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 the density function, p( x ) , at x = 0, 1, 3, 5, and 7,
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 2
av 2
2
(1 e )
2
(1 e )
2
Answer:
w = [-2.8581 2.4218
SolutionofHomework3
Structure of a RBF network (Exact Interpolation)
Numberofhiddenunits=numberofdatapoints.
ThedatapointsxiarethecentersoftheRBF.
Formofthebasisfunctionsarechoseninadvance.
Determining the Weights
Theequationthatdefinestheweightscomesfrom
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 assistant in the lab.
Late submission is not allowed unless i
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 assistant in the lab.
Late submission is not allowed unless i
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 assistant in the lab.
Late submission is not allowed unless i
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 independent
samples x1 , K, x n . Let n denote the sample mean.
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 probability 1 - p.
Assume that the probability of answering a
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 set available from National Institute of
Standards and Te
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 Engineering
National University of Singapore
Email: mpech
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 neighbor method for classification, what will be the decisi
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 starting point is randomly
initialized in the open interval (0
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 assistant in the lab.
Late submission is not allowed unless i
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)
Number of hidden units = number of data points.
The data poi
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)
The stop criterion for the gradient descent learning al
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()
?
Online/Offline
Why SVM?
Data Storage
K-NN
Query Time
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 Engineering
National University of Singapore
Email:mpe
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 probability 1 - p.
Assume that the probability of answering
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 probabilities. In order to
design a good classifier, you are gi
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 the density function, p( x ) , at x = 0, 1, 3, 5, and 7
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 k-nearest neighbor method for classification, what will
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 probabilities. In order to design a
good classifier, you are given
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
samples x1 , K, x n . Let n denote the sample mean.
a.
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 directly to the
teaching assistant (who is going to ma
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 + b^
i=1
Consider the following three choices of activ
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 assistant in the lab.
Late submission is not allowed unless i
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
+ = ln(
1+
)
1
1+
Let = ln(1), we have
+ = 0
Thus, th
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, and download the database at
https:/drive.google.com/fil