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Questions tagged [hessian-matrix]

Hessian matrix is an N x N matrix containing second partial derivatives of a function with respect to its input variables.

Hessian matrices are used extensively in second-order optimization methods such as Newton's method. They give information about the curvature around a point x0 on a function surface.

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Hessian Matrix of the image

I am wondering what information does an Hessian Matrix of an image provides? Does it provide the information of the stable points? What is Hessian matrix used for?
kcc__
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How calculating hessian works for Neural Network learning

Can anyone explain to me in a easy and less mathematical way what is a Hessian and how does it work in practice when optimizing the learning process for a neural network ?
Iulian Rosca
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Using CUDA to solve a system of equations in non-linear least squares fashion

Using CUDA, I would like to solve a system of equations with a non-linear least squares solver. These methods are discussed in an excellent booklet that can be downloaded here. The Jacobian matrix in my problem is sparse and lower triangular. Is…
Nicholas Kinar
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Implementing automatic differentiation for 2nd derivative: algorithm for traversing the computational graph?

I am attempting to implement automatic differentiation for a Python statistics package (the problem formulation is similar to optimization problem formulations). The computational graph is generated using operator overloading and factory functions…
John Salvatier
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Optimizing in R using multiple variables using Rsolnp

I had asked this question earlier, and wanted to continue with a follow-up since I tried some other things and they didn't quite work out. I am essentially trying to optimize an NLP type problem in R, which has binary and integer constraints. The…
prateek1592
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SIFT Keypoint Location

I am currently working in SIFT, I had generated the difference of Gaussian and the extrema image layers. Can anyone explain to me how to use Hessian matrix to eliminate the low contrast keypoint?
tsann
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defining the Hessian as zero

While using scipy.optimize.minimize with the trust-constr method I got this UserWarning: scipy\optimize\_hessian_update_strategy.py:187: UserWarning: delta_grad == 0.0. Check if the approximated function is linear. If the function is linear better…
theother
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Hessian Matrix in Maximum Likelihood - Gauss vs. R

I am struggling with the following problem. In a nutshell: Two different software packages (Gauss by Aptech and R) yield totally different Hessian Matrices in a Maximum Liklihood Procedure. I am using the same procedure (BFGS), the exact same data,…
timsad
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R: error with optim and nlme

library(nlme) mydat <- structure(list(class = c(91L, 91L, 91L, 91L, 91L, 91L, 92L, 92L, 92L, 92L, 92L, 92L, 92L, 92L, 92L, 92L, 92L, 92L, 92L, 92L, 92L, 92L, 93L, 93L, 93L, 94L, 94L, 94L,…
Adrian
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Keras & TensorFlow: getting 2nd derivative of f(x) wrt x, where dim(x) = (1, n)

I'm working in Keras with TensorFlow under the hood. I have a deep neural model (predictive autoencoder). I'm doing something somewhat similar to this: https://arxiv.org/abs/1612.00796 -- I'm trying to understand influence of variables in a given…
iramusa
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Hessian in theano with respect to matrix input

I'm trying to get a vectorized version of theano gradient and hessian, i.e. I want to compute gradient and hessian at several points, given in a matrix as shown below: I have a function: f(x_1,x_2,..,x_n)=exp(x_1^2+x_2^2+...+x_n^2) and I want to…
p0l00ck
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Combining scalars and vectors in Theano for computing Hessian

I'm trying to use Theano to compute the hessian of a function with respect to a vector as well as a couple scalars (edit: that is, I essentially want the scalars appended to the vector that I am computing the hessian with respect to). Here's a…
Kevin Zielnicki
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How to find ridges by using Hessian matrix

I want to find ridges for a given image. (Ridges not edges!) An example is like the image below I think Hessian matrix will work intuitively. So I hard coded Hessian matrix kernel by starting from a 2D-Gaussian equation as the links below…
SimaGuanxing
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Hessian in SAS?

Is there any way to get the Hessian matrix in the proc logistic in SAS? Or which will be an option to calculated it taking from departure the proc logsitic? I have been reading the function documentation but cannot see that there is a way to include…
user1571823
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Detect wrinkle with Hessian matrix

Currently, I am trying to use Hessian matrix to detect wrinkles on the forehead. How could I remove out noises around these wrinkles? Below are my current code and result. from skimage.feature import hessian_matrix, hessian_matrix_eigvals image =…
Richard Tran
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