Application Of Persistent Homology In Hand-written Digit Recognition

Persistent homology is an algebraic method for calculating topological features of space,it standardizes multi-scale organized methods using mathematics.We can detect more stable features over a wide range of spatial scales,and with respect to sampling,noise,or specific parameters,these features can be considered more likely to represent the true features of the underlying space.In recent years,the application of persistent homology has been in full swing and deepening.Hand-written character recognition is a basic but widely used and challenging field.Since the early development of computer science,it has become an important research field and a natural way for computers to interact with people.Due to the important role of topological features in hand-written recognition,the use of persistent homology tools to deal with handwritten digital recognition may be a new approach.The introductory part of the thesis discuss the procedure of handwritten digit recognition,introduces the origin and history of persistent homology,and discusses the causes of the introduction of persistent homology in hand-written digit recognition.The first chapter introduces the mathematical foundations required for the paper,including simplicial complex and persistent homology.In the second chapter,we first give an example of the calculation of homology class vectors.We introduces how to use the concept of filtration in persistent homology to analyze ten hand-written numbers,then further introduce homology class vectors to obtain feature vectors that correspond to images one by one,and perform some pre-processing during actual processing to improve the degree of differentiation of the digital image correspondence vector,and the algorithm details of extracting,truncating,and classifying the homology class vectors are given,as well as the discussion on results of persistent homology.Finally,the hierarchical clustering method is used to analyze the data clustering degree of the homology class vector.The third chapter presents the calculation results in the form of a recognition matrix and discusses the existing problems and areas for improvement in the future.This thesis mainly shows by using the concept of the filtration in the persistent homology and homology class vectors defined in the thesis,as well as using scaled conjugate gradient method,we train the data and obtain the softmax function.It has a good effect in the recognition of hand-written digits.