Inferring Definite-Clause Grammars Inferring Definite-Clause Grammars to Express Multivariate Time Seriesto Express Multivariate Time Series

Gabriela Guimarães and Luís Moniz Pereira

CENTRIA (Centre for Artificial Inteligence), UNL, Portugal

ContentContent

Introduction Introducing Abstraction Levels for

Temporal Pattern Recognition Temporal Grammatical Rules Definitive Clause Grammars An Application in Medicine Conclusions

IntroductionIntroduction

Rule Induction for multivariate time series– Usually, a set of strings defined on a specific alphabet

is used as the set of examples for the induction process. – For multivariate time series no sequence of strings

exists. This means that the time series has to be transformed into a string-based representation.

– This transformation may include the discovery of inherent patterns in time series using unsupervised methods, such as Self-organizing neural Networks [Kohonen 82].

Introducing Abstraction LevelsIntroducing Abstraction Levels

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SOM SOM SOM…PrimitivePatterns

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Temporal Patternssimilar sequences with small variations of the events within the sequences

Sequencestipical sequences of events that occur more than once

Eventsmore or less simultaneously occurring successions at different primitive pattern-channels

Successionsimmediately succeding primitive patterns in timeat the same primitive pattern-channel

Primitive Patternselementary patterns or structures in selections of features obtained from the time series

Featurestransformation of all time series

Temporal Grammatical RulesTemporal Grammatical Rules

A Primitive pattern is a‘primitive_pattern_name’

if‘feature i’ [mini, maxi]

and‘feature j’ [minj, maxj]

and…and‘feature k’ [mink, maxk]

An event is a ‘event_name’

if

‘succession i1’ or … or ‘succession 1n’

is more or less simultaneous

‘succession j1’ or … or ‘succession jm’

is more or less simultaneous

…

is more or less simultaneous

‘succession k1’ or … or ‘succession kn’

A sequence is a ‘sequence_name’ [min, max]

if

‘Eventi’: ‘name of event i [mini, maxi]’

followed by [followed after [mintj, maxtj] by]

‘Eventj’: ‘name of event j [minj, maxj]’

…

followed by [followed after [mintl, maxtl] by]

‘Eventl’: ‘name of event l [minl, maxl]’

A temporal pattern is a

‘temporal_pattern_name’ [min, max]if

‘sequencei’ [mini, maxi]’or‘Sequencej’ [minj, maxj]’

or…or‘Sequencek’ [minv, maxv]’

Definitive Clause GrammarsDefinitive Clause Grammars– Idea:

Basically, DCGs are built up from cf-rules. In order to provide context-dependency, a DCG extends a cf-grammar by augmenting non-terminals with arguments.

– DCGs extend cf-grammars in three important ways: arbitrary tree structures that are built up in the course of parsing context-dependency in a grammar extra conditions

– Advantage of DCGs in dealing with context-dependency: efficient implementation of DCG-rules as logic statements by

definitive clauses or Horn clauses nonterminals are written as Prolog atoms and terminals as facts

An Application in MedicineAn Application in MedicineSleep Apnoea

– Sleep Disorder with high prevalence.– Identification of different types of

sleep disorders, apnoea and hypopnoeas.

– Quite different patterns may occur for the same disorder type, and even for the same patient.

– Strong variation of the duration.– For an automated classification, all

signals have to be analyzed simlutaneously.

– Usually a visual classification is made.

ResultsResults

All events and temporal patterns can describe the main properties of SRBDs, such as hyperpnoe, hypopnoea, obstructive snoring, obstructive apnoea

Altogether 15 Primitive Patterns, 6 Events, 6 Sequences and 4 Temporal Patterns were found.

Sensitivity of 0.762 and specificity of 0.758

Results for one Apnoea typeResults for one Apnoea type

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Event2

Event3

Event5

Event Tace t

No ribcage and abdomina lmovements without snoringS trong ribcage and abdomina l movementsReduced ribcage and abdomina lmovements without snoringTace t

No a irflow without snoring

S trong a irflow with snoring

Tace t

Airflow

Ribcage movements

Abdomina l movements

S noring

Temporal Grammatical Rules for Temporal Grammatical Rules for Sleep ApnoeaSleep Apnoea

A primitive pattern is a ‘A2’‘no airflow without snoring’

if‘no airflow’ [0.951, 1]

and‘reduced airflow’ = 0

and‘snoring intensity’ [0, 0.241]

An event is a

‘Event3’: ‘strong breathing with snoring’if

(‘strong airflow with snoring’or

‘reduced airflow with snoring’or‘tacets’)

is more or less simultaneous‘strong ribcage and abdominal movements’

A sequence is a ‘Sequence1’ [40 sec, 64 sec] if

‘Event1’: ‘no airflow and no chest and abdomen wall movements without snoring’ [13 sec, 18 sec]

followed by

‘Event2’: ‘no airflow and reduced chest and no abdomen wall movements without snoring’ [20 sec, 39 sec]

followed after [0,5 sec, 5 sec] by ‘Event3’: ‘strong breathing with snoring’ [6 sec, 12 sec]

Implementation in PrologImplementation in PrologRules

succession(S,D) --> succ(S), op, duration(D), cp.…transition(T,D) --> trans(T), op, duration(D), cp.…succes(’E5’,D1) --> succession(’A4’,D) ; succession(’A1’,D) ; transition(T,D).succes(’E5’,D2) --> succession(’B6’,D).…event(’E5’,D) --> succes(’E5’,D1), simultaneity, succes(’E5’,D2),range(’E5’,LR,UR), {D is (D1+D2)/2, D<UR, D>LR}.…sequence(’S1’,D) --> event(’S1’,D1), followedby, event(’S1’,D2), followedafter, transition(T,D3), event(’S1’,D4),{uplimit(’S1’,UD), lowlimit(’S1’,LD), D is D1+D2+D3+D4, D<UD, D>LD}.duration(D) --> [D],{number(D)}.range(D) --> [D],{number(D)}.uplimit('S1',<value>).lowlimit('S1',<value>).

Implementation in PrologImplementation in Prolog

Facts

trans(T) --> [transition,period].op --> [’[’]. cp --> [’]’,sec].and --> [and].or --> [or].followedafter --> [followed,after].followedby --> [followed,by].simultaneity --> [is,more,or,less,simultaneous,with].succ(’A4’) --> [strong,airflow,with,snoring].succ(’A1’) --> [reduced,airflow,with,snoring].succ(’B6’) --> [intense,ribcage,and,abdominal,movements].

ConclusionsConclusions

– The induction of temporal grammatical rules for multivariate time series is feasible, if we introduce abstraction levels.

– Self-organizing Neural Networks are integrated into the rule induction process.

– Definitive Clause Grammars are suitable for an efficient implementation of temporal context.

– This approach was successfully applied to an application in medicine.