1

Visualizing the topology of mental disorders using self-

organizing feature maps*

Gal Kazas Michael Margaliot†

Mental disorders have a large impact on individuals, families, and communities, and are

one of the main causes worldwide of disability and distress. Correct diagnosis of mental

disorders is essential in clinical practice, pharmacological research, and successful

treatment. Unfortunately, the aetiology and pathogenesis of many mental disorders are

still unknown. Psychiatrists must thus resort to classifying disorders according to their

symptoms. This provides little information on the topology of the disorders, that is, how

one disorder relates to another and why certain disorders bunch together. Here we

propose an algorithmic approach for visualizing the topology of mental disorders using

a self organizing feature map (SOFM). A SOFM is a specific type of artificial neural

network that can be trained to produce a low-dimensional representation (called a map)

of a high-dimensional input space. This map preserves the topology of the original input

space. We trained a SOFM to produce a two-dimensional map of 27 relatively well-

known mental disorders. Each disorder is represented by an 82-dimensional input

vector describing the symptoms associated with the disorder, as described in the

Diagnostic and Statistical Manual of Mental Disorders (DSM-IV-TR). The map shows

distinct clusters of mental disorders. Each cluster contains disorders that are similar to

one another, and separate from those in other clusters. This provides a way to clearly

visualize the topology of these mental disorders. We demonstrate three more

applications of the resulting map: automatic classification of disorders based on

apparent symptoms; rigorous estimation of the relative importance of various symptoms

in the diagnostic process; and adding a dimensional component to psychiatric diagnoses.

* Research supported in part by research grants from the Israeli Ministry of Science and the Israeli

Science Foundation (ISF).

† Corresponding author: Dr. Michael Margaliot, School of Elec. Eng.-Systems, Tel Aviv University,

Israel 69978. Tel: +972 3 640 7768; Fax: +972 3 640 5027; Email: michaelm@eng.tau.ac.il

2

1. Introduction

Mental disorders have a large impact on individuals, families, and communities,

and are one of the main causes worldwide of disability and distress.1 Correct

diagnosis of mental disorders is essential in clinical practice, pharmacological

research, and successful treatment. Unfortunately, the aetiology and pathogenesis of

many mental disorders are still unknown. Psychiatrists and psychologists must thus

resort to symptom-based classification of mental disorders. Clinical interviews with

the patient (and sometimes family relatives), and observations of the patient's attitude

and behavior are used to elicit symptoms and then establish a diagnosis.

A ubiquitous assessment tool is the Diagnostic and Statistical Manual of Mental

Disorders (DSM-IV-TR)2, compiled by the American Psychiatric Association.

The DSM provides diagnostic criteria for about 300 mental disorders. McHugh3 notes

that: "Just as Roger Tory Peterson's A Field Guide to the Birds distinguishes a

prothonotory from a yellow- or blue-winged warbler by the bird's coloring, voice, and

range, the DSM distinguishes and then arranges mental disorders by their

appearance…". This type of classification provides little information on the

relationship between different mental disorders. Indeed, McHugh continues to note

that: "Because the manual fails to identify what underlies the symptomatic expression

of a condition, it cannot suggest intelligible principles relating one disorder to another

or illuminate why certain of them bunch together." Westen, Shedler, and Bradley4

state that: "The diagnostic criteria were not selected or organized in a way that allows

clinicians to form coherent mental representations of the disorders…". Sullivan and

Kendler5 note that the DSM "contains many assumptions about the classification of

psychiatric disorders." For example, alcohol and nicotine dependence are grouped

together as two specific types of substance-related disorders, separated from anxiety

and mood disorders. These types of assumptions have profound influence on both

clinical practice and research. Yet, empirical studies of their validity are scarce.

Here we suggest using the algorithmic tool of self-organizing feature

maps (SOFMs)6 to visualize the topology of different mental disorders (or, more

precisely, of the set of symptoms that defines each disorder). A SOFM is a

cooperative-competitive artificial neural network trained to produce a low-

dimensional representation (called a map) of a high-dimensional feature space. This

dimensionality reduction process preserves the topology in the high-dimensional

feature space. The map is usually two- or three-dimensional, and thus provides a way

3

to visualize the topology of the high-dimensional space. Our work was motivated by

the idea of semantic maps7 that are SOFMs trained using input sets that represent

abstract data, such as words. Semantic relationships are preserved by the

dimensionality reduction process, so that clusters of points in the low-dimensional

map indicate similarity between the corresponding abstract data points.

To avoid cluttering the results, we selected a small set of 27 relatively well-

known mental disorders listed in the DSM-IV-TR, and trained a SOFM to produce the

corresponding two-dimensional map. Each disorder was represented as a point in

an 82-dimensional input space, corresponding to the symptoms that are/are not

associated with this disorder. The resulting map provides a way to visualize the

relationships between various disorders. Clear clusters of disorders are formed. Each

cluster represents disorders that are similar to one another, and are different from the

disorders in other clusters. This provides a rigorous and algorithmic approach for

studying the topological structure of mental disorders.

We believe that the semantic map may help to address several important

questions in the nosology of mental disorders. To demonstrate this, we describe three

more potential applications of the map. The first is classification of disorders (that

were not necessarily presented during the SOFM training process) based on apparent

symptoms according to their proximity to other disorders on the map. The second is

estimating the relative importance and contribution of a specific symptom in the

diagnostic process. The third is adding a quantitative measure to the diagnosis.

A different yet related field of research is modeling mental disorders using

artificial neural network models. Typically, this is based on building a neural network

model representing a cognitive or neural functioning in a healthy or normal subject,

and then artificially "lesioning" the model or, alternatively, feeding the model with

imbalanced input signals. The goal here is to study various disorders from a

computational point of view. For more details, see the review papers by Levine8 and

Grossberg9, and the volume edited by Reggia, Ruppin, and Berndt.10 Solan and

Ruppin used a SOFM to model confusion in human perception of similar stimuli.11

The remainder of this paper is organized as follows. Section 2 describes the

preliminary step of representing the diagnostic criteria in a form suitable for

algorithmic manipulation. Section 3 reviews the SOFM. Section 4 analyzes the

resulting map. Section 5 describes three more potential applications of the semantic

4

map. Section 6 contains a discussion of the results and some suggestions for further

research.

2. Knowledge representation

Each disorder listed in the DSM-IV-TR is associated with a set of diagnostic

criteria. This set is divided into two subsets: inclusion criteria and exclusion criteria.

The first [second] subset includes symptoms that must [not] be present in order to

qualify for a diagnosis. For example, inclusion criteria for a major depressive episode

include: "depressed mood most of the day nearly every day", and "markedly

diminished interest or pleasure in all, or almost all activities, most of the day nearly

every day...." Exclusion criteria for this disorder include "the symptoms are not due

to the direct physiological effects of a substance (e.g. a drug of abuse, a medication)

or a general medical condition (e.g. hypothyroidism)."‡

To avoid cluttering the results and to make this paper more accessible to people

who are not necessarily mental health professionals, we chose to focus on a small set

of relatively well-known mental disorders. Specifically, we selected 27 disorders

listed in the DSM-IV-TR: (1) Mental retardation; (2) Autistic disorder; (3) Asperger's

disorder; (4) ADHD (combined); (5) Anorexia; (6) Bulimia; (7) Schizophrenia;

(8) Dementia of the Alzheimer's type; (9) Delirium (due to a general medical

condition); (10) Primary insomnia; (11) Primary hypersomnia; (12) Narcolepsy;

(13) Sleepwalking; (14) Alcohol intoxication; (15) Alcohol abuse; (16) Alcohol

withdrawal delirium; (17) Feeding disorder of infancy or early childhood;

(18) Amphetamine induced psychotic disorder; (19) Amphetamine intoxication;

(20) Amphetamine abuse; (21) Amphetamine induced sleep disorder;

(22) Amphetamine induced depressive disorder; (23) Psychotic disorder; (24) Major

depressive disorder; (25) Schizoaffective depressive disorder; (26) Reading disorder;

and (27) Mathematics disorder.

We extracted from the descriptions of the 27 disorders in the DSM-IV-TR a

total of 82 different diagnostic criteria. We represented the criteria for disorder i ,

{1,2,..., 27}i∈ , as a feature vector 82{ 1,0,1}ix ∈ − , where each inclusion criteria is

represented by 1+ , each exclusion criteria by 1− , and irrelevant criteria (i.e. those

‡Hypothyroidism is a disease state caused by insufficient production of thyroid hormone by the thyroid

gland. One possible symptom is depression.

5

that do not appear in the criteria for this disorder at all) by 0 . For example, in our

representation, entry 72 in each feature vector corresponds to "depressed mood most

of the day nearly every day", entry 76 to "drug abuse", and entry 5 to "comma or

stupor". Since inclusion [exclusion] criteria for Major depressive episode include

"depressed mood most of the day nearly every day" ["drug abuse"], the corresponding

feature vector, 23x , satisfies 23(72) 1x = and 23(76) 1x = − . Since "comma or stupor"

is not one of the criteria associated with Major depressive episode, 23(5) 0x = . In this

way, we coded each of the 27 disorders into an 82-dimensional ternary vector.

Roughly speaking, we would like to produce a figure depicting the 27 feature

vectors 1 27,...,x x in order to visualize how they are related to each other. Such a

figure can also be used to classify disorders based on their proximity to the 27 feature

vectors. However, since each of these vectors is of dimension 82, we must first reduce

the dimension of each feature vector to 2 (or 3) in order to plot such a figure. This

dimensionality reduction process should maintain as much as possible of the

topological relations between the original 82-dimensional vectors. We trained

an SOFM to yield such a map in 2R .

3. The SOFM

A SOFM, pioneered by Teuvo Kohonen,12 is a type of artificial neural network

that can be trained to produce a discretized low-dimensional representation of the

input space of the training samples. A SOFM utilizes the idea of a neighborhood

function to preserve the topological properties of the input space. SOFMs are a

flexible tool for visualizing and clustering high-dimensional data based on the low-

dimensional representation.13

3.1 SOFM structure

Our SOFM consists of 225 artificial neurons organized in a planar 15 15× grid.

Neuron i , {1,2,..., 255}i∈ , has a location vector 2ir R∈ describing its position (row

and column) in the planar grid. For example, the neuron on the lower left [upper right]

corner of the grid has (1,1)ir = [ (15,15)ir = ]. The distance between two neurons i

and j is defined as: || ||i jr r− , where || ||⋅ denotes the Euclidean norm. For example,

the distance between the neuron on the lower left corner of the grid and that on the

6

upper right corner is 2 2(1,1) (15,15) ( 14) ( 14) 14 2.− = − + − = We say that two

neurons are close [far] if the distance between them is small [large].

Each neuron also has a weight vector. We use iw to denote the weight vector of

neuron i . The dimension of the weight vectors is equal to that of the feature vectors,

so in our case 82iw R∈ for each {1,2,..., 255}i∈ . The weight vectors (or simply

weights) are adapted during a learning process. The learning procedure we

implemented is rather standard and is described in Appendix A. All the simulations

were performed using the MATLAB software. We refer to the SOFM after training is

completed as the trained SOFM

4. The resulting map

We presented the 27 symptom vectors to the trained SOFM and found the

winning neuron for each vector. For example, neuron 67 is the winning neuron for

Mental retardation. The weight vector 67w (which is an 82-dimensional vector)

cannot be easily visualized. The location of neuron 67 in the planar 15 15× grid

is 67 (7,5)r = . Thus, we associate location (7,5) in the grid with Mental retardation.

When this is done for the winning neuron for each of the 27 disorders, we obtain the

map depicted in Fig. 1.

Fig. 1: SOFM map after training. Only the winning neurons for

the 27 disorders are shown.

16

Feeding disorder of infancy

or early childhood

2 4 6 8 10 12 14 0

2

4

6

8

10

12

14

16

Mental retardation

Autistic disorder

Asperger's disorder

ADHD (combined)

Anorexia

Bulimia Schizophrenia

Dementia of the Alzheimer's type

Delirium

Primary insomnia

Primary hypersomnia

Narcolepsy Sleepwalking

Alcohol

intoxication

Alcohol abuse

Amphetamine induced

psychotic disorder

Amphetamine

intoxication

Amphetamine abuse

Amphetamine induced sleep disorder

Amphetamine induced depressive disorder

Psychotic disorder

Major depressive disorder

Schizoaffective depressive disorder

Reading disorder

Mathematics disorder

Alcohol withdrawal delirium

7

Here the location of each winning neuron is plotted on the 15 15× grid and

labeled with the name of the corresponding disorder.

The map allows us to visualize the topological relationships between the

disorders. Distinct clusters of related disorders can be observed. To demonstrate this,

Fig. 2 depicts the map with the different clusters manually delineated using curves.

The lower right part of Fig. 2 shows disorders belonging to the DSM category

"disorders usually first diagnosed in childhood, or adolescence." These include:

Mental retardation; Autistic disorder; Asperger's disorder; ADHD (combined);

Feeding disorder of infancy or early childhood; Reading disorder; and Mathematics

disorder. Within this cluster we see two separate sub-clusters: learning disorders

(including Reading disorder and Mathematics disorder), and pervasive developmental

disorders (Asperger's disorder and Autistic disorder), with the distinct ADHD and

Mental retardation nearby.

In the top right corner, we see a cluster containing eating disorders including

Anorexia, Bulimia, and Feeding disorder of infancy or early childhood. It is

interesting to note that the latter is located at the lower part of this cluster close to the

other childhood disorders.

At the bottom left corner, we see a cluster of sleep disorders including Primary

insomnia; Primary hypersomnia; Narcolepsy and Sleepwalking.

A cluster of substance-related disorders (including Alcohol intoxication;

Alcohol abuse; Alcohol withdrawal delirium; Amphetamine induced psychotic

disorder; Amphetamine intoxication; Amphetamine abuse; Amphetamine induced

sleep disorder; Amphetamine induced depressive disorder) appears at the top left

corner. Note that this includes two distinct pairings: Alcohol abuse and Amphetamine

abuse are close to each other, as are Alcohol intoxication and Amphetamine

intoxication.

At the top of the central portion of Fig. 2, we see the Major depressive disorder;

to its left the Amphetamine induced depressive disorder connects it to the cluster of

substance-related disorders. To its right lies the Schizoaffective depressive disorder

that connects it to two other psychotic disorders: Schizophrenia and Psychotic

disorder. Finally in the center we find a cluster of cognitive disorders including

Dementia of the Alzheimer's type, Delirium, with Alcohol withdrawal delirium

relating them to the cluster of Substance related disorders.

8

Fig. 2: SOFM map after training. Only the winning neurons for the 27

disorders are shown. Clusters are delineated using curves.

Note that all of this topological information was in no way part of the input

presented to the SOFM during training. Rather, it emerged due to the topology-

preserving property of the map.

Since the map provides a two-dimensional representation of a high-dimensional

topological space, some of the original topological information must be distorted

leading to some results that may be different than expected. For example, we may

expect Amphetamine induced sleep disorder to be located midway between the cluster

of substance-related disorders and that of sleep disorders, but this is not the case.

Summarizing, the two-dimensional map depicts clear clusters and inter-cluster

relations that seem to agree well with various categories defined in the DSM-IV-TR.

This provides a graphic description of the topological relations between the disorders

(or more precisely, the symptom vector corresponding to each disorder).

5. Applications of the map

In this section, we describe three more potential applications of the trained map:

automatic classification of mental disorders; estimating the relative importance of a

specific symptom to correct diagnosis; and adding a quantitative aspect to the

16

Feeding disorder of infancy

or early childhood

2 4 6 8 10 12 14 0

2

4

6

8

10

12

14

16

Mental retardation

Autistic disorder

Asperger's disorder

ADHD (combined)

Anorexia

Bulimia Schizophrenia

Dementia of the Alzheimer's type

Delirium

Primary insomnia

Primary hypersomnia

Narcolepsy Sleepwalking

Alcohol intoxication

Alcohol abuse

Amphetamine induced

psychotic disorder

Amphetamine

intoxication

Amphetamine abuse

Amphetamine induced sleep disorder

Amphetamine induced depressive disorder

Psychotic disorder

Major depressive disorder

Schizoaffective depressive disorder

Reading disorder

Mathematics disorder

Alcohol withdrawal delirium

9

diagnostic process. These applications are directly related to important questions in

the nosology of mental disorders and received considerable attention in the literature.

5.1 Automatic classification of mental disorders

Psychiatric diagnoses are derived according to clinical interviews and human

expert opinion rather than biological findings. Recently, this symptom-based

classification approach is attracting considerable criticism. It may take decades of

professional training to develop the required diagnosis expertise. Diagnosis is further

complicated by diagnostic comorbidity (i.e. several disorders occurring together) that

is prevalent in psychiatry.14

Empirical studies of the diagnostic stability of psychiatric disorders suggest a

worrisome proportion of inaccurate diagnoses. Baca-Garcia et al.15 analyzed data on

patients that were diagnosed several times and found that the temporal consistency of

mental disorders diagnosis was poor. Shear et al.16 compared the diagnoses in clinical

charts to those obtained using the Structured Clinical Interview for DSM-IV (SCID)

and found that clinical and SCID diagnoses had poor agreement.

Designing an automatic tool that can assist in the diagnosis of mental disorders

is a desirable goal. One example in this direction is the Mood Assessment

Program (MAP).17 The MAP is a computerized assessment program designed to

assist general physicians with the diagnosis and management of mood disorders.

The MAP uses decision rules based on clinical expertise to analyze information

provided by the patient, and then generates a report that includes a possible diagnosis

and treatment suggestions. Other examples of automatic classification tools include an

algorithm for identification of schizophrenia based on the lexical and syntactical

features of patients' written text,18 and an algorithm for distinguishing between

Alzheimer's disease, mild cognitive impairment, and normal aging based on magnetic

resonance images of the hippocampus.19

The trained SOFM may also be used for assisting in the classification of mental

disorders. The basic idea is to question the patient for a set of symptoms, represent

these as an input vector, present it to the trained SOFM, and plot the location of the

winning neuron on the map. The position of the wining neuron with respect to other

disorders, already marked on the map, provides important information that can assist

in the diagnostic process.

To demonstrate this, we coded the description of the disorder vascular dementia

with depressive mood in the DSM-IV-TR into an 82-dimensional input

10

vector 28 82{ 1,0,1} .x ∈ − Note that this vector was not presented during the training

process of the SOFM. Fig. 3 depicts the location of the winning neuron for this input

vector. It may be seen that the winning neuron is close to the winning neuron for

Dementia of Alzheimer's type, and is not far from the winning neurons for the

depression related disorders. This seems reasonable as vascular dementia is in fact

the second most common form of dementia after Alzheimer's disease. This simple

experiment suggests that the map may indeed provide relevant information for the

diagnostic process.

Fig. 3: SOFM response for the symptom vector of vascular dementia

with depressive mood.

5.2 Estimating the importance and relevance of a symptom for correct diagnosis

Many mental disorders are associated with a functional impairment (or

disability). This refers to decrements in performing daily-life tasks due to the disorder.

Reaching a diagnosis (and determining its level of severity) using the DSM-IV-TR

depends on functional disabilities. For example, severe disability in Major depressive

disorder is defined as "clear-cut, observable disability (e.g., inability to work or care

for children)."

16

Feeding disorder of infancy

or early childhood

2 4 6 8 10 12 14 0

2

4

6

8

10

12

14

16

Mental retardation

Autistic disorder

Asperger's disorder

ADHD (combined)

Anorexia

Bulimia Schizophrenia

Dementia of the Alzheimer's type

Delirium

Primary insomnia

Primary hypersomnia

Narcolepsy Sleepwalking

Alcohol intoxication

Alcohol abuse

Amphetamine induced

psychotic disorder

Amphetamine

intoxication

Amphetamine abuse

Amphetamine induced sleep disorder

Amphetamine induced depressive disorder

Psychotic disorder

Major depressive disorder

Schizoaffective depressive disorder

Reading disorder

Mathematics disorder

Alcohol withdrawal delirium

Vascular dementia with depressed mood

11

There is a considerable on-going debate about whether functional impairment

on its own is a valid diagnostic criterion for a mental disorder. Ustun and Kennedy20

suggest that "no functioning or disability should appear as part of the threshold of the

diagnosis" of any disorder. Reasons for this include: (1) the definition of disability is

rather "fuzzy", it depends on the interaction between a person and the environment,

and varies between different societies and cultures; (2) many disabilities may be due

to normal variations in traits such as intelligence and shyness, and it is not the

disability itself but how it is caused that makes it pathological.21

The SOFM approach provides an algorithmic testbed for evaluating the role of a

specific symptom (or a specific set of symptoms) in determining the topology of the

disorders. This can be done by eliminating the specific symptom from all the feature

vectors, training a SOFM using the modified vectors, and comparing the resulting

map with the original one. By analyzing the topological relationships in the original

and modified maps, it is possible to gain information on the importance of the specific

symptom. If the symptom plays a minor or redundant role, the overall topology of the

disorders should not change much, whereas deleting a symptom that is important

should lead to a severely distorted map. Furthermore, studying which specific clusters

of disorders were affected may shed light on the symptom's capability of

discriminating between similar disorders.

To demonstrate this, we eliminated the 10 features related to functional

impairment from all our 82-dimensional symptom vectors. Theses features are:

occupational impairment, self care impairment, use of community resources

impairment, health impairment, home living impairment, social impairment, safety

impairment, leisure impairment, academic impairment, and self direction impairment.

We trained a new SOFM, using precisely the same training procedure, but with the set

of 72-dimentional vectors. The resulting map is depicted in Fig. 4.

Note that when comparing two maps, the measure of distortion is not the

absolute location of the disorders on the map, but rather the forms of clusters that

appear on the map and their relations.

It may be seen that all of the clusters that appeared previously appear on the

new map as well. However, the topological locations of Alcohol abuse, Amphetamine

abuse, Dementia of the Alzheimer's type, and Feeding disorder of infancy or early

childhood have changed. Amphetamine abuse and Alcohol abuse may now be found

in the bottom right corner of the map. This pair now shares a single neuron that is

12

isolated from the other disorders and, surprisingly, is as far as possible from the

cluster of substance-related disorders.

Fig. 4: Map of a SOFM trained without 10 functional impairment features.

Disorders that are no longer placed in the original clusters are marked

in bold.

To explain this, we examined the symptom vectors of the substance-related

disorders, and found that in the DSM-IV-TR there is no generic unifying symptom

such as, say, alcohol- or amphetamine-related. The reason for this is the implicit

assumption that the clinician performing the diagnosis is aware of this information

beforehand. In other words, the fact that a disorder is related to, say, alcohol appears

in the title of the disorder, but not as a specific symptom. The SOFM, that only uses

the symptom vectors as input, cannot recognize the relationship between such

disorders. The reason that these disorders were previously clustered together

successfully is that their impairment symptoms share a common pattern (see Table 1).

Yet, once these impairment symptoms are deleted, the SOFM fails to identify the

topological relationship between these disorders.

The other changes in the map can be explained in a similar manner. For

example, Feeding disorder of infancy or early childhood now appears in the upper

right corner, among the other disorders diagnosed in childhood. It no longer bridges

16 2 4 6 8 10 12 14 0

2

4

6

8

10

12

14

16 Feeding disorder of infancy

or early childhood

Mental retardation

Autistic disorder

Asperger's disorder

ADHD (combined)

Anorexia Bulimia

Schizophrenia Dementia of the Alzheimer's type

Delirium

Primary insomnia

Primary hypersomnia

Narcolepsy

Sleepwalking

Amphetamine induced

psychotic disorder

Amphetamine

intoxication

Amphetamine induced depressive disorder

Psychotic disorder

Major depressive disorder

Reading disorder

Mathematics disorder

Amphetamine induced sleep disorder

Schizoaffective Depressive

disorder

Alcohol

intoxication

Alcohol withdrawal

delirium

Amphetamine abuse

Alcohol

abuse

13

the gap between the cluster of childhood disorders and the two tightly paired eating

disorders. An examination of the feature vectors shows that indeed Feeding disorder

of infancy or early childhood and Anorexia and Bulimia share only one feature other

than their pattern of functional impairments.

It is interesting to note that although we eliminated a substantial share of the

data describing each disorder (10 features out of 82), the topological map was not

substantially distorted. Experiments with deleting other features demonstrate a major

distortion in the resulting map. This may suggest that the functional impairment

criteria do not play a critical role in establishing the topological relationships between

the disorders.

14

Self

direction

imp.

Academic

imp.

Leisure

imp.

Health

imp.

Safety

imp.

Social

imp.

Use of

community

resources

imp.

Home

living

imp.

Self

care

imp.

Occupa-

tional

Imp.

1 1 1 1 1 1 1 1 1 1 Mental retardation

0 1 0 0 0 1 0 0 1 1 Autistic disorder

0 0 0 0 0 1 0 0 0 1 Asperger's disorder

0 1 0 0 0 1 0 0 0 1 ADHD (combined)

0 0 0 1 0 0 0 0 0 0 Anorexia

0 0 0 1 0 0 0 0 0 0 Bulimia

0 1 0 1 1 0 0 1 1 1 Dementia of the Alzheimer's type

0 1 0 1 1 0 0 1 1 1 Delirium

0 1 0 0 1 1 0 0 0 1 Primary insomnia

0 1 0 0 1 1 0 0 0 1 Primary hypersomnia

0 1 0 0 1 1 0 0 0 1 Narcolepsy

0 1 0 0 1 1 0 0 0 1 Sleepwalking

0 1 0 1 1 1 0 1 1 1 Alcohol intoxication

0 1 0 1 1 1 0 1 1 1 Alcohol abuse

0 0 0 1 0 0 0 0 0 0

Feeding disorder of infancy or early childhood

0 1 0 1 1 1 0 1 1 1

Amphetamine-induced psychotic disorder

0 1 0 1 1 1 0 1 1 1 Amphetamine intoxication

0 1 0 1 1 1 0 1 1 1 Amphetamine abuse

0 1 0 0 0 0 0 0 0 0 Reading disorder

0 1 0 0 0 0 0 0 0 0 Mathematics disorder

0 1 0 1 1 1 0 1 1 1 Alcohol withdrawal delirium

Table 1: Functional impairment symptoms for several disorders (imp. is

shorthand for impairment).

5.3 Dimensional diagnosis

The DSM-IV-TR is a categorical diagnosis tool. The net result of the diagnostic

process is a dichotomous classification, namely, the patient either suffers from a

specific disorder or does not. This binary choice implies the existence of an implicit

diagnostic threshold, and consequently small changes in diagnostic criteria may lead

15

to substantially different diagnoses. As noted by Helzer et al.,22 identified cases in the

general population tend to aggregate near the diagnostic threshold. In clinical

applications, this may translate into treating patients with minimal need on the one

hand, and denying treatment from patients who clearly need it on the other hand. A

possible remedy is adding a dimensional component to official taxonomies such as

the DSM-IV-TR, namely, a diagnosis-specific quantitative score.23

The SOFM map can also be used to provide a dimensional and easy to visualize

component to the diagnosis. Consider, for example, a patient diagnosed as suffering

from, say, Schizophrenia. The vector representing this patient's symptoms may be

presented to the trained map. Let i denote the number of the winning neuron for this

input vector, and let j denote the number of the neuron on the map that is the

winning neuron for Schizophrenia. One may view jw as a "prototype" of (the

symptoms associated with) Schizophrenia. The distances || ||i jw w− or || ||i jr r−

then provide a quantitative measure for how far the patient is from this prototype. The

advantage of the second measure of distance is that it allows easy visualization by

plotting the locations of neurons ,i j on the two-dimensional grid.

To demonstrate this, we introduced three synthetic input vectors

denoted ,Ax ,Bx and Cx that are all modifications of the symptom vector

corresponding to Schizophrenia 8x . Ax is closest to 8x . The only difference is

that 8(71) 0x = whereas (71) 1Ax = . In our representation, feature 71 corresponds to

the symptom "recurrent thoughts of death, recurrent suicidal ideation, attempt or

plan". In other words, Ax corresponds to an (imaginary) patient whose symptoms are

identical to the symptoms characterizing Schizophrenia except for the addition of the

symptom "recurrent thoughts of death, recurrent suicidal ideation, attempt or plan".

The vector Bx is identical to Ax except for modifying entries 2 and 3, corresponding

to "psychomotor disturbance" and "anxiety", respectively, from 0 to 1, and changing

entries 25 and 24, corresponding to "grossly disorganized or catatonic behaviour" and

"disorganized speech", respectively, from 1 to 1− . Cx is identical to Bx except for

modifying entries 23, 26, 27, 28, and 33, corresponding to "hallucinations", "affective

flattening", "alogia", "avolition", and "disturbance in executive functioning",

respectively, from 1 to 0.

16

Fig. 5: Response of the trained SOFM response to the three input

vectors ,Ax ,Bx and Cx .

Fig. 5 depicts the response of the trained map when presented with Ax , Bx ,

and Cx as input vectors. The winning neurons are all located in the upper part of the

map. The winning neuron for Schizophrenia is neuron 252 located at 252 (12,15)r = .

The winning neuron for Ax is neuron 252. The winning neuron for Bx is located

one neuron to the left of neuron 252. The winning neuron for Cx is located three

neurons to the left of neuron 252 and is between the winning neurons for

Schizoaffective depressive disorder and Major depressive disorder. This seems

reasonable, as in Cx most of the typical features of Schizophrenia where altered,

while the two features that were changed from 0 to 1, namely "psychomotor

disturbance" and "anxiety", are prominent features of depressive disorders. Note that

the map provides a visual and dimensional description of the gradual transition from

the diagnosis corresponding to Ax to that of Cx .

Patient C

Feeding disorder of infancy

or early childhood

2 4 6 8 0

2

4

6

8

10

12

14

16

Mental retardation

Autistic disorder

Asperger's disorder

ADHD (combined)

Anorexia

Bulimia Schizophrenia

Dementia of the Alzheimer's type

Delirium

Primary insomnia

Primary hypersomnia

Narcolepsy Sleepwalking

Alcohol intoxication

Alcohol abuse

Amphetamine induced

psychotic disorder

Amphetamine

intoxication

Amphetamine abuse

Amphetamine induced

sleep disorder

Amphetamine induced depressive disorder

Psychotic disorder

Major depressive Disorder

Schizoaffective depressive disorder

Reading disorder

Mathematics disorder

Alcohol withdrawal delirium

Patient A Patient B

10 12 14 16

17

6. Discussion

The contemporary symptom-based diagnosis approach in psychiatry leads to

difficult nosological questions.24 For example, which behavioral or psychological

syndromes should be categorized as mental disorders? What is the relationship

between various disorders? Why do some disorders group together? How can one

estimate the importance of a symptom for the correct diagnosis of a disorder?

More specifically, many researches challenged the validity of categories of

mental disorders that appear in the DSM. For example, Langenbucher et al.25 refer to

substance abuse (which is a milder version of substance dependence) as a "category

without content".

Many of these problems could be clarified by developing a better understanding

of the topology of mental disorders. We described here for the first time an

algorithmic approach for visualizing the relationships between mental disorders (or,

more precisely, of the set of symptoms associated with each disorder). We used an

SOFM for the dimensionality reduction process. There are, of course other (and

perhaps more modern) dimensionality reduction algorithms, but our main point here is

the novel application rather than the specific algorithmic tool.

As a proof of concept, we trained a semantic map using 27 relatively well-

known disorders. The resulting map demonstrates clear clusters of disorders that are

separated from other clusters. We also demonstrated how the map can be used to

address other important questions in the nosology of psychiatric disorders, including

automatic classification of mental disorders; estimating the importance of various

symptoms in the diagnostic process; and adding a dimensional component to the

diagnosis.

Directions for further research include: developing a map depicting all the 300

disorders listed in the DSM-IV-TR, incorporating biological symptoms (e.g. EEG

data), and using other dimensionality reduction algorithms (e.g. Laplacian

eigenmaps26). Another intriguing question is how to incorporate into the topological

map a point representing a healthy individual.

We believe that tools from the field of computational intelligence have a huge,

and still largely unexplored, potential in the field of psychiatry.

18

Acknowledgements. We are grateful to Yaniv Assaf, Moshe Koppel, Ron Meir, and Eytan Ruppin for helpful comments. Appendix A: Learning procedure

At each learning step, one of the feature vectors is selected and presented to

the SOFM as an input vector x . A winner neuron *i is determined such that:

*i jw x w x− ≤ − , for all {1,2,...,225}j ∈ .

Intuitively, the neurons "compete" among themselves, and the winning neuron is the

one whose weight vector is most similar to the input vector x .

Each of the weight vectors is then adapted according to:

i i iw w w← +∆ ,

where

*( , )( )i i i iw D r r x wρ∆ = − .

Here 0ρ > is the learning rate, and

2**

2( , ) exp( )

2

i ii i

r rD r r

σ

−= − is a neighborhood

function . Note that *( , )i iD r r monotonically decreases with the distance between the

two vectors ir and *ir . In other words, for the winning neuron and for neurons that

are close to it, the weight is adapted so that it becomes more similar to the input

vectorx , whereas the weight vectors of neurons that are far from the winning neuron

remain almost unchanged. Intuitively, neurons that are close to each other (in terms of

their r values) "cooperate" to form distinct topological neighborhoods based on

mutual similarity of their weight vectors.

We presented the 27 symptom vectors (corresponding to the 27 mental

disorders) to the SOFM in a cyclic manner for a total of 100,000mk = learning steps.

The parameters ρ and σ are updated at each learning step k according to:

/

00

/

00

( ) ,

( ) ,

m

m

k kf

k kf

k

k

ρρ ρ

ρ

σσ σ

σ

=

=

19

with 0 0.8ρ = , 0.01fρ = , 0 10.5σ = , and 0.5fσ = .27 Note that since 0

1fρ

ρ< , ( )kρ

decreases monotonically from 0

0 00

(1)fρρ ρ ρ

ρ

≈ =

to

1

00

( )f

m fkρ

ρ ρ ρρ

= =

.

The parameter ( )kσ behaves similarly with 0(1)σ σ≈ and ( )m fkσ σ= . In other

words, in the initial learning steps the weight updates are large, and encompass a wide

neighborhood of the winning neuron. As learning progresses, the updates become

smaller, and more concentrated near the winning neuron.

Initial weight vector values were drawn randomly from the uniform

distribution [ 0.5,0.5]U − . For the sake of consistency, the same random seed was used

throughout the various simulation conditions described below.

20

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