# What is scaled conjugate gradient?

## What is scaled conjugate gradient?

The scaled conjugate gradient (SCG) algorithm, developed by Moller [Moll93], is based on conjugate directions, but this algorithm does not perform a line search at each iteration unlike other conjugate gradient algorithms which require a line search at each iteration. Making the system computationally expensive.

What is the purpose of the conjugate gradient method?

Conjugate Gradient algorithm is used to solve a linear system, or equivalently, optimize a quadratic convex function. It sets the learning path direction such that they are conjugates with respect to the coefficient matrix A and hence the process is terminated after at most the dimension of A iterations.

A more important advantage of the conjugate gradient method is the especially simple formula that is used to determine the new direction vector. This simplicity makes the method only slightly more complicated than steepest descent.

### Why conjugate gradient is better than steepest descent?

It is shown here that the conjugate-gradient algorithm is actually superior to the steepest-descent algorithm in that, in the generic case, at each iteration it yields a lower cost than does the steepest-descent algorithm, when both start at the same point.

What is scaled conjugate gradient backpropagation?

Backpropagation is used to calculate derivatives of performance perf with respect to the weight and bias variables X . The scaled conjugate gradient algorithm is based on conjugate directions, as in traincgp , traincgf , and traincgb , but this algorithm does not perform a line search at each iteration.

What are conjugate directions?

This Conjugate Directions method is sometimes called the direct search method or Powell’s method, after it originator. The basic idea behind this method is to use a series of one-dimensional searches to locate the optimum which is a function of variables X1, X2..

#### What is the main drawback of conjugate direction method?

The fundamental limitation of the conjugate gradient method is that it requires, in general, n cycles to reach the minimum. We need a procedure which will perform most of the function minimization in the first few cycles.

Is steepest descent a conjugate gradient?

Conjugate gradient methods represent a kind of steepest descent approach “with a twist”. With steepest descent, we begin our minimization of a function f starting at x0 by traveling in the direction of the negative gradient −f′(x0) − f ′ ( x 0 ) .

BFGS optimization A simple approach to this is gradient descent — starting from some initial point, we slowly move downhill by taking iterative steps proportional to the negative gradient of the function at each point.

Adam is a replacement optimization algorithm for stochastic gradient descent for training deep learning models. Adam combines the best properties of the AdaGrad and RMSProp algorithms to provide an optimization algorithm that can handle sparse gradients on noisy problems.

What is a conjugate of a vector?

If u,v are conjugate vectors any two vectors parallel to u and v respectively are also conjugate. So you’ll often hear speak of conjugate directions rather than vectors as the scale doesn’t matter. Also, any set of mutually X-conjugate vectors for some positive definite n×n matrix X is also linearly independent.

How does the scaled conjugate gradient algorithm work?

The scaled conjugate gradient algorithm is based on conjugate directions, as in traincgp, traincgf, and traincgb, but this algorithm does not perform a line search at each iteration. See Moller ( Neural Networks, Vol. 6, 1993, pp. 525–533) for a more detailed discussion of the scaled conjugate gradient algorithm.

### What is conjugate gradient backpropagation?

Conjugate Gradient Algorithms The basic backpropagation algorithm adjusts the weights in the steepest descent direction (negative of the gradient). This is the direction in which the performance function is decreasing most rapidly.

How do you do conjugate gradient with variable feedback?

are variable feedback gains. The conjugate gradient method can be applied to an arbitrary n -by- m matrix by applying it to normal equations ATA and right-hand side vector ATb, since ATA is a symmetric positive-semidefinite matrix for any A. The result is conjugate gradient on the normal equations (CGNR).

How is the step size of a conjugate gradient determined?

In most of the conjugate gradient algorithms, the step size is adjusted at each iteration. A search is made along the conjugate gradient direction to determine the step size, which minimizes the performance function along that line.