We attempt to bring to the forefront the often-overlooked circularity in a wide variety of tasks linked to Case-Based Reasoning (CBR). This motivates the need for a methodical examination of circularity to arrive at new paradigms in CBR. In our previous work on RelCBR, we have illustrated that the current CBR paradigm can benefit from the consideration of circularity. We propose several other directions of research wherein the state-of-the-art approaches are still agnostic to circularity and argue why the incorporation of circularity can yield improvement in performance. Approaches proposed for resolving the diverse variety of circularities can serve as templates for circularities of similar nature that emerges in diferent contexts.
The well-known -Means algorithm also deals with an inherent circular problem: ‘In order to
identify the cluster centroids, the instances have to be assigned to clusters. But such an assignment
is not possible unless the cluster centroids are known.’ The involved circularity is resolved using
the Expectation Maximization (EM) algorithm [
In the context of CBR, there have been past works that have benefited from an appreciation of
circularity. The document segmentation approach for the construction of cases by segmenting
raw text documents, as presented in [
Our recent work on quantifying the reliability of cases in the case base [
A knowledge source is considered reliable if it provides trustworthy solutions to problems, and a solution is deemed to be trustworthy if it is supported by reliable knowledge sources.
Our experiments have shown improvements due to the consideration of circularity. We
further posit that a systematic study of circularity can impact research in the following ways:
1. Identifying tasks that involve inherent circularity but have been traditionally addressed
via approaches that are agnostic to such circularity.
2. Proposing novel approaches to resolve the involved circularities and identifying situations
in which these can be extended to circularities that manifest in other contexts.
3. A paradigm level shift might be necessary that inherently respects circularity, as a result
of which the various manifestations of circularity might disappear. The Holographic
paradigm [
In this section, we describe our research objectives and a rough outline of our roadmap towards realizing our goals.
Several approaches in the CBR literature have not paid explicit attention to the underlying circularity in the tasks they attempt to address. Our objective is to highlight the importance of circularity by identifying its underlying nature in CBR tasks such as retrieval, adaptation, and maintenance in the traditional CBR. We further hypothesize the need for a novel paradigm in CBR that may inherently handle such instances of circularity at a deeper level.
Finally, the techniques proposed for the resolution of circularity hold the potential to serve as
a template for circularity resolution in situations that arise in contexts that appear to be distinct
on the surface but share similar inherent structures. For instance, the circularity resolution
technique employed in the PageRank algorithm can be used for arriving at preferability scores
of products in recommender systems domain, as illustrated in [
In our recent submission, we have highlighted the importance of circularity in a variety of tasks relating to CBR in an unsupervised setting, some of which are listed below.
When a reasoner is equipped with a multitude of similarity functions (possibly learned
bottomup; see [
A statement of circularity, with nature very similar to the one above, can be proposed
when a reasoner learns adaptation rules in a data-driven fashion (say using the case diference
heuristic [
One aspect of the maintenance of a case-based reasoner is the removal of noisy and redundant cases from the case base. Literature for the detection of noisy cases is often based on a noncircular definition, the limitations of which are discussed in Section 3. Our approach for the identification of noisy cases (via estimating their reliability) is grounded upon the following circular definition, which has been shown to outperform its non-circular counterparts.
A case is reliable if it can be solved by its reliable neighbors.
The Footprint Algorithm [
A possible circular extension for arriving at the competence of cases is presented. Notice that it makes use of the heuristic that a case with a higher competence score is likely to be retained. A case is likely to be retained if the cases it solves are not already solved by cases that are likely to be retained.
We would like to emphasize the fact that the identified circular dependencies disappear in the presence of knowledge from a domain expert. In particular, if top-down knowledge is available to the reasoner concerning the reliability of similarity functions (or adaptation strategies) in an ensemble, or the competence of cases in the case base, the proposed circularities cease to exist.
We aim to demonstrate the efectiveness of methods that address circularity over those that are agnostic of it. For instance, the problem-solving ability of a reduced case base constructed using a non-circular definition to eliminate cases can be compared against that when a method that takes the underlying circularity into account is employed. In settings involving multiple similarity functions (or adaptation strategies), the closeness of the predicted solution to the ground truth can be quantified in order to compare approaches that make use of circularity with those that do not.
We also intend to investigate whether the proposed solution techniques can be reused to resolve circularities of similar nature that manifest in a diferent context.
In our work submitted to ICCBR 2023, we demonstrate that diverse CBR research contexts share an underlying circularity. We examine the root cause of such circularities and present fundamental impossibility results in this context. We show how a systematic study of circularity can motivate the quest for novel CBR paradigms and lead to novel approaches that address circularities in traditional CBR retrieval, adaptation, and maintenance tasks. Furthermore, such an analysis can help in extending the solution of one problem to solve an apparently unrelated problem, once we discover the commonality they share deep down in terms of the circularities they address.
Our prior work, RelCBR [
We have proposed RelCBR, which takes the reliability of the neighbors of cases into account. The underlying circular definition states that
A case is reliable if it can be solved by its reliable neighbors.
Obtaining reliability based on such a circular definition serves two key benefits. First, cases with
reliability under a predefined threshold can be presented to a domain expert for inspection.
Further, these reliability scores can be used to undermine the contribution of unreliable cases when
addressing a new query. Our experiments have shown statistically significant improvements
over the baseline methods [
Our work is centered around the claim that diverse research problems in CBR such as retrieval, adaptation, and maintenance can benefit from an appreciation of the underlying circularity. RelCBR is a case in point. In the long run, a systematic study of circularity can motivate the exploration of novel CBR paradigms. Finally, we foresee wider implications of circularity in the context of Artificial Intelligence.