In contrast to the symbolic approach, neural networks seldom are designed to explain what they have learned. This is a major obstacle for its use in everyday life. With the appearance of neuro-fuzzy systems which use vague, human-like categories the situation has changed. Based on the well-known mechanisms of learning for RBF networks, a special neuro-fuzzy interface is proposed in this paper. It is especially useful in medical applications, using the notation and habits of physicians and other medically trained people. As an example, a liver disease diagnosis system is presented

Brause, Rüdiger W.

Friedrich, F.

English

Hochschulschriftenserver - Universität Frankfurt am Main

A Neuro-Fuzzy Approach as Medical DiagnosticInterfaceR. Brause, F. FriedrichJ.W.Goethe-University, Frankfurt a. M., Germanybrause@cs.uni-frankfurt.deIn contrast to the symbolic approach, neural networks seldom are de-signed to explain what they have learned. This is a major obstacle forits use in everyday life. With the appearance of neuro-fuzzy systemswhich  use  vague,  human-like  categories  the  situation  has  changed.Based on the well-known mechanisms of learning for RBF networks, aspecial neuro-fuzzy interface is proposed in this paper. It is especiallyuseful in medical applications, using the notation and habits of physi-cians and other medically trained people. As an example, a liver diseasediagnosis system is presented.1  IntroductionThe decision and diagnostic power of neural networks are needed in many tasks ofeveryday life. Successful example applications show that especially in medicine hu-man diagnosis abilities are significantly worse than those of neural diagnosis systems,see [1]. Nevertheless, the set of tools of neural networks is rarely used by physicians.Why?First, the models and language of neural networks are more mathematically for-mulated, a language that most doctors do not know how to use and are not interestedin to learn. Second, in contrast to the symbolic approach, neural networks seldom aredesigned to explain what they have learned. The possibility using the experience ofthe physician and explaining the diagnosis by the proper medical terms is crucial forthe question whether a diagnostic system is used or ignored.Now, with the appearance of fuzzy systems which use vague, human-like catego-ries [2] the situation has changed. Based on the well-known mechanisms of learningin RBF networks, a special neuro-fuzzy interface is proposed in this paper. The intui-tive and instructive interface is useful in medical applications, using the notation andhabits of physicians and other medically trained people. In Fig. 1 this concept is visu-alized.   Data parameters rules,   training data terms     physician              learning algorithmScreenmasksneuralnetFig. 1 Interactive transfer of vague knowledgeHere, the user interface must use the typical human properties and formulate the diag-nosis by the vague, inexact language of physicians.Proc.  European  Symposium  on  Artificial  Neural  Net-works ESANN 2000, Elsevier Publ., 2000, pp. 201-2062  Interface Design DecisionsThe neuro-fuzzy interface design has to meet several constraints.1.  It has to serve for a non-computer experienced public which has neither knowl-edge nor time or interest to invest in program design2.  It has to use the human attention as a major resource, i.e. it has to be understoodvery fast by medical people3.  The interface must be simple and consistent4.  The user necessary actions should be minimized, e.g. default  values  should  beused whenever possible5.  The language and the mental model of the user group should be usedThese are the most important design  principles.  When  we  examine  some  of  theseconstraints, we remark that we might cover points 1,2 and 5 just by using appropriatemedical terms, keywords and assumptions: the medical mental model. Thus will becovered by the next section.2.1  Medical terms and notationsThere are several kinds of terms which are involved in a medical description of apatient state. The chemical analysis covers¨  The exact quantitative notation, e.g. blood sugar 120 mg/dl¨  The semi-quantitative notation, e.g.semi-quantitativeresultValue  range[g/dl]Linguistic meaning0 0 - 0,1 Not existent+ 0,1 - 0,25 Slightly elevated++ 0,25 - 0,5 elevated+++ 0,5 - 2 Strongly elevated++++ > 2 Very strongly elevatedTable 1  Semi-quantitative results for urine sugar test¨  The qualitative, categorical notation, e.g. test result positive/negativeAll medical diagnosis for a variable reference an interval which is typical for the stateof “healthy” people. For a Gaussian distribution of mean m and variance s this is theinterval of [c-2s,c+2s] with 95.5 % of the population. All values distributed betweenc ± 2s and c ± 3s lie in the limit region while all values outside are pathological.2.2  Transferring the Medical Knowledge to the NetIn contrast to the precisely defined fuzzy sets, we use only the idea of fuzzy terms,called “vague terms”, and is description by membership functions. All other mathe-matical implications like computing rules are not used in this paper. As example, inFig. 2 the assignment of the vague linguistic terms of the medical variable SGOT tothe vague variable x (concentration IE/l) is shown. Formally, this can be defined asmembership function mi(x) : X ® [0,1] with the vague variable X = [0,50] and thevague set F(X) = { mi(x) }= {low, normal, slightly elevated, highly elevated }with the core intervals “low”=[0,4], “normal”=[5,18], “slightly elevated”=[20,30], “highlyelevated”=[35,50]which results in a vague set of membership functions showed in Fig. 2.m(x)      low normal  slightly elevated    highly elevated1.00.50.00 10 20 30 40 50Fig. 2 The vague set of the linguistic variable SGOTFor each term of a vague set, we have to attach a name. This name or linguistic termshould follow some restrictions. According to section 2.1, our system provides¨  Exact notation. The membership function is defined exactly for each value of avague variable.¨  Semi-quantitative notation. The multiple values of the example in Table 1 can bemapped to standard membership functions as shown in Fig. 2.¨  Quantitative, categorical notation. This can be easily mapped by using a rectan-gular membership function.For the sake of an easy, robust interface for network initialization purposes (informa-tion stream from left to right in Fig. 1)we do not assume any knowledge about appro-priate membership functions by the user which is certainly true for most of the physi-cians. Instead, we use the most simple membership function which is in coherencewith the medical expert intuition: a simple trapezoidal bell shaped function which isdirectly assigned to the Radial Basis Function of a RBF neuron. A trapezoidal shapedfunction with its final support converges faster than Gaussian  RBFs [3]. Additionally,the ramp inclination provides a simple mean of shifting from vague notation to cate-gorical notation. In conclusion, by using a trapezoidal function as standard member-ship function we can easily satisfy all the demands of the medical interface. As freeparameters the lower and upper core limits [min,max] are chosen as the medical rangelimits while the ramps are assumed standard.So far, we considered the mapping of vague terms to single radial basis functions.Now, several terms of different variables might also be coupled to a vague rule like"IF  SGOT=strongly_elevated  AND  GGT=pathological  THEN  sensitive_for_li-ver_disease". This can be modeled by combining the two one-dimensional member-ship functions to a two-dimensional radial basis function of one RBF neuron. Whenthe two terms are active, the RBF neuron will output a high activity. So, the corre-sponding RBF network is a conventional two layer network; the first layer imple-ments the rules in parallel while the second layer weights each conclusion and com-bines it to the final diagnosis.2.3  Transferring the Neural Network knowledge to the UserThe initialization of the network by the user is one of the interface functions. Theother, more important function is to provide the user with the results of the networklearning in an understandable way. Here, we encounter several problems. The firstone is the representation of the network state by the medical linguistic terms, and thesecond problem which we have to deal with is the vast number of possible rules.Network state approximation with linguistic termsSince we might use a growing neural network approach (see e.g. [4],[5]), the networkmight slightly or heavily differ from the initial configuration¨  The location and  extensions  of  the membership  functions may  have  changed;they may have shifted or expanded.¨  The number of neurons and therefore the number of possible membership func-tions may be smaller or bigger after the learning processThese two problems are hard to solve. Certainly, we might ignore all user suppliedlinguistic information and generate pure synthetic linguistic terms like "blood sugar Î[250,400]" which indicates that there is a vague term with the core region in the inter-val of [250,400] of the variable "blood sugar". But this approach is not very  userfriendly and ignores completely nearly all interface design demands listed in section2.0. Instead, we developed the following mechanisms:1.  The core region of a vague term is chosen such it covers the [c-2s,c+2s] intervalof the data. The ramps are chosen such that they fit the [c-3s,c+3s] interval.2.  If  the  core  region  has  been  broadened,  the  linguistic  term  "t"  is  changed  to"roughly t" (abbreviated “~t”) which reflects this property in everyday life.3.  For simplifying a rule we sort the terms of one variable according their order.4.  If the new membership function covers two old core regions t1 and t2, we mighttake as new term t the combination of the old ones t="t1 OR t2". Nevertheless, ifwe cover more terms than two, the linguistic approximation should simplify theterm by using a "TO" binding between the first and the last term.5.  Small shifts of terms can be reflected by the preposition "very", but we have topay attention if the term is higher or lower than the norm.6.  Negated terms are too complicated for the ordinary user. We omitted all negationsand use only positive linguistic terms.The linguistic approaches  mentioned  so  far  do  facilitate  the  task  of  mapping newterms to old ones, but do not avoid this completely. In the case where the core regions of the new term is not sufficiently covered by the old core regions si, i.e. when thelinguistic approximation quality Q=(s1+...+sn)/s is less than 50%, we have to generatea new  synthetic term  "t[min,max]"  with  t  the linguistic  variable and  min,max  thevalues of the lower and upper bounds of the core region of the vague variable.Since  this approach might not  be  acceptable  for  all  users,  the  interface  allows  to“freeze” some of the user defined terms during training.Reducing the number of rulesThe neural network might have found a very good classification configuration con-taining several hundreds of neurons. Following our concept of direct mapping  be-tween the rules and the network, this means also a vast number of rules. Therefore, animportant part of the interface consists also of simplifying the rules in order to bereadable.We took the following approach to the problem:1.  All generated rules are weighted by the learned weights of the second networklayer.  Thus,  the  most  important  rules  are  presented  first.  By  a  user-definablethreshold all rules beyond a certain importance are not presented.2.  The reference interval or “normal” term is superfluous and should not be men-tioned in a rule. Instead of presenting all terms, only the extraordinary terms areused.  Additionally,  all  rules  which  becomes  empty  by  this  elimination  aredropped.3.  Noisy training data may cause a target region to cover a region outside the possi-ble range of the vague variable. In this case, the rule is dropped.4.  When the target region is nearly identical to the possible range of the vague vari-able, the rule is always true. In this case the rule can be dropped.3  Simulation and resultsIn this section we present the results of an implementation of the interface and itsusage for the diagnosis of liver disease.3.4  The implementationThe interface design principles were implemented by the means of a standard VisualC++ development system and can be downloaded from [9]. As network type we usedhere the Dynamic Decay Adjustment (DDA) network [6],[7],[8] based on commonRBFs and the  Reduced  Coulomb  Energy  (RCE)  net  which  implements  a  growingnetwork, depending on the training data. This network uses also trapezoids and rec-tangles as Radial Basis Functions. It¨  adapts the different diameters of the bell shaped functions differently in the di-mensions by individual learning rates.¨  implements the weights of the rules in the second layer as the number of trainingsamples where this rule is valid, i.e. the share of the rule.¨  adds a new RBF neuron to the net each time the diagnostic approximation error istoo high. The new neuron RBF has as weight vector (center) the erroneous pat-tern coordinates and a width which does not include the neighbor centers.¨  shrinks a RBF width if the neighbored data belongs to another diagnostic class.Each trapezoidal RBF is represented by two rectangular RBFs: one for the core regionand one for the ramps.3.5  A diagnostic exampleAs demonstration example we took the liver disease data of BUPA Medical Research.Here, we have 345 data classified for 144 (41.74%) cases to “less sensitive for liverdisease” and for 201 (58.26%) cases to “sensitive for liver disease”. The membershipof each class should be expressed by only a few, simple rules.The following six input variables were used¨  MCV mean corpuscular erythrocytical volume, reference [76-96] fl¨  AP alkalic phosphatase [60-170] IE/l¨  SGPT glutamat-pyruvat-transaminase in serum [5-22] IE/l¨  SGOT glutamat-oxalacetat-transaminase in serum [5-18] IE/l¨  GGT gammaglutamyltranspeptidase [5-28] IE/l¨  AD Alcoholic drinks: the number of daily consumed alcohol portions. One por-tion is the equivalent of 250ml of a 5vol% alcoholic beverage, e.g. beer.The system generated several sets of rules. To give an idea for the rules, we presentthose with a weight >6 which were extracted after the adaptation process for the sin-gle class “sensitive for liver disease”. In brackets we show the weight of each rule.[27] -- GGT is normal to pathological AND AD is few to many[18] -- AP is pathologically too small AND SGPT is normal to elevated AND SGOT is normal to slightlyelevated AND GGT is normal to pathological AND AD is few to many[17] -- SGPT is ~ elevated to strongly elevated AND SGOT is slightly elevated to ~ strongly elevated ANDGGT is pathological AND AD is many to very many[10] -- SGPT is ~ elevated AND SGOT is slightly elevated AND GGT is pathological AND AD is ~ mod-erate to many [9] -- MCV is [94 - 101] AND SGPT is normal to elevated AND SGOT is slightly elevated AND GGT isnormal to pathological AND AD is few to many [9] -- SGPT is normal to ~ elevated AND SGOT is ~ slightly elevated to strongly elevated AND GGT isnormal to pathological AND AD is moderate to many [7] -- SGPT is ~ elevated to strongly elevated AND SGOT is slightly elevated to strongly elevated ANDGGT is normal to pathological AND AD is moderate to ~ many [7] -- SGPT is strongly elevated AND SGOT is ~ strongly elevated AND GGT is pathological AND AD isnothing to manyThese are the first 8 rules of 32 covering 104 of the 184 samples. The remaining sam-ples caused the generation of one rule per sample and were therefore discarded.4  DiscussionThe adaptive methods of Neural networks can solve many problems in everyday life.Nevertheless, it is seldom used due to the insufficient or often lacking user interface.In this paper we showed that for the important example of medical diagnosis a neuro-fuzzy approach allows to map the medical mental expert model of the diagnostic datato the input parameters of a neural network.Furthermore, the diagnosis based on the data adapted resulting network parame-ters can be easily converted to user understandable phrases which use the terms andhabitudes of the medical experts.For the presentation of the rules, the most important ones are selected. Even thosewere too many. Additionally, the dropped rules each one representing only a smallnumber of samples are too many but important: they represent half of the samples.Although we chose a constructive approach which generate rules only by the need torepresent the data well, future work will integrate techniques for melting several re-gions (RBF neurons) into one.References[1]  Rüdiger Brause: Revolutionieren Neuronale  Netze  unsere  Vorhersagefähigkeiten?  Zen-tralblatt für Chirurgie 124, S. 692-698 (1999)[2]  Lotfi A. Zadeh, Janusz Kacprzyk: Fuzzy logic for the management of uncertainty, JohnWiley & Sons Inc., New York, 1992[3]  Lei Xu, Adam Krzyzak, Alan Yuille: On Radial Basis Function Nets and Kernel Regres-sion: Statistical Consistency, Convergence Rates, and Receptive Field Size; Neural Net-works, Vol. 7, No.4, pp.609-628, (1994)[4]  B. Fritzke: Growing cell structures - a self-organizing network for unsupervised and su-pervised learning. Neural Networks, 7(9): 1441-1460, 1994[5]  U. Pietruschka, R. Brause: Using growing RBF nets in Rubber Industry Process Control,Neural computing & Applications, Springer Verlag, Vol 8, No. 2 (1999)[6]  Michael R. Berthold, Jay Diamond: Boosting the Performance of RBF Networks withDynamic Decay Adjustment, In G. Tesauro, D.S. Touretzky and T. K. Leen (eds): Ad-vances in Neural Information Processing System, 7, Cambridge MA, MIT Press, 1995[7]  Michael R. Berthold, Klaus-Peter Huber: From Radial to Rectangular Basis Functions: Anew  Approach  for  Rule  Learning  from  Large  Datasets,  Internal  Report,    UniversitätKarlsruhe, 1995[8]  Michael  R.  Berthold,  Klaus-Peter  Huber:  Building  Precise  Classifiers  with  AutomaticRule Extraction, Internal Report, Universität Karlsruhe, 1995[9]  http://www.cs.uni-frankfurt.de/~brause/software/Analyst1.exe

Adam Krzyzak, Alan Yuille: On Radial Basis Function Nets and Kernel Regression: Statistical Consistency, Convergence Rates, and Receptive Field Size;

Diamond: Boosting the Performance of RBF Networks with Dynamic Decay Adjustment, In

Growing cell structures - a self-organizing network for unsupervised and supervised learning.

Janusz Kacprzyk: Fuzzy logic for the management of uncertainty,

Klaus-Peter Huber: Building Precise Classifiers with Automatic Rule Extraction, Internal Report, Universität Karlsruhe,

Klaus-Peter Huber: From Radial to Rectangular Basis Functions: A new Approach for Rule Learning from Large Datasets, Internal Report, Universität Karlsruhe,

Revolutionieren Neuronale Netze unsere Vorhersagefähigkeiten? Zentralblatt für Chirurgie 124,

Using growing RBF nets

A neuro-fuzzy approach as medical diagnostic interface

A neuro-fuzzy approach as medical diagnostic interface

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