Inferring Definite-Clause Grammars to Express Multivariate Time Series

1. Inferring Definite-Clause Grammars to Express Multivariate Time Series Gabriela Guimarães and Luís Moniz Pereira CENTRIA (Centre for Artificial Inteligence), UNL, Portugal

2. Content • Introduction • Introducing Abstraction Levels for Temporal Pattern Recognition • Temporal Grammatical Rules • Definitive Clause Grammars • An Application in Medicine • Conclusions

3. Introduction 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].

4. Introducing Abstraction Levels Temporal Patterns similar sequences with small variations of the events within the sequences E E Temporal Patterns E ... Sequences tipical sequences of events that occur more than once E ... E Sequences E Events more or less simultaneously occurring successions at different primitive pattern-channels E E E Events Successions immediately succeding primitive patterns in time at the same primitive pattern-channel ... Successions Primitive Patterns Primitive Patterns elementary patterns or structures in selections of features obtained from the time series SOM SOM SOM … Selection Features transformation of all time series Selection Feature Extraction Selection

5. Temporal Grammatical Rules

6. Definitive 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

7. An Application in Medicine Sleep 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.

8. Results • 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

9. Results for one Apnoea type

10. Temporal Grammatical Rules for Sleep Apnoea

11. Implementation in Prolog Rules 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>).

12. Implementation 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].

13. Conclusions • 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.