Miquel Sànchez-Marrè1, Ulises Cortés1, Montse Martínez2,. Joaquim Comas2, and Ignasi Rodríguez-Roda2. 1. Technical University of Catalonia,. Knowledge ...
An Approach for Temporal Case-Based Reasoning: Episode-Based Reasoning∗ Miquel Sànchez-Marrè1, Ulises Cortés1, Montse Martínez2, Joaquim Comas2, and Ignasi Rodríguez-Roda2 1
Technical University of Catalonia, Knowledge Engineering & Machine Learning Group, Campus Nord-Edifici Omega, Jordi Girona 1-3, 08034 Barcelona, Catalonia University of Girona {miquel, ia}@lsi.upc.edu 2 Chemical & Environmental Engineering Laboratory, Campus de Montilivi s/n, 17071 Girona, Catalonia {montse, quim, ignasi}@lequia.udg.es
Abstract. In recent years, several researchers have studied the suitability of CBR to cope with dynamic or continuous or temporal domains. In these domains, the current state depends on the past temporal states. This feature really makes difficult to cope with these domains. This means that classical individual case retrieval is not very accurate, as the dynamic domain is structured in a temporally related stream of cases rather than in single cases. The CBR system solutions should also be dynamic and continuous, and temporal dependencies among cases should be taken into account. This paper proposes a new approach and a new framework to develop temporal CBR systems: Episode-Based Reasoning. It is based on the abstraction of temporal sequences of cases, which are named as episodes. Our preliminary evaluation in the wastewater treatment plants domain shows that Episode-Based Reasoning seems to outperform classical CBR systems.
1 Introduction Continuous or dynamic or temporal domains commonly involve a set of features, which make them really difficult to work with, such as: (1) a large amount of new valuable experiences are continuously generated, (2) the current state or situation of the domain depends on previous temporal states or situations of the domain, and (3) states have multiple diagnoses. This means that classical individual case retrieval is not very accurate, as the dynamic domain is structured as a temporally related stream of cases rather than in single cases. The CBR system solutions should be also dynamic and continuous, and temporal dependencies among cases should be taken into account. ∗
The partial support of TIN2004-01368 and DPI2003-09392-C02-01 Spanish projects and IST2004-002307 European project are acknowledged.
H. Muñoz-Avila and F. Ricci (Eds.): ICCBR 2005, LNCS 3620, pp. 465 – 476, 2005. © Springer-Verlag Berlin Heidelberg 2005
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Some typical examples are the monitoring and on-line control of dynamic processes such as power stations control, wastewater treatment plants control, and jet plane control. Some applications in the medical domain are the monitoring of patients in an intensive care unit, or the diagnosis and/or the prognosis and cure of some medical diseases. Also, the forecasting of some meteorological or seismic phenomena and autonomous robot navigation are instances of such temporal domain. Our approach proposes a new framework for the development of temporal CBR systems: Episode-Based Reasoning. It is based on the abstraction of temporal sequences of cases, which are named as episodes. In this kind of domains, it is really important to detect similar temporal episodes of cases, rather than similar isolated cases. Thus, a more accurate diagnosis and problem solving of the dynamic domain could be done taking into account such temporal episodes of cases rather than only analysing the current isolated case. Working with episodes instead of single cases is useful in temporal domains, but also raise some difficult tasks to be solved, such as: • • • • • • •
How to determine the length of an episode, How to represent the episodes, taking into account that they could be overlapping, How to represent the isolated cases, How to relate them to form episodes, How to undertake the episode retrieval, How to evaluate the similarity between temporal episodes of cases, How to continually learn and solve new episodes.
The paper answers almost all of these questions, and proposes a new approach and a new framework to model temporal dependencies by means of the episode concept. The Episode-Based Reasoning framework can be used as a basis for the development of temporal CBR systems. The new framework provides mechanisms to represent temporal episodes, to retrieve episodes, and to learn new episodes. Episode adaptation is not discussed, as it is highly domain-dependant, and will be studied in the near future. An experimental evaluation is presented in the paper as an example of the new framework for temporal domains. 1.1 Related Work From a logical point of view, temporal features in automated reasoning have been widely studied within the field of Artificial Intelligence. For instance, the logic of time work by van Benthem [1]; the work by Allen [2, 3, 4] about the temporal interval logic; or the work of temporal logic by Ma and Knight [5, 6] and by Shoham [7]; or the circumpscriptive event calculus by Shanahan [8]. All these approaches model reasoning processes under temporal constraints, which can modify the truth of logic assertions. In CBR systems, this temporal reasoning in continuous or dynamical domains was not studied until recently. Ma & Knight [9] propose a theoretical framework to support historical CBR, based on relative temporal knowledge model. Similarity evaluation is based on two components: non-temporal similarity, based on elemental cases, and temporal similarity, based on graphical representations of temporal references.
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Most related publications, such as those of [10, 11] use temporal models with absolute references. [12] use a qualitative model derived from the temporal interval logic from Allen. In [13, 14, 15], several approaches are proposed in the field of mobile robots, emphasising the problem of the continuity of data stream in these domains. However, none of these do not give an answer for temporal episodes. In addition, they focused more on the predicting numerical values, which can be described as time series, rather than on using the correlation among cases forming an episode. In [16], we proposed a method for sustainable learning in continuous domains, based on a relevance measure. Anyway, we are not aware of any approach proposing a mechanism for explicit representation for both temporal episodes and isolated cases, and addressing the problem of overlapping temporal episodes. Also the feature dependency among isolated cases forming an episode are not addressed by main known approaches, and rather they provide temporal logic reasoning mechanisms, which cannot solve all related problems. 1.2 Overview This paper is organised as follows. In Section 1, the scope of the problem and some related work are discussed. Section 2 defines the basic terminology of the approach. Section 3 defines the EBR memory model. In Section 4, the episode retrieval step is described. Section 5 details the similarity evaluation between episodes. Section 6 describes a case study where the approach has been used. Conclusions and some future work are outlined in Section 7.
2 Basic Terminology for Episode-Based Reasoning Model Definition 1. An isolated case, or simply a case describing several features of a temporal domain at a given moment t, is defined as a structure formed by the following components: (:case-identifier :temporal-identifier :case-situation-description :case-diagnostics-list :case-solution-plan :case-solution-evaluation )
CI t CD CDL CS CE
An isolated case will have an associated identifier (CI), as well as a temporal identifier (t). This time stamp could be measured in any unit of time, depending on the temporal domain at issue. Thus, it could be the month, the day, the hour, the minute, the second or any other unit. The description of the domain situation at a given moment (CD), is a snapshot of the state of the domain, which will consist of the values (Vi) of the different attributes (Ai) characterising the system: CD = ((A1 V1) (A2 V2) ... (AN VN))
(1)
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In the temporal domains being addressed by our proposal, the basic data stream describing the domain can be structured as a feature vector. This hypothesis is not a great constraint, since most of real temporal systems use this formalism, and also because other structured representations can be transformed into a vector representation. Notwithstanding, some information loss can occur with this transformation process. Formally, an isolated case at a given time t is: Ct =
(2)
For instance, an isolated case in the domain of volcanic and seismic prediction domain, could be as follows: (
:case-identifier :temporal-identifier :case-situation-description
CASE-134 27/11/2004 ((SEISMIC-ACT Invaluable) (DEFORMATIONS mean-value) (GEOCHEMICAL-EVOL normal) (ELECT-PHEN level-1))
:case-diagnostics-list :case-solution-plan :case-solution-evaluation )
(No-eruption, Seismic-pre-Alert) (Alert-Emergency-Services) correct
Definition 2. A temporal episode of cases of length l, which is a sequence of l consecutive cases in time, is a structure formed by the following components: (
:episode-identifier :initial-time :episode-length :episode-description :episode-diagnosis :episode-solution-plan :episode-solution-evaluation :initial-case :final-case )
EI t l ED d ES EE Ct Ct+l-1
Formally, an episode with diagnostic d, length l, which starts at a given instant time t is:
Etd, l =
(3)
From a temporal point of view, an episode with diagnostic d, length l, which starts at initial time t can be described as the sequence of l temporal consecutive cases:
Etd, l = [Ct, Ct+1, Ct+2, …, Ct+l-1]
(4)
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3 Episode-Based Reasoning Memory Model There are several choices to organise and to structure the memory of our EpisodeBased Reasoning (EBR) system. Some previous models in the literature had not taken into account some key points. Main outstanding features to be considered are the following. (1) The same case could belong to different episodes. (2) The description, or state depicted by a case could correspond to several situations or problems (multiple diagnostics) at the same time, and not only one, as it is assumed by most CBR system models. (3) Episodes could overlap among them, and this fact should not imply a case base representation redundancy of the common cases overlapped by the episodes. (4) Episode retrieval, and the case retrieval for each case belonging to an episode, should be as efficient as possible. Taking into account these facts, our memory proposal will integrate hierarchical formalisms to represent the episodes, and flat representations for the cases. Thus, both episode and case retrieval will be fast enough. This representation model will set an abstraction process that allows splitting the temporal episode concept and the real case of the domain. Discrimination trees for the episodes (Episode Base or EpB), and a flat structure for cases (Case Base or CsB) are proposed. The discrimination tree enables to search which episodes should be retrieved, according to the feature values of the current episode description. Episodes have the appropriate information to retrieve all cases belonging to them. This structure of the experience base or memory of the EBR system allows one case to belong to more than one episode. In addition, it allows the overlapping of episodes, and even though the extreme scenario, which is very common in complex temporal real domains, where the exactly same cases form several different episodes. This integration of the hierarchical Episode Base and the flat Case Base is depicted in Figure 1. The nodes are labelled with the predictive features or attributes (Ai) and branches are labelled with the discrete values (Low, Normal or High for instance) of attributes. To increase even more the efficiency and accuracy of the retrieval step, the use of the mechanism of episode abstraction by means of episode prototypes or metaepisodes is proposed. This technique was originally proposed in [17] for a case base. Here it is used for episode categorisation instead. The meta-episodes and induced episode bases are semantic patterns containing aspects considered as relevant. These relevant aspects (features and feature ordering) constitute the basis for the biased search in the general episode base. The use of these relevant aspects is in fact equivalent to using declarative bias during the identification phase, prior to searching cases within the case base. This new step adds the use of domain knowledge-intensive methods to understand and bias the new problem within its context. The setting of several meta-episodes induces the splitting of the general episode base into several episode bases with different hierarchical structures. Each episode base will store similar episodes that can be characterised with the same set and order of predictive features.
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A3 L
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Fig. 1. Mixed memory model using both episodes and cases
NEW EPISODE META-EPISODE BASE
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Fig. 2. Hierarchical three-layered memory structure
FLAT CASE BASE
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In the retrieval step, first, the EBR system will search within the previously established classification to identify which kind of episode it is coping with. For each established class (meta-episode) there will be a possible different set of specific discriminating features and a different episode base. Then, the retrieval will continue in the episode base/s induced by the meta-episode/s best matching the current episode. The memory model of the approach is composed by a set of meta-episodes, which will constitute the Meta-Episode Base (MEpB). For each meta-episode there exists a hierarchical Episode Base (EpB). Cases are organised within a flat case base (CsB).Also there exists a Meta-Case Base (MCsB) for the diagnostic list computation of a case. This hierarchical three-layered structure will allow a more accurate and faster retrieval of similar episodes to the current episode/s. Figure 2 shows this memory structure.
4 Episode Retrieval Retrieval task of episodes is activated each time the EBR system receives a new current case (Cct) with data gathered from the domain, at the current time (ct). First step is getting the possible diagnostics of the current case. This label list can be obtained by different ways. For example, using a set of inference rules, which can diagnose the state or situation of the domain from the relevant features. These classification rules could be directly collected from domain experts or could be induced from real data. Another way is using the meta-cases technique, and to evaluate the similarity between the current case (Cct) and the meta-cases. The current case is labelled with the diagnostic labels of most similar meta-cases. Meta-cases can be obtained, in the same way as the rules: from experts or from an inductive clustering process. In our proposal, meta-cases technique is used. Next step is the generation of possible episodes arising from the current case. This means to check whether some episodes are continuing from prior cases to the current case, and/or to build new episodes, which are starting from the current case. At this time, finished episodes are detected, and the EBR system can learn new episodes, which will be added to the EBR system memory. Figure 3 depicts several alternative episode formation and episode ending from current case. For each possible current episode, most similar episodes must be retrieved. Retrieval task proceeds with the hierarchical three-layered memory structure as explained before in section 3. 1
ct TIME
d3 d3 d3 d2 d4 d4 d4 d2 d6 d6 d5 d5
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Fig. 3. New and/or continued episodes arising from the current case
CASE BASE
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For each one of the retrieved episodes and the corresponding current episode, a degree of similarity is computed. This value is computed through an episode similarity measure, which will be described in next section. Each retrieved episode is added to a sorted list of episodes by decreasing degree of similarity. Thus, at the end of the process, the first episode of the list is the episode with a higher similarity value to a possible current episode. The EBR system will use this episode to solve the domain problem, but other policies, such as user-dependent choice, are envisioned. Similar episode retrieval task can be described as follows: Input: Cct, EpB, MEpB, CsB, MCsB Sorted_Ep_L ← ∅ CDLct ← Get_Diagnostics_Current_Case (Cct, MCsB) for each d ∈ CDLct do if (ct = 1) or (d ∉ CDLct-1) then {new episodes} Retr_Ep ← Retr_Sim_Episodes ( E ctd ,1 , MEpB, EpB) Eval_Ep ← Eval_Sim_Episodes ( E ctd ,1 , Retr_Ep) else
Sorted_Ep_L ← Sorted_Add (Eval_Ep, Sorted_Ep_L) {continued episodes} l ← Comp_Ep_Length (ct, d, CsB) Retr_Ep ← Retr_Sim_Episodes ( E ct − l ,l +1 , MepB, EpB) d
Eval_Ep ← Eval_Sim_Episodes ( E ctd −l ,l +1 , Retr_Ep) Sorted_Ep_L ← Sorted_Add (Eval_Ep, Sorted_Ep_L) endif endfor if ct ≠ 1 then for each (d ∈ CDLct-1) and (d ∉ CDLct) do {ended episodes} l ← Comp_Ep_Length (ct, d, CsB) d EpB ← EpB + Learn_New_Episode ( Ect−l ,l ) {add a new Ep} endfor endif Returns: Sorted_Ep_L {First Ep is the most similar} where the computation of episode length can be done as follows: Input: ct, d, CsB t ← ct – 2 ; l ← 1 if t ≠ 0 then CDLt ← Get_Diagnostics_Case (Ct, CsB) while d ∈ CDLt do l←l+1 t←t–1 endwhile endif Returns: l
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5 Episode Similarity Episodic similarity evaluation is based on the computation of a similarity value within the float interval [0,1], between a possible current episode (Ep_ct) and each one of the retrieved episodes (Retr_Ep). This function could be described as follows: Input: Ep_ct, Retr_Ep Eval_Ep ← ∅ for each Ep ∈ Retr_Ep do Sim_Degree_Ep ← Episodic_Sim (Ep, Ep_ct) Eval_Ep ← Eval_Ep ∪ Build_Pair (Sim_Degree_Ep, Ep) endfor Returns: Eval_Ep Episodic similarity between two episodes is computed based on the aggregation of the similarity values among cases belonging to each episode. Episodes are compared based on a left alignment of cases. There are two different scenarios. For equal length episodes, episodic similarity is computed as an equally weighted mean value among the similarity values between each pair of corresponding cases. For different length episodes, only similarity values for cases until reaching the minimum length of both episodes are considered. The computed value is normalised into the interval [0,1]. This episodic similarity measure can be formalised as: ⎧ 1 l if l1 = l 2 = l ⎪ ∑ SimC (Ct1+ i −1 , Ct 2 + i −1 ) l i =1 ⎪ ⎪ SimEp ( Etd1,l1 , Etd2, l 2 ) = ⎨ mín( l1, l 2) ⎪ 1 ⎪ ∑ SimC (Ct1+ i −1 , Ct 2 + i −1 ) if l1 ≠ l 2 ⎩⎪ max (l1, l 2) i =1
(5)
where SimC can be computed with any case similarity measure. In this approach, L'Eixample measure [18] is proposed, because some performance tests done showed it as one of the best measures.
6 An Experimental Evaluation Biological wastewater treatment is a complex process that involves chemical and biological reactions, kinetics, catalysis, transport phenomena, separations, and so on. The quality of the treated water must be always maintained in a good condition to minimise any environmental impact. Nevertheless, some features such as the inflow changes, both in quantity and in quality, and the population variation of the microorganisms over time, both in quantity and in the relative number of species, makes the process very complex. In addition, the process generates a huge amount of data from different sources (sensors, laboratory analyses and operator’s observations), but these data are often uncertain, subjective or vague. In the wastewater treatment plant (WWTP) operation, problems frequently appearing such as solids separation problems, biological foam in the bioreactors or underloading derived from storms and heavy rains. Some of them affect the process for long periods of time. Due to the lack of a well-defined model capable of simulating
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the process under the influence of these problems, classical control has been ruled out as suitable single control technique. However, operators have to make decisions to manage the process in their day-to-day operation, even when it is affected by multiple problem episodes at the same time. They learn a valuable knowledge that optimally managed can be decisive when facing similar problems in the future. Classical CBR has been successfully applied to manage the biological process of wastewater treatment plants [19, 20, 21], especially to control single non-biological situations with fast dynamics such as mechanical, physical or electrical problems. However, CBR showed limitations to face up complex problems with slow dynamics. A prototype of EBR is currently being validated at the Girona wastewater treatment plant [22] since September, 2004. The tool has been developed to manage solids separation problems in the process. A three-layered architecture has been proposed, and 21 different variables are used to compare and retrieve the episodes (six variables provided on-line from sensors and meters, nine gathered from the laboratory, and the remaining six variables correspond to microscopic observations of the biomass). Preliminary results show that EBR improves the support of the decision-making process when facing problematic situations with temporal dependency of data with respect to conventional CBR systems. Specifically, this initial experimental evaluation enables to state that the EBR approach provides more precise diagnosis of new episodes arising in the process as well as that solution plans of past episodes retrieved (the more similar ones) are more useful than with the conventional CBR approach. The efficiency of EBR in diagnosing new cases was evaluated by using historical cases of the year 2004, which include the situation description (by means of the 21 variables), the diagnosis lists (obtained from real diagnosis of the process) and the solution plan. Through 2004, 28 different episodes of solids separation problems, with episode length varying from 2 days up to 73 days and some of them overlapped, were detected, representing the 69% of the whole year. The results obtained using EBR and CBR approaches were compared with the real diagnosis of the labelled cases of 2004. The conventional CBR approach gave already a high precision of about 91% when diagnosing the current problem [23]. However, an efficiency of 97% in determining the correct diagnosis of episodes was obtained when using the EBR system, including correct diagnosis of isolated cases and correct identification of episodes (determination of initial and final cases). Concerning the usefulness of the solution plans provided by the most similar case/episode retrieved, the use of EBR also contributes to obtain more useful control plans to solve the complex problems arising in the process. The solution plan and solution evaluation retrieved from the most similar episodes helped plant operators to determine a long-term control strategy. An episode control plan, containing all the control actions applied during a whole episode and the evaluation of its application, was more useful for plant operators to solve a slow dynamic problem than the solution plan provided by the isolated case retrieved by the CBR approach. Therefore, during these problematic situations, the retrieval of similar past episodes helped the system to define new control plans to restore the process, proving that EBR can easily manage multiple diagnosis of the process status, giving real support to the operators. The results with the EBR system showed even higher efficiency than when CBR was applied in the same domain of WWTPs but for solving general problems, where around 80% of efficiency was obtained [24].
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7 Conclusions and Future Work In this paper, most of the questions raised in section 1 have been answered. A new framework and a new approach, based on the episode concept have been presented. Episode-Based Reasoning is a promising model to manage the temporal component of many real world domains, with continuous data flow. This approach supports the temporal dependency of data on past cases to solve a new case, improving the accuracy of basic CBR systems. Also, multiple diagnostics of a state or situation of the domain can be managed. Basic model terminology about episodes and isolated cases has been given. The three-layered architecture memory model for the EBR has been proposed, and the retrieval procedure has been detailed. Furthermore, the similarity evaluation step has been explained too, and the learning of new episodes has been outlined within the retrieval algorithm. There are some outstanding features in the proposal. The abstraction procedure from real data, structured in cases, towards temporal episodes is one of them. Multiple diagnostics of real cases are identified and managed by the model. The distinction between episodes and cases allows episode overlapping over the same real data without data redundancy. The hierarchical three-layered structure of the EBR memory, composed by Meta-Episodes, Episode Bases, and the Case Base enables a fast access to similar past episodes to current episodes. This model has been partially tested in a real domain, as explained in section 6. Supervision of WWTP is a hard real problem, which is a very good benchmark for the new EBR approach. Results from the experimentation have shown a very good potential of the EBR model, and an improved performance output has been obtained. One concern to be solved in the future is the uncontrolled increase of the Case Base and the Episode Bases. New Episodes can be learnt only if they are relevant enough, but new cases management is not so easy. A splitting of the Case Base by some time unit: year, month, or so, could be a first approach. There are other features to be taken into account in the near future. The extension of the EBR approach to formalise the adaptation step, and the solution evaluation task should be precisely stated into the main EBR cycle. Of course, some tuning of the approach can be made at several points. Finally, the validation of the whole EBR model should be extended to other real domains to check the usefulness, the consistency, the efficiency and the generalisation of our approach.
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