c-LARS-GIC added

README.md

@@ -16,17 +16,17 @@ The software package __*SAEN-LARS*__ provides an implementation (and examples) o
 1. _"Sequential Adaptive Elastic Net Approach for Single-snapshot Source Localization"_
 2. _"Simultaneous Signal Subspace Rank and Model Selection with an Application to Single-snapshot Source Localization"_
 
-In first paper and accordingly in this package, _sequential adaptive elastic net (SAEN)_ approach applies the complex-valued pathwise method in the weighted elastic-net framework, named as _c-PW-WEN_, sequentially by decreasing the sparsity level (or order) from 3K to K in three stages. SAEN utilizes smartly chosen adaptive (i.e., data dependent) weights that are based on solutions obtained in the previous stage. The c-PW-WEN algorithm computes the WEN solution paths for different values of EN tuning parameter and then selects the best solution. To achieve this in a computationally efficient way, we develop a homotopy method that is a complex-valued extension of the least angle regression and shrinkage (LARS) algorithm for weighted Lasso problem, which we refer to as _c-LARS-WLasso_. It is numerically cost effective and avoids an exhaustive grid-search over candidate values of the regularization parameter.
+In __*first paper*__ and accordingly in this package, _sequential adaptive elastic net (SAEN)_ approach applies the complex-valued pathwise method in the weighted elastic-net framework, named as _c-PW-WEN_, sequentially by decreasing the sparsity level (or order) from 3K to K in three stages. SAEN utilizes smartly chosen adaptive (i.e., data dependent) weights that are based on solutions obtained in the previous stage. The c-PW-WEN algorithm computes the WEN solution paths for different values of EN tuning parameter and then selects the best solution. To achieve this in a computationally efficient way, we develop a homotopy method that is a complex-valued extension of the least angle regression and shrinkage (LARS) algorithm for weighted Lasso problem, which we refer to as _c-LARS-WLasso_. It is numerically cost effective and avoids an exhaustive grid-search over candidate values of the regularization parameter.
 
 NOTE: The c-PW-WEN algorithm contains both
 - [x] Lasso and EN as special cases for unit weights. 
 - [x] Adaptive Lasso and adaptive EN as special cases for data-dependent weights.
 
-For second paper, we develop the _c-LARS-GIC_ method that is a two-stage procedure, where firstly precise values of the regularization parameter, called knots, at which a new predictor variable enters (or leaves) the active sets are computed in the Lasso solution path (using _c-LARS-WLasso_ with unit weights). Active sets provide a nested sequence of regression models and GIC then selects the best model using _c-LARS-GIC_. The sparsity order of the chosen model serves as an estimate of the model order.
+For __*second paper*__, we develop the _c-LARS-GIC_ method that is a two-stage procedure, where firstly precise values of the regularization parameter, called knots, at which a new predictor variable enters (or leaves) the active sets are computed in the Lasso solution path (using _c-LARS-WLasso_ with unit weights). Active sets provide a nested sequence of regression models and GIC then selects the best model using _c-LARS-GIC_. The sparsity order of the chosen model serves as an estimate of the model order.
 
 ## Demo | Example
 
-The package contains a simple demo (Demo.mlx) that explains the usage of algorithms (of first paper) for direction-of-arrival (DoA) estimation with a uniform linear array (ULA) in compressed beamforming (CBF) application. Moreover, an example (Example.m) for set-up 4 in the first paper is also included in the package. Another example (Example_GIC.m) in this package is for second simulation setup (i.e., Fig. 2) of the second paper, when the number of sensors in the ULA is n = 40.
+The package contains a simple demo (Demo.mlx) that explains the usage of algorithms (of first paper) for direction-of-arrival (DoA) estimation with a uniform linear array (ULA) in compressed beamforming (CBF) application. Moreover, an example (Example.m) for setup 4 in the first paper is also included in the package. Another example (Example_GIC.m) in this package is for second simulation setup (i.e., Fig. 2) of the second paper, when the number of sensors in the ULA is n = 40.
 
 NOTE: To have repeatable results, the pseudorandom number generator settings, in terms of seed and type, are provided along with scenarios data in the package as 'seed_data.mat' and 'seed_data_gic.mat'.