The DCT Model as a Novel Regression Framework within a Lagrangian Formulation

TL;DR

This paper presents a unified Lagrangian-based regression framework that incorporates DCT, offering computational benefits and improved convergence over traditional polynomial methods.

Contribution

It introduces the DCT-based model within a variational Lagrangian framework, highlighting its effectiveness and computational advantages for regression tasks.

Findings

DCT model emerges naturally as a regression approach within the Lagrangian formalism.

DCT-based model shows improved convergence compared to polynomial methods.

The DCT model demonstrates potential as a powerful regression tool.

Abstract

This paper introduces a unified regression framework based on the Lagrange formalism, demonstrating how polynomial and logistic regression can all be formulated within a common variational (Lagrangian formalism) structure. Within this framework, the DCT-based (Discrete Cosine Transform) model naturally emerges as a novel and effective approach to traditional or unsupervised regression. The DCT is used as the constraints in the Lagrangian formalism. By leveraging the nearly orthogonal and bounded nature of the cosine basis, the DCT model offers computational advantages and improved convergence properties compared with traditional polynomial methods. The results further support the potential of the DCT-based neuron as a powerful tool for regression analysis and related learning tasks.