Incremental Principal Component Analysis Method

PCA (Principal Component Analysis) provides an approach which can use low-dimensional data to present the main features of complex high-dimensional data. Simply speaking, PCA finds patterns of features in high-dimensional data, and compresses information from a set of variables to several comprehensive indicators, that is, principal components, to highlight the similarities and differences in data patterns. It applies only a few principal components to describe the internal structure of the data set and reduces data's dimension. PCA has been widely used in image compression, face recognition,data analysis and other fields.According to the way of getting data, PCA methods are divided into two categories, the first one is known as batch PCA methods, which have first been proposed, and these methods focus on the eigenvalue decomposition of sample data's covariance matrix, therefore, they require all the data before computation. Another one is known as IPCA (Incremental Principal Component Analysis) methods. They do not require a one-time access to all data used to calculate the covariance matrix, but update the current principal component estimates by using each new gained sample data.With the development of internet and progress of technology, the amount of data people can get has a exponential growth, which means the batch PCA methods have to take a high computational cost to deal with a very large covariance matrix. However, IPCA methods are more applicable in this situation and therefore get attentions by researchers in recent years.The thesis is composed of four chapters. The 1st chapter is the backgrounds of this research. In 2nd chapter, we explain how PCA works and introduce its applications in computer vision. In 3rd chapter, we start with introduction of IPCA and review several existing methods of IPCA. In chapter 4, we discuss problems of error accumulation in the method mentioned in chapter 3, and propose two improved algorithm, then, give the experimental results on different data set. Summary of this thesis appears in chapter 5.