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20 Jun 11:43
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Software Package | SAEN-LARS DOI

  • Version: 1.0.1
  • Title: Sequential Adaptive Elastic Net Approach and Sparsity (or Model) Order Detection with an Application to Single-snapshot Source Localization
  • Short Title: Sequential Adaptive Elastic Net | Sparsity (or Model) Order Detection
  • Authors: Muhammad Naveed Tabassum and Esa Ollila
  • Maintainer: Muhammad Naveed Tabassum
  • Language: MATLAB
  • Date: 19.03.2018
  • Date (Last update): 20.06.2018

Introduction

The software package SAEN-LARS provides an implementation (and examples) of algorithms proposed in our following papers:

  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.

NOTE: The c-PW-WEN algorithm contains both

  • Lasso and EN as special cases for unit weights.
  • 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.

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 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'.

Download | Usage

The SAEN-LARS package contains following files:

README: This file.

Functions: Function files for implementation of algorithms proposed in both above mentioned papers.

  • saen.m: The main function, sequential adaptive elastic net (SAEN) approach.
  • cpwwen.m: Auxiliary function, called by the main function three times.
  • clarswlasso.m: Auxiliary function for finding knots and respective solutions at found knots.
  • clarsgic.m: Auxiliary function for detecting the true sparsity (or model) order and estimating corresponding solution.

Usage: The files for the demo and examples.

  • Demo.mlx: A live script demo.
  • Example.m: An example for DoA estimation with a ULA in CBF application.
  • seed_data.mat: Scenario data and pseudorandom number generator settings.
  • Example_GIC.m: An example for detection of sparsity (or model) order, i.e., the number of sources in CBF application.
  • seed_data_gic.mat: Scenario data and pseudorandom number generator settings for application of c-LARS-GIC.

Download the package and extract the files into a folder with “full control” permission.
Set the MATLAB home directory to the above folder. Thereafter, open either 'Demo.mlx', 'Example.m' or 'Example_GIC.m' file in MATLAB and follow the steps.

DOI

Assets 2

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01 May 07:06
@mntabassm mntabassm
v1.0.0
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Package Repository | SAEN-LARS DOI

  • Version: 1.0.0
  • Title: Sequential Adaptive Elastic Net Approach for Single-snapshot Source Localization
  • Short Title: Sequential Adaptive Elastic Net
  • Authors: Muhammad Naveed Tabassum and Esa Ollila
  • Maintainer: Muhammad Naveed Tabassum
  • Date: 19.03.2018

Introduction

The MATLAB package SAEN-LARS provides an implementation of three algorithms proposed in our paper, titled: "Sequential Adaptive Elastic Net Approach for Single-snapshot Source Localization".

In above 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 (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. 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 Lasso and EN as special cases for unity weights.
  • contains both adaptive Lasso and adaptive EN as special cases for data dependent weights.

Demo | Example

The package contains a simple demo (Demo.mlx) that explains the usage of algorithms 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 paper is also included in the package. To have repeatable results, the pseudorandom number generator settings, in terms of seed and type, are provided along with scenario data in the package as 'seed_data.mat'.

Download | Usage

The SAEN-LARS package contains following files:

README: This file.

Functions: Function files for implementation of three algorithms proposed in the paper.

  • saen.m: The main function, sequential adaptive elastic net (SAEN) approach.
  • cpwwen.m: Auxiliary function, called by the main function three times.
  • clarswlasso.m: Auxiliary function for finding knots and respective solutions at found knots.

Usage: The files for the demo and an example.

  • Demo.mlx: A live script demo.
  • Example.m: An example for DoA estimation with a ULA in CBF application.
  • seed_data.mat: Scenario data and pseudorandom number generator settings.

Download the package and extract the files into a folder with “full control” permission.
Set the MATLAB home directory to the above folder. Thereafter, open either 'Demo.mlx' or 'Example.m' file in MATLAB and follow the steps.

DOI

Assets 2