Case-Based Reasoning: How Machines Learn Like a Mind That Never Forgets

*English translation/summary of a zhichai.net forum post introducing Case-Based Reasoning (CBR).*

What Is CBR?

Case-Based Reasoning is a computational paradigm originating from cognitive science. Instead of solving problems from general rules, it reuses stored past cases and captures new experience for immediate reuse — analogous to an experienced archaeologist guided by memories of similar past digs.

A case F is formalized as a triple (P, E, L):

• P — problem description (attributes/features: numeric, symbolic, images, sequences)
• E — explanation of the solution
• L — the problem solution

CBR improves classification by modifying vocabulary V, the case base CB, or the similarity measure sim — and can combine these modifications.

Knowledge Containers

Following Richter, CBR knowledge lives in four containers: vocabulary, similarity measure, solution transformation, and cases. The first three are *compiled knowledge* (stable), while cases are *interpretive knowledge* usable immediately upon addition. Early systems use simple vocabulary and rough similarity with many cases; over time, refined vocabulary and measures allow fewer cases — like a musician who eventually plays symphonies with fewer notes. Abstracting cases into prototypes and case classes shrinks the case base, speeds retrieval, and improves noise robustness.

Key research questions: what constitutes a case, which similarity measure is appropriate, how to organize large case bases efficiently, how to acquire and refine cases, and how to generalize specific cases.

Similarity

• Cognitive view: similarity is multidimensional and context-dependent (a red bike and a blue bike are similar as bikes, different in color). Systems need dialogue strategies to determine the relevant perspective.
• Mathematical view: the Minkowski metric is the most common measure for technical problems:
\[d^{(p)}{i i'} = \left( \frac{1}{J} \sum{j=1}^{J} |x_{ij} - x_{i'j}|^p \right)^{1/p}\]
• p = 2 (Euclidean): emphasizes large differences
• p = 1 (city-block): treats large and small differences equally
• p = ∞ (max norm): no difference exceeds a predefined value
• Most applications lack prior knowledge, so measures are chosen empirically via error rates or clustering quality. Composite similarity is often a weighted sum: Sim = w1·Sim1 + ... + wn·Simn. Attribute weights are learned via optimization, heuristic search, genetic programming, or case/query ranking. Relevance feedback (learning distance functions from user feedback) is popular in image retrieval.
• Normalization: similarity is scaled to [0, 1] (0 = identical, 1 = unequal). In incremental systems, bounds estimated from limited early data may change over time, causing inconsistent decisions — an open problem requiring adaptive normalization.

Memory Organization

Unlike database retrieval or nearest-neighbor classification, CBR emphasizes conceptual memory structures: directed graphs where internal nodes are superconcepts (prototypes, medoids, or selected instances) with abstract descriptions and pointers to subconcepts. Concept learning uses split, merge, add, and delete operations, making hierarchies insensitive to sample order.

Hybrid approaches combine implicit (statistical models learned via MDL/MML when data is plentiful) and explicit (case base) representation: routine tasks are handled by efficient models; rare events are handled by CBR. This mirrors human short-term and long-term memory, following Schank's dynamic memory theory.

Applications

Meta-Learning for Parameter Selection

Given signal attributes A and domain attributes B, learn a mapping f : A ∪ B → P_i to select processing-algorithm parameters (e.g., SVM kernel width, image segmentation parameters). CBR's incremental behavior suits problems where signals arrive incrementally.

Image Interpretation

CBR applies at every level of the pipeline — preprocessing/segmentation parameter selection, low-level-to-high-level feature mapping, and matching symbolic descriptions to object models. Systems should allow incremental memory updates, starting from few samples and learning as new images arrive (the CBR system lifecycle).

Incremental Prototype-Based Classification

Used in medicine, knowledge management, and image classification. Minimal required functions: classification by similarity, redundancy-reducing prototype selection, feature weighting / similarity-metric learning, and feature-subset selection. Fully incremental operation also requires online weight updates, prototype selection, and case generalization (e.g., handling concept drift via case forgetting).

Novelty Detection

Detecting inputs unlike previous ones is essential when important classes are under-represented. The proposed model combines: 1. Statistical models (learned offline, updated by MDL/MML) with Bayesian decision rules and mixture models to flag novel events 2. A similarity-based reasoning unit that registers novel events into the case base using fuzzy similarity 3. A case-based maintenance unit that suggests when a case class warrants learning a new statistical model

Conclusion

CBR captures general knowledge (case classes, prototypes, higher-order concepts) from new experience, making it both an incremental learning and knowledge-discovery method. It underpins intelligent, flexible, robust data-interpretation systems, with successful applications in medicine, technical diagnostics, image interpretation, GIS, text retrieval, e-commerce, and user support. Future work should focus on incremental prototype-based classification, meta-learning for parameter selection, complex signal understanding, and novelty detection.

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References

1. Perner, P. (2019). Case-Based Reasoning – Methods, Techniques, and Applications. In: CIARP 2019, LNCS 11896, pp. 16–30. Springer. 2. Richter, M. (1998). Introduction to case-based reasoning. In: LNAI 1400, pp. 1–16. Springer. 3. Aha, D.W. (1991). Case-based learning algorithms. DARPA CBR Workshop, pp. 147–158. 4. Perner, P. (2008). Case-Based Reasoning on Images and Signals. Studies in Computational Intelligence, vol. 73. Springer. 5. Schank, R.C. (1982). Dynamic Memory. Cambridge University Press.