It's also often useful to distinguish two kinds of similarity or association between words (Schütze and Pedersen, 1993). Two words have first-order co-occurrence for solving simple analogy problems of the form a is to b as a* is to what?. In such problems, a system given a problem like apple:tree::grape:?, i.e., apple is to tree as grape is to , and must fill in the word vine. In the parallelogram model, illustrated in Fig. 6 .15, the vector from the word apple to the word tree (= # » tree − # » apple) is added to the vector for grape ( # » grape); the nearest word to that point is returned. tree apple grape vine Figure 6 .15 The parallelogram model for analogy problems (Rumelhart and Abrahamson, 1973) : the location of # » vine can be found by subtracting # » apple from # » tree and adding # » grape.