By Knut Aas-Jakobsen, Mathis Grenacher (auth.)

ISBN-10: 3034859767

ISBN-13: 9783034859769

ISBN-10: 3764307315

ISBN-13: 9783764307318

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**Extra resources for Analysis of Slender Reinforced Concrete Frames**

**Example text**

The method is based on the embedding of discriminant tree structures derived from the problem domain. The binary trees are built by looking for the partition that maximizes the mutual information (MI) between the data and their respective class labels. Look at the 3-class problem shown on the top of Fig. 4(a). The standard DECOC algorithm considers the whole set of classes to split it into two sub-sets of classes ℘+ and ℘− maximizing the MI criterion on a sequential forward floating search procedure (SFFS).

In Section 5, the chapter is concluded with a brief summary of the main ideas and discussions on current challenges and future steps. 1 Binary Morphological Operators Let E = Z2 , the Cartesian grid, be the image domain. Each point in E corresponds to a pixel location. The origin of E is denoted 0. Given two points x and y in E, x+y denotes the usual vector addition in E. Given a set X ⊆ E, X c denotes the complementary set with respect to E; Xz = {x + z : x ∈ X} ˇ = {−x : x ∈ X} denotes the transpose denotes the translate of X by z; and X of X.

Then, only J℘+ , J℘− , and J℘− are used. If the new sub-sets improve the classification performance, new sub-classes are formed, and the process is repeated. In the example of Fig. 4, applying the splitting criteria SC over the two sub-sets, two clusters are found for ℘+ = C1 and for ℘− = C2 . Then, the original encoding of the problem C1 vs C2 (corresponding to the second column of the matrix in the center of Fig. 4(c)) is split into two columns marked with the dashed lines in the matrix on the right.

### Analysis of Slender Reinforced Concrete Frames by Knut Aas-Jakobsen, Mathis Grenacher (auth.)

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