August 10th 2010

Optimization scikit: separation of orthogonally convoluted signals

My last blog post on optimization helped me generate orthogonal sequences. Now, I will use those sequences to separate two signals. The basic use case is a linear system with two inputs, one output, and instead of recording the response of one input at a time, one plays both inputs simultaneously with specific sequences so that they can be separated in another process.
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July 27th 2010

Genetic algorithms in Python

Although I’m fond of numerical optimization through gradients, … there are some times where a global optimization is much more powerfull. For instance, I have to generate two sequences/combs that are orthogonal and for which their autocorrelation is almost an impulse. The two combs have a fixed number of impulse, so it’s a perfect job for genetic algorithms.
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June 29th 2010

Optimization scikit: a conjugate-gradient optimization

In my last post about optimization, I’ve derived my function analytically. Sometimes, it’s not as easy. Sometimes also, a simple gradient optimization is not enough.

scikits.optimization has a special class for handling numerical differentiation, and several tools for conjugate gradients.
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April 27th 2010

Optimization scikit: a gradient-based optimization

Last time, I’ve made a simple example of a gradient-free optimization. Now, I’d like to use the gradient of my function (analytical gradient I’ve computed) to be able to get the global minimum in less iterations.
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February 25th 2010

Optimization scikit: Structure and implementation

Some weeks ago, the first release of the optimization scikit was done. I’d like to expose here the internal structure and the way the implementation was thought.
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February 2nd 2010

Annoucement: scikits.optimization 0.1

I’m pleased to announce the first release of one of my projects. This scikits is based on a generic framework that can support unconstrained cost function minimization. It is based on a separation principle and is also completely object oriented.

Several optimizers are available:

  • Nelder-Mead or simplex minimization
  • Unconstrained gradient-based minimization

The usual criterias can be used:

  • Iteration limit
  • Parameter change (relative and absolute)
  • Cost function changer (relative and absolute)
  • Composite criterion generation (AND/OR)

Different direction searches are available:

  • Gradient
  • Several conjugate-gradient (Fletcher-Reeves, …)
  • Decorators for selecting part of the gradient
  • Marquardt step

Finally several line searches (1D minimization) were coded:

  • Fibonacci and gold number methods (exact line searches)
  • Wolfe-Powell soft and strong rules
  • Goldstein line search
  • Cubic interpolation

Additional helper classes can be used:

  • Finite difference differentation (central and forward)
  • Quadratic cost (for least square estimation)
  • Levenberg-Marquardt approximation for least square estimation

Although it is the 0.1 version, the code is quite stable and is used in the learn scikit.

The package can be easy-installed or can be found on PyPI.

Several tutorials are available or will be available on the future at the following locations:

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December 22nd 2009

Optimization scikit: Starting with gradient-free simple optimization

Some months ago, I’ve finished my manifold learning posts serie. As support for the manifold learning toolkit, I’ve also developed an optimization framework, which I’ll be blogging about, starting now.
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