SolutionofHomework1
d d 1 e av
ae av (1 e av ) (1 e av )( a )e av
2ae av
a 4e av
(
)
dv dv 1 e av
(1 e av ) 2
(1 e av ) 2 2 (1 e av ) 2
a (1 e av ) 2 (1 e av ) 2 a
(1 e av ) 2
a
(1
) (1 2 (v)
av
EE5907R Pattern Recognition Part I
Solution #4
1. Consider a set of one-dimensional values sampled from an unknown density p(x):
cfw_1, 1.5, 1.75, 2, 2.5, 2.75, 3, 5, 6, 6.25.
Estimate the value of th
EE5904R/ME5404 Neural Networks: Homework #3
Important note: the due date is 20/03/2014. You may choose to hand in your answer
sheets during the break of the lecture, or directly to the teaching assist
EE5904R/ME5404 Neural Networks: Homework #2
Important note: the due date is 06/03/2014. You may choose to hand in your answer
sheets during the break of the lecture, or directly to the teaching assist
EE5904R/ME5404 Neural Networks: Homework #1
Important note: the due date is 06/02/2014. You may choose to hand in your answer
sheets during the break of the lecture, or directly to the teaching assist
EE5907R Pattern Recognition Part I
Solution #1
1. Suppose that in answering a question in a multiple choice test, an examinee either
knows the answer, with probability p, or he/she guesses with probab
EE5907R Pattern Recognition Part I
Assignment #3
1. We assume the following:
p(x | ) ~ N (, ) and p ( ) ~ N ( 0 , 0 ) ,
where , 0 , and 0 are known, but is unknown. You are given a set D of n independ
EE5907 PATTERN RECOGNITION PROJECT I
The MNIST Database
The MNIST database of handwritten digits has a training set of 60,000 examples, and a test
set of 10,000 examples. It is a subset of a larger se
EE5907R Pattern Recognition Part I
Solution #5
1. Suppose we have two equally likely classes and a total of 4 data points in 1-D.
Class A: x1 3, x2 1 .
Class B: x1 1, x2 2
If we use the k-nearest neig
1
PETER C. Y. CHEN, 2014
EE5904R/ME5404 Part II
Project 2: Q-Learning for World Grid Navigation
Project Description and Requirement
Dr. Peter C. Y. Chen
Associate Professor
Department of Mechanical En
Q1. Rosenbrock's Valley Problem (10 Marks)
Consider the Rosenbrock's Valley function:
f(x,y) = (1 x)2 + 100 ( 2 )2
which has a global minimum at (x,y) = (1,1) where f(x,y) = 0. Now suppose the startin
EE5904R/ME5404 Neural Networks: Homework #2
Important note: the due date is 02/03/2017. You may choose to hand in your answer
sheets during the break of the lecture, or directly to the teaching assist
Form of the basis functions are chosen in advance.
Number of hidden units = number of data points.
The data points xi are the centers of the RBF.
Structure of a RBF network (Exact Interpolation)
Numbe
Neural Networks
Q1 Rosenbrock's Valley Problem (10 Marks)
a) Steepest (Gradient) descent method
The gradient of the given function can be computed as
f ( x, y) 400 x3 400 xy 2 x 2 200( y x 2 )
T
(1)
Q-Learning for World
Grid Navigation
EE5904/ME5404
Part II Project 2
Report due on May 9th 2014
Before this
Why SVM?
Questions
SVM
Offline
Data
Learning
New Data
Discriminant
Prediction
function g()
1
PETER C. Y. CHEN, 2014
EE5904R/ME5404 Part II
Project 1: SVM for Classication of Cancerous Cells
Project Description and Requirement
Dr. Peter C. Y. Chen
Associate Professor
Department of Mechanical
EE5907R Pattern Recognition Part I
Assignment #1
1. Suppose that in answering a question in a multiple choice test, an examinee either
knows the answer, with probability p, or he/she guesses with prob
EE5907R Pattern Recognition Part I
Assignment #2
1. Consider a two-class one-dimensional problem with Gaussian distributions:
p (x | 1 ) ~ N ( 1, 1) , p ( x | 2 ) ~ N (4, 1) , and equal prior probabil
EE5907R Pattern Recognition Part I
Assignment #4
1. Consider a set of one-dimensional values sampled from an unknown density p(x):
cfw_1, 1.5, 1.75, 2, 2.5, 2.75, 3, 5, 6, 6.25.
Estimate the value of
EE5907R Pattern Recognition Part I
Assignment #5
1. Suppose we have two equally likely classes and a total of 4 data points in 1-D.
Class A: x1 = 3, x 2 = 1 .
Class B: x1 = +1, x 2 = +2
If we use the
EE5907R Pattern Recognition Part I
Solution #2
1. Consider a two-class one-dimensional problem with Gaussian distributions:
p( x | 1 ) ~ N ( 1, 1) , p( x | 2 ) ~ N (4, 1) , and equal prior probabiliti
EE5907R Pattern Recognition Part I
Solution #3
1. We assume the following:
p(x | ) ~ N (, ) and p( ) ~ N ( 0 , 0 ) ,
where , 0 , and 0 are known, but is unknown. You are given a set D of n independent
EE5904R/ME5404 Neural Networks: Homework #1
Important note: the due date is 09/02/2017. You may choose to hand in your scripts
(which can be handwritten or typeset) during the break of the lecture, or
EE5904R/ME5404 Neural Networks: Homework #1
Q1 Solution (10 Marks).
According to the signal-ow graph of the perceptron (ignoring the subscript k), the induced
local eld v can be written as
m
X
v=
xiwi
EE5904R/ME5404 Neural Networks: Homework #3
Important note: the due date is 16/03/2017. You may choose to hand in your answer
sheets during the break of the lecture, or directly to the teaching assist
Solution of Homework 1
Answer:
1)
= (vk ) = = +
The decision boundary is
+ =
which is obviously a hyperplane.
2)
= +
The decision boundary is defined as
= (vk ) =
1 evk
=
1 +
1+
= ln (
)
1
EE5907R PATTERN RECOGNITION PROJECT (Part II)
The cross-age face recognition database
For this project, please use the 2,583 images from 287 subjects submitted by all our students of
EE5907R course, a