Chip Design of Fuzzy Neural Networks for Face Recognition in Mobile-Robots

Gin-Der Wu

Department of Electrical Engineering

National Chi Nan University

Puli, Taiwan, R.O. C.

ginderwu@ncnu.edu.tw

Zhen-Wei Zhu

Department of Electrical Engineering

National Chi Nan University

Puli, Taiwan, R.O. C.

s96323910@ncnu.edu.tw

Abstract- Fuzzy neural networks (FNN) have been successfully

applied to classification problems. In this study, we design a

FNN-based chip to achieve the face recognition of

mobile-robots. The underlying notion of the proposed FNN is

to split the generation of fuzzy rules into linear discriminant

analysis (LDA) and Gaussian mixture model (GMM). In LDA,

the weights are updated by seeking directions that are efficient

for discrimination. In GMM, the parameter learning adopts

the gradient descent method to reduce the cost function. The

major contribution of this paper is to propose the hardware

architecture of FNN chip. Furthermore, it has been fabricated

in UMC 90nm technology. Since LDA-derived fuzzy rules

increase the discriminative capability among different classes,

the proposed FNN chip can classify highly confusable

patterns.

Keywords: fuzzy neural networks, linear discriminant analysis

(LDA), Gaussian mixture model (GMM).

I. INTRODUCTION

A fuzzy system provides human-like knowledge that

consists of a group of fuzzy IF–THEN rules. FNN

integrates the capability of fuzzy reasoning in handling

uncertain information and the capability of neural networks

in learning from processes. They have been successfully

applied in areas such as pattern classification, control, and

signal processing [1]-[4]. In particular, fuzzy-rule-based

methods for pattern classification have received

considerable attention [5]-[7]. To create fuzzy IF-THEN

rules, most methods adopt back-propagation to train

parameters of fuzzy rules. Since the training of fuzzy rules

can be regarded as the clustering of input data, the method

of clustering can be also adopted for fuzzy rules generation.

In these FNNs, parameters are learned by minimizing only

the training error (or empirical risk), which does not

account for a small test error. Generalization performance

may be inadequate when the FNN is over-fitted.

In classifiers, Gaussian mapping is the conventional

means to map the input patterns into a feature space. To

consider the noise attack or malice distortion, the most

important aspect of classification is not the training error or

generalization ability. In fact, the kernel is the

discriminative capability. This idea motivates us to split the

generation of fuzzy rules into linear discriminant analysis

(LDA) and Gaussian mixture model (GMM). In LDA, the

weights are updated by seeking directions that are efficient

for discrimination. In GMM, the parameter learning adopts

the gradient descent method to adjust the shape of the

Gaussian membership function and reduce the cost function.

Based on this concept, this work adopts a maximizing

discriminability based self-organizing fuzzy network

(MDSOFN) [8]. In contrast with the other FNN, MDSOFN

has a higher discriminative capability, while preserving the

small network size of FNN. The major contribution of this

paper is to propose the hardware architecture of MDSOFN.

To implement the FNN, this paper uses

hardware/software co-design method. Calculus chain rule is

applied to update the weights of fuzzy-networks. FNN can

implement the nonlinear function to classify confusable

patterns.

Gaussian class

x1 xj xn

Within Class SW & Between Class SB

x1 xj xn

... ... ... ...

y

Layer1

Layer2

Layer3

Layer4

Layer5

w1l

w2l

w3l

t1 tm

Fig. 1 Structure of fuzzy neural network.

II. STRUCTURE OF FNN

This section discusses the optimization of fuzzy rules for

classification problems. The structure of FNN is shown in

2013 10th IEEE International Conference on Control and Automation (ICCA)Hangzhou, China, June 12-14, 2013

978-1-4673-4708-2/13/$31.00 ©2013 IEEE 619

Fig. 1. There are no rules initially in this FNN, and they are

created and adapted by structure learning and parameters

learning. There are five layers in this FNN which realizes a

fuzzy model of the following form:

1 1 2 2

1 1

Rule : IF is and is ... and is ...

Then k

i i i n ni

k Mf

i mi m

k m

x A x A x A

y e a t

(1)

where ix is input variable, iy is the output, and niA

are fuzzy sets. This fuzzy rule is separated into two parts:

GMM and LDA part. The GMM part is formed as kfe ,

which implies the firing strength. This variable is the

Gaussian membership function with two parameters, mean

and variance. LDA transformation can be regarded as a

change of input coordinates. LDA can increase the

discriminability of fuzzy.

Layer 1:The nodes in this layer only transmit input

values to the next layer directly.

(1)

if u and(1)

io f . (2)

where i = 1,2,…, n .

Layer 2: In GMM part, each node corresponds to one

linguistic label of the input variables in Layer 1. With the

Gaussian membership function, the operation performed in

this layer is (2) 2

2

( )i ij

ij

u mf

and

(2) f

ijo e . (3)

where ijm and ij are the center and the width of the

Gaussian membership function.

In LDA part, the between-class matrix BS and

within-class matrix WS are calculated as follows.

( ) ( )

1 1 1

1 1( ( ) )( ( ) )

j jN NJj j T

B j

j n nj j

s N X n X nN N

(4)

( ) ( ) ( ) ( )

1 1

1[ ( ( ) )( ( ) ) ]

jNJj j j j T

W j

j nj

s N X n X nN

(5)

Layer 3: In GMM part, the links are used to perform

precondition matching of fuzzy logic rule. Hence, we use

the following AND operation.

(3)

1

p

ij

i

f u

and (3)

io f . (6)

The output node represents the firing strength of the

corresponding fuzzy rule.

In LDA part, transform the input vector X(j) into T(j) as

follows. ( ) ( )( ) ( )j jT n W X n (7)

where ( )1 2( ) [ ]j T

NX n x x x , ( )1 2( ) [ ]j T

MT n t t t and

W is optimal to increase the discriminability.

Layer 4: In this layer, LDA and GMM are merged

together. The node is the essential node that represents a

fuzzy set of output variable. The center of each Gaussian

membership function ( 0 0i ia m ) is delivered to the next

layer for the LMOM (local mean of maximum)

defuzzification operation. (4)

1

k

Kf

i

k

u e

is the firing strength

of GMM.

(4)a = 0

11

( )k

K Mf

i mi m

mk

e a a t

=01

( )k

K Mf

mi m

mk

e a t

(8)

where mia is the corresponding parameter of variable mt .

In this equation, 0 0ia t with 0 1t implies the center of a

Gaussian membership function ( 0 0i ia m ).

Layer 5: Each node in this layer corresponds to one output

variable. The node integrates all of the actions

recommended by Layer 3 and Layer 4 as follows.

(4)

1

R

i

i

f u

(9)

(4)(5)

1 0(5) 1

(4)

1

( )R MR

i mi mii mi

R

i

i

u a tu

af

u

. (10)

where R denotes the number of input space rules.

III. HARDWARE OF FNN

To calculate mean (mij), variance (σij), and parameter

(amj), the hardware of FNN is proposed in Fig.2. Their

update rules are shown as follows.

(2)(3)0

2(4)

1

( 1)

2( ) ( ) [ ( ) ( )]

ij

M

mi md m i miij kR

k ijii

m t

a t y u mm t y t y t u

u

(11)

(2) 2(3)0

3(4)

1

( 1)

2( ) ( ) [ ( ) ( )]

ij

M

mi md m i miij kR

k ijii

t

a t y u mt y t y t u

u

(12)

(4)

(4)

1

( 1)

( ) [ ( ) ( )]

mi

d imi mR

ii

a t

ua t y t y t t

u

(13)

620

Fuzzifier Module

Defuzzier Module ijm

ij

mia

Mean RAM

Variance RAM

Parameter RAM

24

RAM_GRAM_F

24

24

Gaussian lookup table

ROM

Address generator

fe

2

2)2( )(

ij

iji muf

14

10

10

2424

24

24

12

22

Input

24

ixoutput

ky

610

Address bus

24

Learning Module

Rule count register

ijm

ij

mia

fe

2

2)2( )(

ij

iji muf

24

24

24

12

22

Control Unit

LDA

24

mu

)4(

iu

M

m mmita0

)4(

iu

M

m mmita0

Fig.2 Hardware of fuzzy neural network.

variance

xi

mean

ParameterParameter

LUT(Gaussian)

LDA

ij

ijm

a1i~amiaoi

mju

REG

REG

REG

RAM_F

RAM_G

Input pattern

Fig.3 The architecture of fuzzifier module.

REG

RAM_F

RAM_G

REG output

Fig.4 The architecture of defuzzier module.

The embedded SRAM is produced by UMC 90um

cell-base technology. This memory-based structure can

reduce the control complexity and the power consumption.

The architecture of fuzzifier module is shown in Fig. 3. The

fuzzifier stage will multiply the firing strength from the

Gaussian membership function in layer 2 and store the

firing strength into SRAM (RAM_G). This fuzzifier stage

will run i x j times where i is the number of input nodes,

and j is the number of fuzzy rules. After LDA, the linear

accumulation result will be stored into SRAM (RAM_F).

The architecture of defuzzier module is shown in Fig. 4.

When the defuzzier stage is triggered, it will catch the data

from SRAMs (RAM_G, RAM_F).Finally, the proposed

FNN chip has been successfully fabricated in UMC 90nm

1P9M CMOS technology. Fig. 5 is the die photo of FNN

chip. Table I shows its specification.

Fig. 5 Die photo of FNN chip.

Table I Chip specification

Process UMC 90nm 1P9M COMS

technology

Die Size 2.765mm × 2.765 mm

Gate count 1143539

Power Dissipation 10.3 mA

Operating Frequency 100Mhz

Power Supply 3.3v for I/O, 1v for core

IV. EXPERIMENTS

Due to the commercial or security demands, face

recognition has become one popular research topic in recent

years. To test the chip of FNN in classification problems,

the experiment tests face recognition. The flowchart of face

recognition is shown in Fig. 6.

Dimensionality reduction

face image simple set

DCT transformZig-Zag scan to 1-D vector and select

low frequency bandOutputFNN

Fig. 6 The flowchart of face recognition.

The ORL (http://people.cs.uchicago.edu/~dinoj/vis/orl/)

facial database is adopted. There are 400 facial images.

They include 40 classes and each has 10 facial images.

Each images is 92 × 112 with 256 gray levels. All pictures

are scaled to 46 × 56. The facial features (55 DCT

coefficients) are extracted and stored into embedded

SRAMs. Fig. 7 shows the learning curve. The vertical axis

represents the mean-square-error (MSE) of total patterns.

The total number of fuzzy rules is 23, and the recognition

rate is 90%.

621

Fig. 7 The learning curve of FNN.

V. CONCLUSION

This paper proposes the chip design of FNN for face

recognition in mobile-robots. The generation of fuzzy rules

can be divided into linear discriminant analysis (LDA) and

Gaussian mixture model (GMM). In LDA, the weights are

updated by seeking directions that are efficient for

discrimination. In GMM, the parameter learning adopts the

gradient descent method to reduce the cost function. Since

LDA-derived fuzzy rules increase the discriminative

capability among different classes, the proposed FNN chip

can classify highly confusable patterns. Finally, the chip has

been fabricated in UMC 90nm technology. The experiment

of face recognition verifies that its function works well.

REFERENCE

[1] C. F. Juang, and C. M. Chang, “Human Body Posture Classification by a NeuralFuzzy Network and Home Care System Application,”IEEE Trans.Syst., Mam, Cybern., A, Syst., Hum.,vol. 37, no. 6, Nov. 2007

[2] C. Garcia and M. Delakis, “Convolutional Face Finder:A Neural Architecture for Fastand Robust Face Detection,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, No. 11, Nov. 2004.

[3] R. J. Wai,and C. M. Liu,“Design of Dynamic Petri Recurrent Fuzzy NeuralNetwork and Its Application to Path-TrackingControl of Nonholonomic Mobile Robot,” IEEETran. on industrial electronics, vol. 56, no. 7, July 2009

[4] C. Quek, M. Pasquier, and B. B. Seng Lim, “POP-TRAFFIC: a novel fuzzy neural approach to road traffic analysis and prediction,”IEEE Trans. intelligent transportation systems, vol. 7, no. 2, June 2006

[5] J. S.Wang and C. S. G. Lee, “Self-adaptive neuron-fuzzy inference systems for classification applications,” IEEE Trans. Fuzzy Syst., vol. 10, no. 6,pp. 790–802, Dec. 2002.

[6] L. I.Kuncheva, “Howgood are fuzzy IF–THEN classifiers?,” IEEE Trans.Syst., Man, Cybern. B, Cybern., vol. 30, no. 4, pp. 501–509, Aug. 2000.

[7] H. Ishibuchi and T. Nakashima, “Effect of rule weights in fuzzy rulebasedclassification systems,” IEEE Trans. Fuzzy Syst., vol. 9, no. 4,pp. 506–5z15, Aug. 2001.

[8] G. D. Wuand P.H. Huang, “A Maximizing-Discriminability-Based Self-Organizing Fuzzy Network forClassification Problems,”IEEE Trans. Fuzzy syst., Vol. 18, No. 2, April 2010.

622