Multimodal Dictionary Learning Based On Lorentzian Norm

Dictionary learning is an important branch of machine learning.There are many research areas in different countries are focus on the use of data to learn features.And using these features extract some unknown regular patterns or discriminating abilities to achieve a certain purpose like classification.Dictionary Learning is one of these methods that can reconstruct data from a dictionary to produce new features.The generated features is not only a sparse representation of data,but also a feature selection.And refering multi-modal concept into dictionary learning,it strength the multi-modal information fusion of dictionary learning method.Learning dictionaries from part to whole.It makes us to be in more control of data.The proposed multi-modal dictionary learning method is mainly based on 112 norm,which leads to the problem of non-differentiable.This paper starts from the study of multi-modal dictionaries,adds the Lorentzian norm into it.Avoiding non-differentiable problem.In addition,we present the derivation process of the algo-rithm.And we apply method in image classification tasks.The first part of paper we introduce the development of dictionary learning,and it's significant meaning in machine learning.The research background of this paper,and the main ideas we propose.In the second part,we introduce some background knowledge related to dic-tionary learning.It includes sparse representation and multi-modal fusion.Then we follow the two types of dictionary learning,unsupervised dictionary learning and supervised dictionary learning,giving our model framework.For the third part of this paper,we join the multi-modal concept into our method.We introduce the multi-modal dictionary learning based on l12 norm,and give its algorithm framework.In the last part of this paper,we present a multi-modal dictionary learning algo-rithm based on Lorentzian norm,and give its theoretical derivation,as well as its algorithm framework.It combines the conditions of joint sparse constraints,which promotes the cooperation between multi-modal information.Further more,we take a supervised way of learning,thus the dictionary can be learned with its category.This way can produce a recognition of sparse coding for classification tasks.The experiments are carried out in the three datasets,AR dataset,IXMAS dataset and JAFFE dataset.The experiment results are given in the sixth part of the article.