TAILIEUCHUNG - Independent component analysis P12

ICA by Nonlinear Decorrelation and Nonlinear PCA This chapter starts by reviewing some of the early research efforts in independent component analysis (ICA), especially the technique based on nonlinear decorrelation, that was successfully used by Jutten, H´ rault, and Ans to solve the first ICA problems. e Today, this work is mainly of historical interest, because there exist several more efficient algorithms for ICA. Nonlinear decorrelation can be seen as an extension of second-order methods such as whitening and principal component analysis (PCA). These methods give components that are uncorrelated linear combinations of input variables, as explained in Chapter 6. We. | Independent Component Analysis. Aapo Hyvarinen Juha Karhunen Erkki Oja Copyright 2001 John Wiley Sons Inc. ISBNs 0-471-40540-X Hardback 0-471-22131-7 Electronic 12 ICA by Nonlinear Decorrelation and Nonlinear PCA This chapter starts by reviewing some of the early research efforts in independent component analysis ICA especially the technique based on nonlinear decorrelation that was successfully used by Jutten Herault and Ans to solve the first ICA problems. Today this work is mainly of historical interest because there exist several more efficient algorithms for ICA. Nonlinear decorrelation can be seen as an extension of second-order methods such as whitening and principal component analysis PCA . These methods give components that are uncorrelated linear combinations of input variables as explained in Chapter 6. We will show that independent components can in some cases be found as nonlinearly uncorrelated linear combinations. The nonlinear functions used in this approach introduce higher order statistics into the solution method making ICA possible. We then show how the work on nonlinear decorrelation eventually lead to the Cichocki-Unbehauen algorithm which is essentially the same as the algorithm that we derived in Chapter 9 using the natural gradient. Next the criterion of nonlinear decorrelation is extended and formalized to the theory of estimating functions and the closely related EASI algorithm is reviewed. Another approach to ICA that is related to PCA is the so-called nonlinear PCA. A nonlinear representation is sought for the input data that minimizes a least meansquare error criterion. For the linear case it was shown in Chapter 6 that principal components are obtained. It turns out that in some cases the nonlinear PCA approach gives independent components instead. We review the nonlinear PCA criterion and show its equivalence to other criteria like maximum likelihood ML . Then two typical learning rules introduced by the authors are reviewed of which

TÀI LIỆU LIÊN QUAN
31    426    56
TỪ KHÓA LIÊN QUAN
TAILIEUCHUNG - Chia sẻ tài liệu không giới hạn
Địa chỉ : 444 Hoang Hoa Tham, Hanoi, Viet Nam
Website : tailieuchung.com
Email : tailieuchung20@gmail.com
Tailieuchung.com là thư viện tài liệu trực tuyến, nơi chia sẽ trao đổi hàng triệu tài liệu như luận văn đồ án, sách, giáo trình, đề thi.
Chúng tôi không chịu trách nhiệm liên quan đến các vấn đề bản quyền nội dung tài liệu được thành viên tự nguyện đăng tải lên, nếu phát hiện thấy tài liệu xấu hoặc tài liệu có bản quyền xin hãy email cho chúng tôi.
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.