Wednesday, October 16, 2019

Jacobina, Hessian, gradient, maximum, minum, saddle point

The Jacobian matrix contains information about the local behavior of a function. The Jacobian matrix can be seen as a representation of some local factor of change. It consists of first order partial derivatives. If we take the partial derivatives from the first order partial derivatives, we get the second order partial derivatives, which are used in the Hessian matrix. The Hessian matrix is used for the Second Partial Derivative Test with which we can test, whether a point x is a local maximum, minimum or a so called saddle point .
With the Jacobian matrix we can convert from one coordinate system into another

NHANES National Youth Fitness Survey (NNYFS) 2012

Friday, October 11, 2019

graph isomorphism as encryption tool

As far as I know there is no cryptographic scheme based on Graph isomorphism. The following is the key reasons.
The security of a cryptographic scheme largely depend on one-wayness of the underlying function. For a function to be one-way it's not just need to be hard for few NP instances but must be hard for a random instance. In other words it is very easy to find problems that are hard for very instance but easy for majority of instances . Such problems may not come under P but they arn't one way functions either. One such good example is the encryption scheme based on subset-sum problem, which was eventually broken due to the above specified reason.

weighted adjacency matrix

Q: 0 means no link. but small value means a very close link.

In igraph, direction is from Column to row. The following example show arrow from 2nd and 3rd to 1st.

In Yuan, network exact control paper, the directions are from row to columns. So, is the transpose of the igraph adjacency matrix.



Thursday, September 26, 2019

semantic segmentation (pixel wise classification)

semantic segmentation (pixel wise classification)

segnet :

SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation

Sunday, September 22, 2019


tensor is a general term:
2d tensor is matrix, 1D tensor is vector, 0D tensor is scalar.,
tensor can be more than 3D.