By Robert M. Haralick
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Such approaches are contrasted with table lookup, a method that obviously cannot generalize. 4. 2: Generalization versus abstraction. Abstraction and generalization have been identiﬁed in most approaches with abtracting approaches pitted against table lookup. Extended with analogical reasoning, table lookup also generalizes. based reasoning to table lookup, memory-based learning is capable of going beyond the data as well, and on top of that keeps all the data available. We will show that this is useful for NLP tasks: in such tasks, lowfrequency or atypical examples are often not noise to be abstracted from in models, but on the contrary an essential part of the model.
To remedy this, distanceweighted voting can be used. A voting rule in which the votes of different members of the nearestneighbor set are weighted by a function of their distance to the query was ﬁrst proposed by Dudani (1976). 2. 11) where d j is the distance to the query of the j’th nearest neighbor, d1 the distance of the nearest neighbor, and dk of the furthest (k’th) neighbor. 3, further proposed the inverse distance weight (henceforth ID). 12 a small constant is added to the denominator to avoid division by zero (Wettschereck, 1994).
In these methods, examples (labeled with their class) are represented as points in an example space with as dimensions the numeric features used to describe the examples. A new example obtains its class by ﬁnding its position as a point in this space, and extrapolating its class from the k nearest examples in its neighborhood. Nearness is deﬁned as the reverse of Euclidean distance. An early citation that nicely captures the intuitive attraction of the nearest-neighbor approach is the following: This ”rule of nearest neighbor” has considerable elementary intuitive appeal and probably corresponds to practice in many situations.