Research On Finsler Geometry Learning Algorithm

The choice of metric is one of the core issue of the machine learning, mainly formulti-manifold data dimensionality, we introduce the Finsler Metric and present the FinslerGeometry Learning Algorithm, which includes the contents:(1) We present the Finsler metric-based KNN algorithm, and verify the effectivenessof the Finsler metric by experiments.(2) To solve the problem of the multi-manifold data dimensionality reduction, wepresent the Finsler Geometri Learning Algorithm.(3) The application of Finsler Geometry Learning Algorithm in handwritten digitrecognition and face recognition experiments shows that Finsler Geometry LearningAlgorithm of data being conducive to the subsequent data anlysis and processing.The characteristics and innovations of this paper are concluded as follows:(1) Using the Finsler Metric which is more general than the Euclidean distance willbetter reflect the differences between the samples.(2) The Finsler metric is introduced into the multi-manifold data analysis will increasethe degree of difference between the manifold data, while maintaining the characteristics ofthe internal structure of single-manifold data, via dimensionality reduction, there will beconducive to the subsequent data processing dan analysis.