Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Multivariate Gaussian densities are pervasive in pattern recognition and machine learning. A central operation that appears in most of these areas is to measure the dierence beten two multivariate Gaussians. Unfortunately, traditional measures based on the Kullback{ Leibler (KL) divergence and the Bhattacharyya distance do not satisfy all metric axioms necessary for many algorithms.   propose a modication for the KL divergence and the Bhattacharyya distance, for multivariate Gaussian densities, that transforms the two measures into distance metrics. Next,  show how these metric axioms impact the unfolding process of manifold learning algorithms. Finally,  illustrate the ecacy of the proposed metrics on two dierent manifold learning algorithms when used for motion clustering in video data. Our results show that, in this particular application, the new proposed metrics lead to boosts in performance (at least 7%) when compared to other divergence measures.
['Karim T. Abou-Moustafa', 'Frank P. Ferrie']
I am writing a research paper on a idea A Note on Metric Properties for Some Divergence Measures: The Gaussian Case
[{"from": "human", "value": "I am writing a research paper on a idea A Note on Metric Properties for Some Divergence Measures: The Gaussian Case"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Multivariate Gaussian densities are pervasive in pattern recognition and machine learning. A central operation that appears in most of these areas is to measure the dierence beten two multivariate Gaussians. Unfortunately, traditional measures based on the Kullback{ Leibler (KL) divergence and the Bhattacharyya distance do not satisfy all metric axioms necessary for many algorithms.   propose a modication for the KL divergence and the Bhattacharyya distance, for multivariate Gaussian densities, that transforms the two measures into distance metrics. Next,  show how these metric axioms impact the unfolding process of manifold learning algorithms. Finally,  illustrate the ecacy of the proposed metrics on two dierent manifold learning algorithms when used for motion clustering in video data. Our results show that, in this particular application, the new proposed metrics lead to boosts in performance (at least 7%) when compared to other divergence measures."}]