The analysis and feature extraction of high-dimensional data can help people solve various problems in current industry applications, and manifold learning is a type of data dimensionality reduction method developed b...
详细信息
ISBN:
(数字)9798350363609
ISBN:
(纸本)9798350363616
The analysis and feature extraction of high-dimensional data can help people solve various problems in current industry applications, and manifold learning is a type of data dimensionality reduction method developed based on the concept of topological manifolds. Locally linear embedding (LLE) algorithm, as a classic manifold learning algorithm, has attracted much attention due to its low computational complexity and strong scalability. However, the objective function of LLE algorithm may contain absolute value terms and cannot be guaranteed to be convex. Traditional derivative dependent solving methods are difficult to obtain its optimal solution, making it impossible to achieve effective feature extraction of data. In this paper, an LLE based on gannet optimization algorithm (GOA) has been proposed, and it is supposed to be used as a derivative-free optimization method to effectively solve the problems of non-differentiable of non-convex objective function, premature convergence, and easy to fall into local optimum in the process of solving the objective function of LLE.
Manifold learning is a nonlinear dimensionality reduction technique that reveals the essential features and structure of data through dimensionality reduction. This technique has enormous theoretical research and indu...
详细信息
ISBN:
(数字)9798350363609
ISBN:
(纸本)9798350363616
Manifold learning is a nonlinear dimensionality reduction technique that reveals the essential features and structure of data through dimensionality reduction. This technique has enormous theoretical research and industry application value in fields such as data visualization, denoising, and anomaly detection. Locally linear embedding (LLE) is a classic algorithm in manifold learning, which projects high-dimensional data into a low-dimensional space while maintaining the same algebraic structure. However, the optimization objective function of LLE uses L2 norm to measure linear approximation error, which can easily amplify and reduce the error. Therefore, in this paper, L1 norm is used instead of L2 norm to overcome this deficiency, but it also brings about the problem of non-smoothness in the optimization objective function. To address this issue, in this paper, a derivative-free optimization method called Neiderreit sequence initialize Ali Baba and the forty thieves (NSAFT) algorithm has been proposed, and demonstrates its effectiveness in finding the optimal solution for the objective function of LLE through numerical experiments.
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