Changes between Version 2 and Version 3 of ExpertRecommender

Timestamp:

09/04/08 15:44:11 (17 years ago)

Author:

fmittag

Comment:

--

ExpertRecommender

@@ -78 +78 @@
 == Suggestion ==
 
+=== Comparing features ===
+
 Define a similarity metric that compares two features x and y of the same (direct) type. Until now, the value of a feature is only the applicability value of the feature.
 {{{
@@ -88 +90 @@
 This means, that two features with the same applicability have the distance 0 and thus the similary 1 - 0/2 = 1. Two features with applicability -1 and 1 would have the distance 2 and the similarity 1 - 2/2 = 0. (TODO: prove the properties of a metric)
 
+=== Comparing items ===
+
+The similarity of two items is defined through the similarity of their features. The outline of a potential algorithm looks like this:
+
+ * The similarity of two items is the arithmetic mean of the similarities of all features
+ * Features that are not annotated will be ignored
+ * If a feature type is only annotated in one item, feature values need to be inferred until they can be compared
+
+Example:
+
+Let there be a simple feature-hierarchy as follows:
+{{{
+  A
+ / \
+B   C
+}}}
+
+Example similarities would be: ("-" means: not annotated)
+{{{
+  1      -1
+ / \  ;  / \      => similarity = 0
+-   -   -   -
+}}}
+{{{
+   1       1
+  / \  ;  / \     => similarity = (1 + 0) / 2 = 0.5
+-1   -   1   -
+}}}
+
+Some non-trivial cases:
+{{{
+   -      -1                               -       -
+  / \  ;  / \     => similarity = ?       / \  ;  / \     => similarity = ?
+-1   -   -   -                          +1   -   -  -1
+}}}
+
+Suggestion: Propagate possible values as intervals up or down the hierarchy
+
+We extend the distance metric on intervals, where x1 and x2 denote the interval bounds of x = [x1;x2] (if x1 = x2, we just write [x1], which is equal to the value x1)
+{{{
+dist(x,y) = (|x1-y1| + |x2-y2|) / 2
+}}}
+
+The above example can then be compared:
+{{{
+   -      -1        [-1;+1]       -1
+  / \  ;  / \   =>   /   \   ;    / \    => similarity = (sim(-1,[-1]) + sim([-1;+1],-1)) / 2 = (1 + 0.5) / 2 = 0.75
+-1   -   -   -     -1     -    [-1]  -
+}}}