{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture1 - Adaptive Algorithms for PCA Review of Principal...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Adaptive Algorithms for PCA
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Review of Principal Component Analysis Solves the matrix equation Diagonalizes the covariance matrix of the input signal, The eigenvectors become eigenfilters and they span the frequency spectrum of the input signal. This is true only if the dimensionality of the data is very high. (From the spectral decomposition property of eigenvectors) The eigenvectors being linearly independent form the most optimal basis for any vector space. This is the motivation for using eigenvectors in data compression (KLT) Λ = V RV Λ = RV V T
Image of page 2
How to solve PCA using adaptive structures? Although there are many numerical techniques (SVD) to solve PCA, for real-time applications, we need iterative algorithms that solve PCA using one sample of data at a time. MATLAB programmers use eig function. I METHOD - Minimization of mean square reconstruction error N N M Input=x Y=W T x Wy x = ˆ Desired response is the input itself. { } 2 ˆ x x E J - =
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Minimize the cost function using gradient method with constraint The weight matrix will converge to a rotation of the eigenvector
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern