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Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

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Published on: October 27, 2016

Lagrangian support vector regression via unconstrained convex minimization.

S Balasundaram¹, Deepak Gupta¹, Kapil¹

¹School of Computer and Systems Sciences, Jawaharlal Nehru University, New Delhi 110067, India.

Neural Networks : the Official Journal of the International Neural Network Society

|December 31, 2013

Summary

This summary is machine-generated.

A new method, Unconstrained Lagrangian Support Vector Regression (ULSVR), reformulates SVR as an unconstrained problem. This approach offers faster learning speeds and comparable generalization performance to conventional SVR.

Keywords:

Generalized derivative approach Smooth approximation Support vector regression Unconstrained convex minimization

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Area of Science:

Machine Learning
Optimization

Background:

Support Vector Regression (SVR) is a powerful tool for regression tasks.
Conventional SVR formulations can be computationally intensive.

Purpose of the Study:

To propose a novel, computationally efficient reformulation of the 2-norm SVR.
To introduce the Unconstrained Lagrangian SVR (ULSVR) method.

Main Methods:

Reformulated the Lagrangian dual of 2-norm SVR as an unconstrained minimization problem.
Addressed the non-smooth 'plus' function using smooth approximation and generalized derivatives.
Evaluated ULSVR on synthetic and real-world benchmark datasets.

Main Results:

ULSVR exhibits a strongly convex objective function with only m variables (number of data points).
Achieved generalization performance comparable to conventional SVR.
Demonstrated significantly faster learning speeds and training times close to least squares SVR.

Conclusions:

ULSVR offers a superior alternative to conventional SVR due to its efficiency.
Both smooth approximation and generalized derivative approaches effectively solve the ULSVR optimization problem.