Online ADMM based Extreme Learning Machine for Sparse Supervised Learning in Python

Sparse learning is an efficient technique for feature selection and avoiding overfitting in machine learning research areas. Considering sparse learning for real-world problems with online learning demands in neural networks, an online sparse supervised learning of extreme learning machine (ELM) algorithm is proposed based on alternative direction method of multipliers (ADMM), termed OAL1-ELM. In OAL1-ELM, an ℓ ₁ -regularization penalty is added in loss function for generating a sparse solution to enhance the generalization ability. This convex combinatorial loss function is solved by using ADMM in a distributed way. Furthermore, an improved ADMM is used to reduce computational complexity and to achieve online learning. The proposed algorithm can learn data one-by-one or batch-by-batch. The convergence analysis for the fixed point of the solution is given to show the efficiency and optimality of the proposed method. The experimental results show that the proposed method can obtain a sparse solution and have strong generalization performance in a wide range of regression tasks, multiclass classification tasks, and a real-world industrial project.