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Everything about Hyperrectangle
Generalization of a rectangle for higher dimensions
In geometry, a hyperrectangle, is the generalization of a rectangle and the rectangular cuboid to higher dimensions. A necessary and sufficient condition is that it is congruent to the Cartesian product of finite intervals. This means that a -dimensional rectangular solid has each of its edges equal to one of the closed intervals used in the definition. Every -cell is compact. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: HyperrectangleA 5-minute orientation
- Skim a recent paper: Distributionally robust optimal power flow based on multi‐transport hyperrectangle ambiguity setInfluential work since 2022
- Pick up a classic book: HyperrectangleThe most-reprinted book on the subject
- Read the landmark paper: A nearest hyperrectangle learning methodCited 128 times
- Go sideways: Hypercubic honeycombA closely related topic
- Go sideways: HypercubeA closely related topic
📖 Definitions
Noun An orthotope.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
A nearest hyperrectangle learning method
An experimental comparison of the nearest-neighbor and nearest-hyperrectangle algorithms
IRAHC: Instance Reduction Algorithm using Hyperrectangle Clustering
Hyperrectangle Embedding for Debiased 3D Scene Graph Prediction From RGB Sequences
A Nearest Hyperrectangle Learning Method
Latin Hyperrectangle Sampling for Computer Experiments
An Experimental Comparison of the Nearest-Neighbor and Nearest-Hyperrectangle Algorithms
Large margin principle in hyperrectangle learning
🆕 Influential since 2022
Distributionally robust optimal power flow based on multi‐transport hyperrectangle ambiguity set
Clustering explanation based on multi-hyperrectangle
A clustering hyperrectangle model based on kernel density estimation for product quality detection
The phase transitions of diameters in random axis-parallel hyperrectangle intersection graphs
A Multiclustering Evolutionary Hyperrectangle-Based Algorithm
📚 Books worth reading
- 📕HyperrectangleAden Ellias · 2016
- 📕Mining for empty hyperrectangles by way of data reduction techniquesKiran Chaudhry · 2001
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Hypercubic honeycomb In geometry, a hypercubic honeycomb is a family of regular honeycombs (tessellations) in n-dimensional spaces with the Schläfli symbols {4,3...3,4} and…
- Hypercube In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract. It is…
- 5-cube In five-dimensional geometry, a 5-cube (or penteract) is a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and…
- Regular polytope In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. In…
- Rectified tesseract In geometry, the rectified tesseract, rectified 8-cell is a uniform 4-polytope (4-dimensional polytope) bounded by 24 cells: 8 cuboctahedra, and 16 tetrahedra…
- Tesseract In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter…
- Duoprism In geometry of 4 dimensions or higher, a double prism or duoprism is a polytope resulting from the Cartesian product of two polytopes, each of two dimensions…
- Cube A cube is a three-dimensional solid object in geometry. It has eight vertices and twelve straight edges of the same length, so that these edges form six…