A semi-supervised Laplace skyhawk optimization depth nuclear extreme learning machine for classification

0, Preface

The semi-supervised Laplacian deep kernel extreme learning machine classification method optimized by Skyhawk: First, the Laplacian semi-supervised deep ELM-AE is used to extract abstract features, and then the extracted abstract features are used to train a SkyhawkAn optimized kernel extreme learning machine implements classification.Semi-supervised Laplacian deep kernel extreme learning machine is actually composed of semi-supervised Laplacian multi-layer extreme learning machine + KELM.

1. Introduction to Theory

1.1 ELMAE

Both ELMAE and ELM are three-layer network structures, but ELM-AE is an unsupervised learning algorithm, and its output is consistent with the input.

The formula for calculating the output weight of ELMAE is as follows:

1.2 Multilayer Extreme Learning Machine ML-ELM

ML-ELM uses ELM-AE for layer-by-layer training, when ML-ELM uses ELM-AE training, the numerical relationship between the output of the ith hidden layer and the output of the (i-1)th hidden layer can use the following formulameans:

1.3 Semi-Supervised Laplacian Deep ELM (Lap-ML-ELM)

The document "Laplace Multilayer Extremely Fast Learning Machine" introduces the manifold regularization framework into the Multilayer Extremely Fast Learning Machine model, and proposes the Laplacian Multilayer Extremely Fast Learning Machine (Lap-ML-ELM).The model structure of Lap-ML-ELM is the same as that of ML-ELM, but Lap-ML-ELM trains labeled samples and unlabeled samples together. The biggest difference between Lap-ML-ELM and ML-ELM is the final output weight.The calculation method is different: ML-ELM is directly obtained by minimizing the generalized regularization cost function estimated by least squares, and Lap-ML-ELM is obtained by using the manifold regularization framework.

Assuming that Lap-ML-ELM has k hidden layers, the kth hidden layer output Hk can be obtained through the above formula (2).We find the output weights by minimizing the following cost function

Where ,nk is the number of nodes in the kth hidden layer in Lap-ML-ELM.

1.4 Semi-Supervised Laplace Deep Kernel Extreme Learning Machine

The semi-supervised Laplacian deep kernel extreme learning machine first uses the semi-supervised Laplacian depth ELM (Lap-ML-ELM) to extract the input data layer by layer to obtain more effective features, which is conducive to easy differentiationThe type of confusion improves the classification accuracy; and based on these more abstract features rather than the original input sample data, the kernel function calculation is used to replace the inner product operation of the high-dimensional space, so as to realize the mapping of features to a higher-dimensional space for decision-making,It is beneficial to further improve the accuracy of classification and the generalization performance of the algorithm.The structure of the semi-supervised Laplacian deep kernel extreme learning machine is as follows:

2. Skyhawk optimizes semi-supervised Laplacian deep kernel extreme learning machine

Considering that the final classification effect of the semi-supervised Laplacian deep kernel extreme learning machine is affected by the kernel parameters, the Skyhawk optimization algorithm is used for optimization, and the fitness function is the classification accuracy.

3. Effect comparison

The general ELM classification effect is as follows:

The lap-ML-ELM classification effect is as follows:

The semi-supervised Laplacian deep kernel extreme learning machine classification effect is as follows:

It can be seen that the semi-supervised Laplacian deep kernel extreme learning machine has the highest classification accuracy.