# Gradient Descent Batch Clustering for Image Classification

## DOI:

https://doi.org/10.5566/ias.2905## Keywords:

batch clustering, gradient descent, image classification, principal component analysis, stochastic process## Abstract

The batch clustering algorithm for classification application requires the initial parameters and also has a drifting phenomenon for the stochastic process. The initial parameters are critical for the clustering to con-verge to the partial optimum. The drifting phenomenon in original batch clustering still has space to be improved thus to speed up the convergence based on the initial parameters. This paper proposes an unsupervised clustering method by addressing these two issues. Firstly, the estimation method for the initial parameters has been given in preliminary with a hierarchical manner of principal component analysis (PCA). The nonlinear parameters have been estimated based on a mathematical connection between PCA and clusters membership. With initial parameters, the drifting issue is addressed by combing the gradient descent and the batch clustering on an auxiliary objective to refine the initial parameters. The efficiency of the clustering process is proved based on the relationship between two quadratic functions followed by a justification. In addition, the effectiveness of the proposed method has been validated with the statistical F measure in classification application. The validation results show that the efficiency of the proposed gradient descent batch clustering has been improved significantly with trade-off to the accuracy in comparison of the original algorithms under the mean squared error (MSE) criterion.

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Copyright (c) 2023 Jae-Sam Park

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*Image Analysis and Stereology*,

*42*(2), 133-144. https://doi.org/10.5566/ias.2905