May 2016 7CCSMPNN
1. Question one is compulsory
a. What is Pattern Recognition?
b. Draw a block diagram of the key components of a pattern recognition system.
Copyright By PowCoder代写 加微信 powcoder
c. Sketch a diagram to show a two-dimensional two-class dataset of the following cases. Use cross to indicate class 1 and circle to indicate class 2.
i. Linearly separable
ii. Nonlinearly separable
iii. Multi-modal
d. Given the Minimum Error Rate Classifier for class ωi with the discriminant function
P(ωi) 1 T−1 gi(x)= exp − (x−μi)Σi (x−μi),
d/2 (2π) |Σi| 2
determine if the following discriminant functions can be used to achieve
minimum error rate classification. Explain your answer. i. gi(x) + 5
ii. 25 × gi(x) 3
iii. sin(gi(x))
iv. −1(x−μi)TΣ−1(x−μi)− dln(2π)− 1ln(|Σi|)+ln(P(ωi))
where x denotes a sample, ωi denotes class i, P (ωi) is the prior probability,
μi is the mean vector, Σi is the covariance matrix, sin is the sinusoidal function and ln is the natural logarithm function.
SEE NEXT PAGE
May 2016 7CCSMPNN
2. a.Drawablockdiagramofamulticlassdiscriminantfunctionclassifierand explain how it works for classification.
[10 marks]
b. Describe the Sequential Multiclass Perceptron Learning Algorithm using pseudocode.
c. Consider the training dataset shown in Table 1.
Feature vector
[−2, 6] [−1, −4] [3, −1] [−3, −2] [−4, −5]
1: Training dataset.
a new feature vector x = [−2,0] with the
Determine the class of
k-nearest-neighbour classifier using Euclidean distance and the following values of k:
i. k = 1 ii. k = 3 iii. k = 5
SEE NEXT PAGE
3. a. Name three feature extraction techniques
b. Consider the dataset in Table 2.
Class Feature vector xT 1 [1,2]
2 [6,5] 2 [7,8]
Table 2: Training dataset.
i. Using Linear Discriminant Analysis (LDA), given a projection vector
wT = [1, 2], find the projection of the feature vectors. Is the dataset
in the projection space linearly separable? Explain your answer.
ii. Using Fisher’s method, determine which of the following projection weights is more effective in the context of Linear Discriminant Analysis (LDA). Explain your answer.
•wT =[−1,5] •wT =[2,−6]
SEE NEXT PAGE
[14 marks]
May 2016 7CCSMPNN
4. A diagram of 3-layer partially connected neural network is shown in Figure 1.
Input layer x1 /
Hidden layer Output layer
Figure 1: A diagram of 3-layer partially connected neural network.
a. Given that the output of the neural network in Figure 1 can be expressed as
z =fW fW x+W +W 1 kj ji j0 k0
1 and f(·) is any activation function, determine the
matrices Wji, Wkj, Wj0 and Wk0.
QUESTION 4 CONTINUES ON NEXT PAGE
SEE NEXT PAGE
May 2016 7CCSMPNN
b. A classifier is designed as y = sgn(z1) where sgn(z1) = 1 if z1 ≥ 0,
−1 ifz1<0 y = 1 represents class 1 and y = −1 represents class 2. Considering a
sample x = −6 and the activation function f(·) as a logarithmic
sigmoid function, i.e., f(n) = 1 , determine which class the
sample belongs to.
c. Consider the activation function in all the input, hidden and output units
as a linear function. The neural network is trained with the stochastic
backpropagation algorithm using the cost J = 12∥z1 − t∥2 where ∥ · ∥
denotes the l2 (or Euclidean) norm operator. Given the only training 1
sample x = 5 and its target output t = 0.8, determine the updated value of w20 at the next iteration using the learning rate η = 0.01.
[12 marks]
SEE NEXT PAGE
May 2016 7CCSMPNN
5. a. What are Linguistic Hedges in the context of fuzzy set?
b. Name three categories of Linguistic Hedges in the context of fuzzy set? Briefly describe them.
c. Consider a 2-input single-output Sugeno fuzzy inference system with the following 4 rules:
Rule 1: IF x is Small and y is Small THEN z is −x+y+1 Rule2:IFxisSmallandyisLargeTHENzis −y+3 Rule3:IFxisLargeandyisSmallTHENzis −x+3
Rule 4: IF x is Large and y is Large THEN z is x + y + 2
where the membership functions are define as μx
1 , 1 + e−x
(x) = 1 , μy
and μy Large
1. 1 + e−y+5
Given that the fuzzy “AND” operation is the “product” operation, determine the output of the Sugeno fuzzy inference system for x = 1 and y = 8.
[12 marks]
SEE NEXT PAGE
May 2016 7CCSMPNN
6. A support vector machine (SVM) classifier is employed to classify the following samples:
1 Class1:x1= 2 .
7 10 Class2:x2= 8 ,x3= 15 .
a. Identify the support vectors by inspection.
b. Design an SVM classifier to correctly classify all given samples.
[15 marks]
c. What is the margin given by the hyperplane obtained in Question 6.b? [3 marks]
FINAL PAGE
程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com