Abstract
 Add to MetaCart
Isn’t it an artificial, sterilized, didactically pruned world, a mere sham world in which you cravenly vegetate, a world without vices, without passions without hunger, without sap and salt, a world without family, without mothers, without children, almost without women? The instinctual life is tamed by meditation. For generations you have left to others dangerous, daring, and responsible things like economics, law, and politics. Cowardly and wellprotected, fed by others, and having few burdensome duties, you lead your drones ’ lives, and so that they won’t be too boring you busy yourselves with all these erudite specialties, count syllables and letters, make music, and play the Glass Bead Game, while outside in the filth of the world poor harried people live real lives and do real work.