# hw2 - BIOMETRICS CSE190 Fall 2006 Assignment 2 Due 1 Duda...

• Homework Help
• PresidentHackerCaribou10582
• 2

This preview shows pages 1–2. Sign up to view the full content.

BIOMETRICS CSE190 Fall 2006 Assignment 2 Due: October 31, 2006 1. Duda, Hart, Stork 3.35. Let the sample mean μ n and the sample covariance matrix C n for a set of n samples x 1 …x n (each of which is d-dimensional) be defined by = = = t n i n i n n i i n x x n C n ) )( ( 1 1 1 1 μ μ μ x We call these the “nonrecursive” formulae. (a) What is the computational complexity of calculating μ n and C n by these formulae? (b) Show that the alternative” recursive techniques based on successive addition of new samples x n+1 can be derived using the recursive relations t n n n n n n n n n n x x n C n n C n ) )( ( 1 1 1 ) ( 1 1 1 1 1 1 μ μ μ μ μ + + = + + = + + + + x (c) What is the computational complexity of finding μ n and C n by these recursive methods? (d) Describe situations where you might prefer to use the recursive method for computing μ n and C n, , and ones where you might prefer the nonrecursive method? 2. Consider a normal p(x)=N( μ , σ 2 ) and Parzen window function φ (x) = N( μ ,1). Show that the Parzen window estimate

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ∑ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = n i n i n n h x x nh x p 1 1 ) ( ϕ has the following property E[p n (x)] = N( μ , σ 2 +h n 2 ) 3. Consider the following set of two dimensional vectors from three categories: ω 1 ω 2 ω 3 X 1 X 2 X 1 X 2 X 1 X 2 10 0 5 10 2 8 0 -10 0 5 -5 2 5 -2 5 5 10 -4 (a) Plot the decision boundary resulting from the nearest neighbor rule just for categorizing ω 1 and ω 2. Find the sample mean m 1 and m 2 and on the same figure sketch the decision boundary corresponding to classifying x by assigning it to the category of the nearest sample mean. (b) Repeat part (a) for categorizing only ω 1 and ω 3. (c) Repeat part (a) for categorizing only ω 2 and ω 3. (d) Repeat part (a) for three-category classifier, classifying ω 1, ω 2 and ω 3....
View Full Document

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern