There are different sorts of analogy. Predictive analogy "is the process of inferring further similarities between two given situations based on some existing similarities," Bipin Indurkhya , Predictive Analogy and Cognition in Analogical and Inductive Inference, K. P. Jantke, Ed., Springer-Verlag, 1992. In Asa H predictive analogy is performed by dot product similarity measure between cases. Input vector components are compared between cases and output vector components are inferred.
Proportional analogies are "of the form: A is to B as C is to D" Scott O'Hara, A Model of the 'Redescription' Process in the Context of Geometric Proportional Analogy Problems, also in Analogical and Inductive Inference. In Asa H proportional analogy is performed by vector case extrapolation like: vector V4 = vector V3 - C*(vector V1 - vector V2).