Pattern recognition using a hybrid computer

N°8 - avriZ

1978

AnneXes de ~ ' A s s o e i a # i o n

internationals

pour le CaZau~ ana~ogiqua

PATTERN RECOGNITION USING A ~ Y B R I D C.A.P.G.

van

~

COMPUTER"

der H a s t **

SUMMARY A method i s deveZopsd fo~ h y b r i d eCmu~ation o f a ~ m s a r aequent~a~ ~ea~ning aZgor~thm. Up to 80 ~¢~gh~e ocm be eorreeted very fast almuZtaneoueZy. Computing t~mes a r e - -

mainZy dependent on speed o f p r e s e n t a t i o n o f t h e p a t t e r n s to the ana£agua computer. One t~pe of analegue eir~ui~ seemed most s u i t a b l e for i m p l e m e n t a t i o n i n speoia~ p u r p o s e hardwa~e. The method i s c o n v e n i e n t ~or i n t e r a e t i e n with the user.

INTRODUCTION

analo~te

linkage

digital

In pattern recognition it is sometimes possible to

E(~ )

elassiflcatlo~

classify in the paLtcrsspaee by linear )nyperplanes, which may be computed wit ~ ~ learning algorithm and some sequ~ntlally

m(k) =d L (k)

m(k), L(k)

from store

start cowhand

offered learning patterns. Nillson (!) shows this byuslng a

z(k)=sign(~(k).w (k))

simple Threshold l~glc Unit (TLU) or a network of TLU's. The eorrectlon

next pattern ns~ed

dual elasslfication z (z = +I, z = -I) of a TLU is realized

(last)

by fJxin~ the sign of the dotproduct of thu kth p~ttern vector

x(l~st)

w(k+1)-wIk)+L(k) cCk) X(k)

~(k) of the learning sequence and the present weight vector ~(k) (wit~{ components eel} ~d ~elghts), which deflate th~ or~ ~ntntion of the hypurplane. z (k) =

sign(~{k).z(k))

(I)

Suppose z (k) # L (k), th~ kno%~ class (L (k) = +I~ L (k) =

-I}

learning

iteration,

of ~(k). This error can be rectified by moving the hyperplane towards ( k )

I : Organization

Fig. All

fixed

patterns

w (las~)

number

of the are

hybrid

offered

is the w e i g h t

computation.

during

each

vdctor after a

of iterations.

cr~atlag a new weight vector:

~(k+1) = a(k) + n(k).e(k).(k)

Two types of scale&nat circuits were used, see fi~ure~ 2a

(2)

end 2b. I n ~ o t h eases the weight vector is stored in integrators Depending on the value of the correction increment c (k)

and corrected by integrating L(k).x (k) during a slmudt~meonsly

(c tk) • O) different correction rules exist, which are qu~raeteed

3o£1cslly computed time proportional to c (k). In figure 2a

to converge to a solution (~).

digital coeffieien~

Several TLU's c~n be used together in "piece-wlse linear" and

is multiplied according to ~ tlme-divislon principle, whleh seems

"layered" networks to s~parate two or

more classes (~). Because

units are used as multipli~rs~ in figure 2b

to he most suitable to implement in special p~rpose hardware. The

digital programs of this concept may take very large eomputlng times

elrcuits between A and B are repeated for each ten,count of the

and because it may be rather incollvenient to evaluate them, an

vectors.

ii~esti~ation w ~

started to learn the possibilities of }~brid computing

cmneerning:

x(k)

I. Minimization of computing costs.

~_(I)

x(k)

~ , ~ . , ~ _ . ~ckl , ~ , c~k~ ~ _D : ~, LC~ .l

~. Optimization of m~/machins interface. 3. Testing of a r~]i~ble hardware implementation by a simulation

L (I

z(k)

of the concept at a flexi~lo general-purpose computer.

HYBRID I-KPLEMENTAT[OM

A

Compute%ion, simultaneously controlled by parallel logic, is a typical analogue f~ature. Typical digital features are large

I _x(k)

H(1)

(a}

B

memory and high accuracy. In this case the analogue computer will execute tbe class{ flcation and a parallel correction of the total weight-

L

D/~

"-

x(k) ,,,,Ck)

~

(k)

vector. The digital e~mputer will perform the presentation of patterns sad initial conditions to the analogue one and will

c~ocK

-

-

"

.....

test the learned hypcrplancs. The colnputationa] Organization is shown in fiL~re I.

A

i

I

k~'K

(~)

B

an&logue con~ectioa *

Manuscript

#* Delf¢ The

received

University

Netherlands.

on S e p t e m b e r

18,

: l o g i c a l ccnuectinn

lgFl.

of T e c h n o l o g y ,

Fig.

2 : TWO t y p e s

of

analogue

oir~uits

(a)

and ( b ) .

¢4

AnnaZea

de

ZIAasooiation

internat4onale

pour

~¢ C~ZouZ ana~oo4que

N~2 - avri~

19?2

The inbegrators were scaled at z = 100 microseconds (unity 100

hyperplanes using 3 parallel TLU's. Because shout 90 parallel

volt),

weights were needed we reduced the features by a systematic drop-out

sO c l a s s i f l c a t l o n

and c o r r e c t i o n

have been f i n i s h e d w i t h i n

100 ~s, independent on the number of dimensions, The presentation

process leaving successively the dimension with the smallest w ~ h t

of the patterns wi33. take ~p most of the time. In spite of the

a s learning was finished. For each TLU a different n-tupple r~mKised,

relatively small accuracy, because of the fast tlme-scale of integratlo,,

With n-tupples of 2, 3 an~ 5 features an optimal identification

the required number of iterations was not enlarged compared to a

rate of 93% was reached in about 5 learning iterations.

low tlme-scale of integration. The analogue computer we used*allows p r o g r a m ~ n g of maxlmum

Computing time of the experimental program was for each iteration of 300 learning patterns (of 10 features) about 2~0 ms for presentation

60 slmu~taneous dlmens~ons of one or more weight v~cbors.

of the patterns and m a x i m ~ ~ me for classification and simultaneous

To perform larger TLUIs a partial correction of ~ may be suceesfull:

correction of the three hyperplanes.

then grasps of welgbus are corrected in turn to redt|ee the n%lmber of inte~rKtors. First trials yielded good results. Partial correction of 15% of the weights of ~ 29-dimenslonal TLU satisfied wlthouL loss of "learning speed".

DISCUSION Hybrid computing techniques can be usefull for ~attern recognition with linear sequential learning algorithms. It is qu~te simple to implement the different (!) correction' methods in an elegant wa~y. A simultaneous hybrid TLU is very fast, hut

EXAMPLE 300 veetorcardiograms (VOO's) of 5 healthy men had to t,e ida,tilled Because of an investigation into the rellabi]~hy of repeated records of a persons ~CG. Each VCG existed of 28 samples of the QRg-complex. First we identified, by using a ~ h r i d programmed T L U ~ i t h 28 weights, the VCG's from all col2eetlens of t~io mun separately. Then We tried to separate the 5 classes by 3

the numhmrc~ parallel dimensions is limited. For larger TLU's or networks of it, it man be posslhle to compute the weizhts simultaneously in groups. The ways to do this have to be studied. One advantage of this hybrid method is that it is convenient for interaction with the user. The total computing time is mainly determined By the digital part of the hybrid installation. As to the costs for the hybrid method they a~pear to be the same or less than for a purely digital method. For implementation in special purpose hardware the tlme-d/vlslon circuit seemed most suitable.

REFERENCE * The ADh/IBM 1800 hybrid computer of the Compubihg Centre of the Delft Unlversity of Technology.

(1) Nillson, N.J,, Learning Machlnee, McGraw-Hill, New ~ork, 1965.