Modifying an expert system construction to pattern recognition solution

ELSEVIER

Artificial Intelligence in Medicine 8 (1996) 15-21

Modifying an expert system construction recognition solution * YrjG Auramo

a, Martti Juhola

Artificial intelligence in Medicine

to pattern

b, *

aDepartment of Computer Science, University of Turku, 20520 Turku, Finland b Department of Computer Science and Applied Mathematics, University of Kuopio, P.O. Box 1627, 70211 Kuopio, Finland Received December 1994; accepted April 1995

Abstract Medical expert systems are a successful field of applied artificial intelligence. We constructed an otoneurological expert system in our previous research, and in this study we consider its reasoning method. The reasoning process can be described as a modified nearest neighbour solution derived from pattern recognition. The expert system was tested and functions reliably. Keywords:

Medical expert Otoneurology; Vertigo

systems;

Pattern

recognition;

Nearest

neighbour

method;

1. Introduction

Expert systems are built for many purposes, particularly in medical informatics, where they are applied as a software tool of computer-aided diagnoses to support medical decision making. In our previous research [1,21, we developed an otoneu-

rological expert system called One and validated it by comparing it [3,4] to another existing otoneurological expert system called Vertigo [5,6]. In this study we describe and widen the theoretical basis of our concept on which the expert system

* This work was partially supported by the Academy of Finland. * e-mail [email protected]; Fax (+ 358-71) 162595; Tel. (+ 358-71) 162560. 0933-3657/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved SSDZ 0933-3657(95)00017-8

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One was formed. Our aim has been to transform an expert system problem of reasoning correct diagnoses into a pattern recognition problem where the diagnoses are obtained in classification. Otoneurology is a subspeciality of otology where vertigo and dizziness are diagnosed. Vertigo is described as a feeling of rotation, and dizziness as a vague nonspecific feeling of imbalance. Henceforth, for convenience we call them both vertigo, which is a common problem associated with many diseases and balance disorders of different origins. The transformation of the expert system problem into a pattern recognition problem is useful and practical, since we can then formulate the latter strictly and unambiguously. In addition, the solution of the pattern recognition problem will be clear and effectively computed.

2. Otoneurological expert system One We have programmed the expert system One with C + + programming language by applying a kind of versatile scoring system which takes into account both patient history and many clinical tests for reasoning. The system includes a user interface, query data base, answer data base, knowledge base, knowledge editor, and inference engine, which are explained elsewhere [1,2,4] in detail. We came to our specific scoring computation after having found major problems with other approaches in this application. For instance, a typical problem in probabilistic technique was that it tended to overgeneralize the commonest diseases at the cost of more infrequent diseases. It can sometimes be hard to find out uncommon cases. Rule-based methods were not very good in otoneurology, because it turned out that it was difficult to form unambiguous rules, and especially hard to try to represent the available knowledge in the form of rules. For instance, much information in our application is mapped as curves or other graphical descriptions. Thus, we developed our own idea for reasoning, which utilizes weights given for questions pertaining to diseases. Some of questions are answered by a user, but some may remain unanswered. Consequently, the system functions with incomplete information. Answers are given at different scales as in per cent or binary (logical), the types of which depend on the questions. We developed this reasoning approach by using a scoring scheme where scores are computed in real scale for different diseases. A score given to a disease corresponds to how well the patient’s symptoms and results of clinical tests match the description of the disease stored in the knowledge base. The expert system infers one or more diagnoses. The one with the highest score is seen as the most plausible disease, but possibly others inferred can be treated too. Naturally, the ultimate decision will be made by a physician, but One can help him or her, since it contains much perused knowledge and “intelligence”. One succeeded well in our tests [3,4]. At the moment, One includes 18 diseases incorporated in vertigo, like Menibre’s disease; 170 questions and a large knowledge base.

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3. Reasoning

by means of pattern recognition

Let d in (l,..,m) be a disease defined in One, and n(d) be the number of questions for disease d in the query data base. We define a logical variable Xi(d) equal to 1 if the user of the expert system enters an answer to the ith question, and equal to 0 if he does not. Value Pi(d) is set to pair (i,d) by the the knowledge base according to the answer given the ith question so that it is between minimum Li(d) and maximum Q(d) values stored in the knowledge base. Score S(d) of disease d is calculated with formula n(d)

S(d)

= xxi(d)&(d).

(1)

i=l

Hence, we see that n(d)

OsS(d)

I x&(d).

(2)

i=l

The knowledge base contains extensive descriptions of the diseases connected to vertigo. Weight Pi(d) defines the significance of the ith question to disease d. Weights Pi(d) vary, depending on how much the symptoms and other factors of the questions affect diseases. Minimum &Cd) and maximum Q(d) weights vary between different diseases, and can include either negative and positive real numbers and zero or only nonnegative real numbers. By modifying affirmative questions to their negations or vice versa, we can exclude negative weights and henceforth consider only nonnegative weights. These weights were selected to the knowledge base during 3 years by employing data from several hundred patients, comprehensive otoneurological literature and the knowledge of otoneurological specialists. The magnitudes of the minimum Li(d) and maximum Q(d) do not directly affect a final result to be computed, since it is always normalised, as will be seen later. Nevertheless, they can vary between different diseases and questions and this variation emphasises the different meaning and impact of the questions on the diseases. If a weight is zero, we cannot reason anything with that question for a given disease, but some other diseases can have nonzero weights with this question. In reasoning of One we compute also a lower l(d) and upper u(d) bound for the score s(d) with each d. These three scores are normalised: n(d) ‘Cd)

=

C i=l

s(d)

=

S(d)/

u(d)

=

n(d) {Xi(d)Pi(d)

+ (1 -Xi(d))‘i(d)}/

C i=l

Ui(d),

n(d) CXi(d)Ui(d), i=l

(3)

n(d) C i=l

n(d) {Xi(d)‘,(d)

+

(1

-Xi(d))Ui(d)}/

C i=l

U,(d)*

Scores l(d), s(d) and u(d) are all less than or equal to 1, according to (2).

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The lower bound I(d) encompasses the scores of the entered answers, and for unanswered questions, the minimum scores. The upper bound u(d) incorporates the scores of the answers entered, and for unanswered questions, the maximum scores. Bound l(d) represents the lowest and u(d) the highest possibility for the occurrence of disease d. In addition to score s(d) we can consider also the difference of I(d) and u(d), and those between u(d) or l(d) and s(d). Symptoms are defined in two categories, necessary and supportive. Disease d has its own set of such symptoms. The three scores are not computed for such diseases which are deduced to be inappropriate, including at least one necessary symptom absent. Most diseases are thus usually passed over during the reasoning process. The magnitudes of the resulting normalised scores are crucial, since the greatest normalised score corresponds to the diagnosed disease. This decision is not inevitably statistically the most probable, but rather such that it best fits the symptoms and the results of the pertinent clinical tests. If the lower and upper bounds differ greatly, more information (answers) is necessary to improve and refine reasoning. The principle of the best fit of reasoning is next formulated anew. We rewrite s(d) of (3) together with (1) in the following form

(4) where we denote the binary vector x, equal to (X,(d),...,X,,,,(d>>, real vectors & and & (correspondingly z,), the components nonnegative. The reasoning process can be written as max sd

lsdsm

and similarly

of which are

(5)

where every sd is between 0 and 1, resulting from (2) and (3). Moreover, on the basis of (2), for every d, equation (4) obeys

which implies

because the denominator of (6) is always positive, viz. there exists at least one component Xi(d)U(d)i which is greater than zero. In reality, there are several such positive components according to answered questions in the case of processing disease d. Next, we alter (7) a little and return to the reasoning process as

(8)

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in which form the minimisation is analogous to the maximisation of (5). Formula (8) is quite similar to the basic form of the nearest neighbour classification in classical pattern recognition, in which the corresponding form is the following [7]: min led - ZI.

(9)

lsdsm

In process (9) we minimise distances between class reference vectors cd and the object vector z to be classified into some of the classes. Comparing (8) to (9), the former is slightly more complicated, because its object pd depends on disease d. Furthermore, there is the binary vector xd involved in the process. The binary vector is dependent on d, too. The utilisation of & corresponds to reducing the originally applied space I@” of all possible questions in the query base to a subspace [w‘cd) because those other N - n(d) questions do not concern disease d. Actually, we do not use the whole subspace, but exploit only a bounded part of the subspace defined with the closed intervals (in W) of the questions

x ... x [ L;($),qy) c Wd)

([ Ll;i”,uy]

(10)

where, for i = l,..,n(d), Lp

=

min LJd)

lsdsm

andQm” = *~d~~4W*

(II)

The utilisation of xd and the dot product means that we do not apply the Euclidean metric of (9), but the City Block (Manhattan) metric in the sense n(d) D(IJd,&)

= C&(d)lQ(:(d) i=l

--Pi(d

(12)

In fact, subspace IWncd)can be understood to be reduced further, because of some unanswered questions, from n(d) to smaller n’(d). Minimisation (9) is computed as distances in Euclidean metric. In our process of (8), or originally (5), we compute distances in City Block metric in different subspaces. This metric expresses differences between the input and maximum values in respect of individual dimensions (questions) and sums them up. Each

Fig. 1. This simplified example illustrates finding the nearest neighbour in a reduced two-dimensional subspace with City Block metric where i, and i, are questions answered in the case of all three diseases d,, d, and d,. The minimum distance indicates d, to be the most suitable selection.

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Y Auramo, M. Juhola /Artificial Intelligence in Medicine 8 (1996) 15-21

Fig. 2. Vectors z, and ud determine the corners of a surface inside which a vector defining a score for disease d can occur in a reduced two-dimensional subspace of answered questions i, and i,.

subspace defines the interesting parameters of the corresponding disease d. Minimisation (8) can be depicted as simplified to two-dimensional space in Fig. 1, where the object (case of patient) is classified into some of the classes, according to the nearest vector. Thus, we have formulated our reasoning problem of the expert system One to a pattern recognition problem of the nearest neighbours classification. Lower and upper bounds from (3) can also be illustrated in the sense of (8) as in Fig. 2, in which the bounds restrict a surface of possible cases with the current disease. Advantages of formulating the reasoning problem in this way are that we can very clearly set the parameters, easily define the metric space and subspaces and effectively compute the whole process. The system can be unambiguously and exactly defined and well understood as a whole. The computation of the process is fast. Let us treat formulae (1) and (3). In (31 the numerators and denominators consist of multiplications and additions, the numbers of which are linearly related to n(d), number of the questions for disease d. Any other computation in the process, such as searching for the maximum, depends on m or small constants. As mentioned, the maximal n(d) is less than or equal to N. Therefore, when the number of diseases is m, the time (worst case) complexity of the whole process is O(mN), which means very fast running times. Obviously values m and N will be increased from the current values of 18 and 170.

4. Discussion We have tested our expert system One for 365 randomly selected patients [3,4] from the Equilibrium Laboratory at the University Central Hospital of Helsinki, Finland. To summarize these results, One succeeded in generating the highest score to the correct diagnosis in 78.9% of cases. It could partially solve 18.4% of them, which means that the correct diagnosis was either second best or third best fit disease when at most three suggestions were accepted. In 0.5% of cases it could not reason any disease, and in 2.2% it failed. However, these 2.7% were such that

Y. Auramo, M. Juhola /Artificial Intelligence in Medicine 8 (1996) 15-21

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the answers were rather incomplete; only responses were given to a part of the available questions. Thus, One seems to be effective and reliable. Naturally, the knowledge base will further be tuned by collecting still more cases and by refining weights and other parameters. In the present paper we have described how the reasoning process of an expert system can efficiently function by using a kind of modified nearest neighbour classification. Operating with the concept of subspaces instead of the original space with dimension N, we extract the meaningful and essential features of each disease. In a way, unanswered questions still condense the subspace, but this reduces also the amount of available information and is not of course aspired after. The process can be executed quickly in a well-defined environment of the parameters as diseases to be diagnosed and their symptoms as well as other pertinent factors.

Acknowledgements

The authors are grateful to Prof. Ilmari Pyykko, M.D., from the Department of Otorhinolaryngology, University Central Hospital of Helsinki, Finland, for his invaluable otoneurological advice and expertise, and for the test material.

References 111 Y. Auramo, M. Juhola and I. Pyykko, An otoneurological expert system for the diagnosis of dizziness and vertigo, Proc. Finnish Artificial Intelligence Conference, Espoo, Finland (1992) 80-89. [2] Y. Auramo, M. Juhola and I. Pyykkd, An expert system for the computer-aided diagnosis of dizziness and vertigo, Med. Inform. 18 (1993) 293-305. [3] Y. Auramo, M. Juhola and I. Pyykko, Examination of results of two otoneurological expert systems, Proc. Finnish Conference on Artificial Intelligence Research in Finland, Turku, Finland (19941 85-89. [4] Y. Auramo and M. Juhola, Comparison of inference results and validation of two otoneurological expert systems, Int. J. Rio-Med. Comput. (1994) accepted. [5] E. Mira, R. Schmid, P. Zanocco, A. Buizza, G. Magenes and M. Manfrin, A computer-based consultation system (expert system) for the classification and diagnosis of dizziness, in: E. Pirodda, ed., Clinical Testing of the Vestibular System, Adv. Oto-Rhino-Latyng. 42 (Karger, Basel, 1988177-80. [6] E. Mira, A. Buizza, G. Magenes, M. Manfrin and R. Schmid, Expert systems as a diagnostic aid in otoneurology, J. Oto-Rhino-Laryng 52 (1990) 96-103. [7] R. Schalkoff, Pattern Recognition: Statistical, Structural and Neural Approaches (John Wiley and Sons, Singapore, 1992).