Friday, December 25, 2015

vector01 Because the binormal vector is defined to be the cross product of the unit tangent and unit normal vector we then know that the binormal vector is orthogonal to both the tangent vector and the normal vector.

Because the binormal vector is defined to be the cross product of the unit tangent and unit normal vector we then know that the binormal vector is orthogonal to both the tangent vector and the normal vector.

http://tutorial.math.lamar.edu/Classes/CalcIII/TangentNormalVectors.aspx

Complex-Valued Neural Networks: Utilizing High-Dimensional Consider two tangent vectors
[PDF]Transformation Invariance in Pattern Recognition - Tangent ...
yann.lecun.com/exdb/publis/pdf/simard-00.pdf
Yann LeCun
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by PY Simardi - ‎Related articles
we introduce the concept of tangent vectors, which compactly represent ..... of tangent vectors in neural network, with the tangent propagation algorithm. The last ...

Neural Networks: Tricks of the Trade - Page 259 - Google Books Result

https://books.google.com/books?isbn=3642352898
Grégoire Montavon, ‎Geneviève Orr, ‎Klaus-Robert Müller - 2012 - ‎Computers
If the network does not have enough capacity, it will not benefit from the extra knowledge introduced by the invariance. Interleaving of the Tangent Vectors: Since ...

Industrial Applications of Neural Networks

https://books.google.com/books?isbn=0849398029
Lakhmi C. Jain, ‎V. Rao Vemuri - 1998 - ‎Computers
Tangent. Vectors. Along. Shape. Boundary. A constant number of sample points that ... the shape of the boundary is necessary for input to the neural network.

Neural Networks - Ufldl

ufldl.stanford.edu/wiki/index.php/Neural_Networks
Apr 6, 2013 - Neural networks give a way of defining a complex, non-linear form of ... noting that another common choice for f is the hyperbolic tangent, or tanh, function: ... to apply to vectors in an element-wise fashion (i.e., f([z1,z2,z3]) ...

[PDF]arXiv:1502.04434v2 [stat.ML] 2 Nov 2015

arxiv.org/pdf/1502.04434
arXiv
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by S Demyanov - ‎2015 - ‎Cited by 1 - ‎Related articles
algorithm that trains a neural network to be robust to variations and noise in the ..... because the standard BP iteration must be repeated for each tangent vector.

Activation function - Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Activation_function
Wikipedia
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This is similar to the behavior of the linear perceptron in neural networks. ... is a sigmoidal activation function in the form of a hyperbolic tangent. ... Support vector machines (SVMs) can effectively utilize a class of activation functions that ...

[PDF]Adaptation in statistical pattern recognition using tangent ...

https://www-i6.informatik.rwth-aachen.de/.../K...
RWTH Aachen University
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by D Keysers - ‎2004 - ‎Cited by 62 - ‎Related articles
Index Terms—Statistical pattern recognition, adaptation, tangent vectors, linear models. ж ..... C.M. Bishop, Neural Networks for Pattern Recognition. Oxford Univ.

Mathematics of Neural Networks: Models, Algorithms and ...

https://books.google.com/books?isbn=1461560993
Stephen W. Ellacott, ‎John C. Mason, ‎Iain J. Anderson - 2012 - ‎Computers
3.1 Local Orientation Extraction A simple and robust estimate of the tangent vector at a point is the dominant eigenvector of the covariance matrix of a square ...

Neural Networks for Pattern Recognition

https://books.google.com/books?isbn=0198538642
Christopher M. Bishop - 1995 - ‎Computers
Let the vector which results from acting on xn by this transformation be denoted by s(a,xn) which is defined so that s(0, xn) = xn. Then the tangent to the curve M ...

Complex-Valued Neural Networks: Utilizing High-Dimensional ...

https://books.google.com/books?isbn=1605662151
Nitta, Tohru - 2009 - ‎Computers
Consider two tangent vectors e = X.c. a0 i=1 – 6 - f - - and e' =X.c' 60 We define the inner product of two tangent vectors e and e” as (e.e) =X.ccg, by Fisher ...

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