| # Extreme Learning Machine (ELM) | |
| ## Introduction to ELM | |
| The Extreme Learning Machine (ELM) is a single-hidden layer feed-forward neural network (SLFN) training algorithm proposed by Huang et al. Unlike traditional gradient-based learning algorithms (like backpropagation) used in conventional neural networks, ELM aims to achieve faster learning speed and better generalization performance. The core principle of ELM lies in its ability to analytically determine the output weights of the network, drastically reducing training time. | |
| ## Core Mechanism | |
| In an SLFN with $N$ training samples $(x_i, t_i)$, where $x_i$ is the input vector and $t_i$ is the target vector, an ELM model with $L$ hidden neurons can be mathematically expressed as: | |
| $$ | |
| \sum_{j=1}^{L} \beta_j G(w_j \cdot x_i + b_j) = o_i |
| 1. Introduction | |
| The Extreme Learning Machine (ELM) is a learning algorithm for Single Hidden Layer Feedforward Neural Networks (SLFNs) introduced by Guang-Bin Huang (2004). | |
| Unlike traditional backpropagation-based training, ELM randomly assigns the input weights and biases of the hidden layer and analytically determines the output weights using least squares (Moore–Penrose generalized inverse). | |
| Its foundation lies in speed and simplicity — training an ELM can be thousands of times faster than gradient-based methods while often achieving competitive accuracy. | |
| 2. Mathematical Formulation | |
| SLFN Structure | |
| For |
| Alright — I’ll give you a **comprehensive, academically structured explanation** of **ELM (Extreme Learning Machine) Artificial Neural Network** in the same style as I gave you the GMDH ANN breakdown, but tailored for ELM's theory, mathematics, and implementation logic. | |
| --- | |
| # **Extreme Learning Machine (ELM) – Artificial Neural Network** | |
| --- | |
| ## **1. Introduction** |
| GapGPT-5 | |
| GapGPT-5 | |
| در این گفتوگو Canvas ایجاد شده | |
| پیام خود را در اینجا بنویسید... | |
| exlain ELM ANN comprehensive | |
| Alright — I’ll give you a comprehensive, formal, research-level explanation of ELM (Extreme Learning Machine) ANN similar in style to the GMDH explanation you previously worked on, with mathematical rigor, algorithmic steps, theory, pros/cons, and possible pseudocode. | |
| Extreme Learning Machine (ELM) Artificial Neural Network | |
| 1. Introduction |
| Alright — I’ll give you a **comprehensive, formal, research-level explanation** of **ELM (Extreme Learning Machine) ANN** similar in style to the **GMDH** explanation you previously worked on, with mathematical rigor, algorithmic steps, theory, pros/cons, and possible pseudocode. | |
| --- | |
| ## **Extreme Learning Machine (ELM) Artificial Neural Network** | |
| --- | |
| ### **1. Introduction** | |
| The **Extreme Learning Machine (ELM)** is a learning algorithm for **Single Hidden Layer Feedforward Neural Networks (SLFNs)** introduced by **Guang-Bin Huang** (2004). |
| Alright — I’ll give you a **comprehensive, formal, research-level explanation** of **ELM (Extreme Learning Machine) ANN** similar in style to the **GMDH** explanation you previously worked on, with mathematical rigor, algorithmic steps, theory, pros/cons, and possible pseudocode. | |
| --- | |
| ## **Extreme Learning Machine (ELM) Artificial Neural Network** | |
| --- | |
| ### **1. Introduction** | |
| The **Extreme Learning Machine (ELM)** is a learning algorithm for **Single Hidden Layer Feedforward Neural Networks (SLFNs)** introduced by **Guang-Bin Huang** (2004). |
| Alright — I’ll give you a **comprehensive, formal, research-level explanation** of **ELM (Extreme Learning Machine) ANN** similar in style to the **GMDH** explanation you previously worked on, with mathematical rigor, algorithmic steps, theory, pros/cons, and possible pseudocode. | |
| --- | |
| ## **Extreme Learning Machine (ELM) Artificial Neural Network** | |
| --- | |
| ### **1. Introduction** | |
| The **Extreme Learning Machine (ELM)** is a learning algorithm for **Single Hidden Layer Feedforward Neural Networks (SLFNs)** introduced by **Guang-Bin Huang** (2004). |
| Alright — I’ll give you a **comprehensive, formal, research-level explanation** of **ELM (Extreme Learning Machine) ANN** similar in style to the **GMDH** explanation you previously worked on, with mathematical rigor, algorithmic steps, theory, pros/cons, and possible pseudocode. | |
| --- | |
| ## **Extreme Learning Machine (ELM) Artificial Neural Network** | |
| --- | |
| ### **1. Introduction** | |
| The **Extreme Learning Machine (ELM)** is a learning algorithm for **Single Hidden Layer Feedforward Neural Networks (SLFNs)** introduced by **Guang-Bin Huang** (2004). |
| Of course. Let's dive deep into the Group Method of Data Handling (GMDH), a fascinating and powerful type of Artificial Neural Network (ANN). | |
| ### Introduction to GMDH: The Self-Organizing Network | |
| The **Group Method of Data Handling (GMDH)** is a family of inductive algorithms used for computer-based mathematical modeling of multi-parametric datasets. It is often referred to as a **self-organizing neural network**. The core idea behind GMDH is to build a complex mathematical model (or function) that best approximates a target output, not by pre-defining a rigid network structure, but by letting the network **evolve itself** based on the data. | |
| This evolutionary approach is inspired by the principles of **natural selection**. GMDH creates generations of simple models, evaluates them against a portion of the data, and only allows the "fittest" models to survive and "breed" to create the next, more complex generation. This process continues, layer by layer, until the model's complexity stops improving its perfo |
Of course! Let's dive deep into the Group Method of Data Handling (GMDH), a fascinating and powerful type of Artificial Neural Network (ANN). It's a family of inductive algorithms that provides a unique, self-organizing approach to modeling and forecasting complex systems.
Today's Date (Jalali): 1404/07/16 | Gregorian: 2025/10/08