org.apache.spark.mllib.optimization
Compute an updated value for weights given the gradient, stepSize, iteration number and regularization parameter.
Compute an updated value for weights given the gradient, stepSize, iteration number and regularization parameter. Also returns the regularization value regParam * R(w) computed using the *updated* weights.
- Column matrix of size dx1 where d is the number of features.
- Column matrix of size dx1 where d is the number of features.
- step size across iterations
- Iteration number
- Regularization parameter
A tuple of 2 elements. The first element is a column matrix containing updated weights, and the second element is the regularization value computed using updated weights.
:: DeveloperApi :: Updater for L1 regularized problems. R(w) = ||w||_1 Uses a step-size decreasing with the square root of the number of iterations.
Instead of subgradient of the regularizer, the proximal operator for the L1 regularization is applied after the gradient step. This is known to result in better sparsity of the intermediate solution.
The corresponding proximal operator for the L1 norm is the soft-thresholding function. That is, each weight component is shrunk towards 0 by shrinkageVal.
If w > shrinkageVal, set weight component to w-shrinkageVal. If w < -shrinkageVal, set weight component to w+shrinkageVal. If -shrinkageVal < w < shrinkageVal, set weight component to 0.
Equivalently, set weight component to signum(w) * max(0.0, abs(w) - shrinkageVal)