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A. Four-sets, B. , and C. .. , 33 2.2 The six valid patterns of the Boolean proportion (left), and the ten invalid patterns (right)

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. , For an item i that u has not rated, the prediction?rprediction? prediction?r ui is set as the solution of the analogical equation 2 : 4 :: 3 :?, i.e. ? r ui = 3 ? 2 + 4 = 5, using the arithmetic proportion, The four users a, b, c, u are in proportion for every item j that they have commonly rated

. , RMSE and MAE of our clone-based algorithms on the MovieLens-100k and 1M datasets

.. .. , 115 5.5 FCP of our rank prediction algorithm on the MovieLens-100k dataset, p.115

, Two 4-itemsets and their related proportions, with corresponding truth value (A), p.123

. , The ten best item proportions with a support of more than 200 common ratings, using A

. , 8 The ten best item proportions with a support of more than 200 common ratings, using A

.. .. , 145 6.3 f is not SAP because f (a) : f (b) :: f (c) : y is not solvable

, A geometrical analogy problem: figure A is to figure B as figure C is to which candidate, p.17

, Analogical equation solving process as in [RA05]. The solution is here D 2, p.18

. , Analogies between words in the Word2Vect model. Image source

, Snapshot of Copycat during an equation solving process. Image taken from

. , The two domains S and T in Cornuéjols' model

A. , B. , C. , V. , and W. , general, U

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. , The, vol.36

. , The 12 non-flat parallelograms in B 3 : the six faces of the cube, and 3 × 2 diagonal parallelograms

, A classification problem in B 3. Labels f (x) are on the right cube, p.43

S. With, }. We-have-e-f-*-s-=-{-c, and }. .. ,

S. With and }. We-have-x-?-e-f-s,

. , Class equations are all assumed to be solvable

, The analogical dissimilarity AD(a, b, c, d) is equal to the distance ?(d, d ), p.62

. .. , Classification process of an extended analogical learner. ? f (x) = f (d ), p.63

, Accuracies (left) of the 1-NAN and 1-NN algorithms over different Boolean functions (m = 8) and training set sizes, with corresponding values of ?, ?, and theoretical accuracy (right). The x axis corresponds to the size of the training set, p.72

. , Four users a, b, c, u that are in proportion

, 107 5.3 Distribution of average support for Spearman's rho (RankAnlg) and MSD (k-NN), p.116

. , The quality of a proportion is defined as the fraction of component-proportions that stand perfectly

. , The quality of a proportion is defined as the fraction of components that make up perfect proportions, Quality of the 993 proportions

. .. , 135 by three 0, and each 0 is surrounded by three 1. Note that solving any (solvable), A naive application of the analogical inference principle in R 2

. , Also, we see that we have here a classification problem that is highly non-linearly separable

. , f (b), f (c)) = f (d)

. , A real function f that is piecewise affine

. , Proportion between sets (i)

. , Proportion between sets (ii)

. , Proportion between sets (iii)

. , Boolean proportion (i)

. , Boolean proportion (ii)

.. .. Analogical-root,

.. .. Analogical,

.. .. Conservative,

. , Analogical dissimilarity for real vectors

. .. Analogical-dissimilarity-for-boolean-values, 66 3.10 Quality of the analogical extension ? f

.. .. ,

.. .. Cosine,

.. .. Pearson-similarity,

.. .. Affine,

.. .. ,