introducon to informaon retrieval 20 nearest neighbor

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Unformatted text preview: erated data]   In par)cular, asympto)c error rate is 0 if Bayes rate is 0.   Assume: query point coincides with a training point.   Both query point and training point contribute error → 2 )mes Bayes rate   A single atypical example.   Noise (i.e., an error) in the category label of a single training example.   More robust alterna)ve is to find the k most ­similar examples and return the majority category of these k examples.   Value of k is typically odd to avoid )es; 3 and 5 are most common. 19 Introduc)on to Informa)on Retrieval Sec.14.3 kNN decision boundaries Introduc)on to Informa)on Retrieval Sec.14.3 Similarity Metrics Boundaries are in principle arbitrary surfaces – but usually polyhedra Government Science Arts kNN gives locally defined decision boundaries between classes – far away points do not influence each classifica)on decision (unlike in Naïve Bayes, Rocchio, etc.) Introduc)on to Informa)on Retrieval 20   Nearest neighbor method depends on a similarity (or distance) metric.   Simplest for con)nuous m ­dimensional instance space is Euclidean distance.   Simplest for m ­dimensional binary instance space is Hamming distance (number of feature values that differ).   For text, cosine similarity of h.idf weighted vectors is typically most effec)ve. 21 Sec.14.3 Illustra)on of 3 Nearest Neighbor for Text Vector Space 22 Introduc)on to Informa)on Retrieval 3 Nearest Neighbor vs. Rocchio   Nearest Neighbor tends to handle pol...
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