C.N. Ziegler Cetane sps Fig. 2. Small fragment from the Amazon. com book taxonomy Po=T to node pa =dke. Function sib(p)returns the number of p's siblings, while sco(p) returns p's score: m∈{0,1,,q-1}:sco(m)=F Scores are normalized, i. e, all topic score that ais profile assigns to nodes from axonomy C amounts to some fixed value s. Hence, high product ratings from agents with short product rating histories have higher impact on profile generation than product ratings from persons issuing rife ratings. Score s is divided evenly among all products that contribute to ai's profile makeup. Factor K permits fine-tuning the extent of super-topic score inference, depending on the underlying taxonomy's depth and granularity Example 1(Topic Score Assignment). Suppose the taxonomy given in Figure 2 which represents a tiny fragment from the Amazon. com book taxonomy, and propagation factor K=l Let user a; have mentioned 4 books, namely Matrix Analysis, Fermat's Enigma Snow Crash, and Neuromancer For Matrix Analysis, 5 topic descriptors are given,one of them pointing to leaf topic ALGEBRA within our small taxonomy. are Pure, Mathematics, Science, and top element Books. Score 50 hence must be divided among these topics according to Equation 3. Score 29. 087 becomes accorded to topic Algebra. Likewise, we get 14.543 for topic Pure, 4.848 for Mathematics, 1.212 for Science, and 0.303 for top element Books. These values are then used to build the profile vector of user ai Success or failure of our approach largely depends upon taxonomy C used for clas- sification. The more thoroughly crafted and fine-grained the latter taxonomy, the more meaningful our profile information becomes Clearly, topic descriptors f(bk) for prod ucts bk must be chosen skillfully, too. By virtue of inference of fractional interest for super-topics, one may establish high user similarity for users which have not even rated one single product in common, as has been indicated before. According to our scheme, the more score two profiles have accumulated in same branches, the higher their com- puted similarity84 C.-N. Ziegler Books Science Mathematics Reference Sports Archaelogy Medicine Applied Pure Nonfiction Discrete Algebra History Astronomy Fig. 2. Small fragment from the Amazon.com book taxonomy p0 =  to node pq = dke . Function sib(p) returns the number of p’s siblings, while sco(p) returns p’s score: ∀m ∈ {0, 1,...,q − 1} : sco(pm) = κ · sco(pm+1) sib(pm+1)+1 (3) Scores are normalized, i.e., all topic score that ai’s profile assigns to nodes from taxonomy C amounts to some fixed value s. Hence, high product ratings from agents with short product rating histories have higher impact on profile generation than product ratings from persons issuing rife ratings. Score s is divided evenly among all products that contribute to ai’s profile makeup. Factor κ permits fine-tuning the extent of super-topic score inference, depending on the underlying taxonomy’s depth and granularity. Example 1 (Topic Score Assignment). Suppose the taxonomy given in Figure 2 which represents a tiny fragment from theAmazon.com book taxonomy, and propagation factor κ = 1. Let user ai have mentioned 4 books, namely Matrix Analysis, Fermat’s Enigma, Snow Crash, and Neuromancer. For Matrix Analysis, 5 topic descriptors are given, one of them pointing to leaf topic Algebra within our small taxonomy. Suppose that s = 1000 defines the overall accorded profile score. Then the score assigned to descriptor Algebra amounts to s / (4 · 5) = 50. Ancestors of leaf Algebra are Pure, Mathematics, Science, and top element Books. Score 50 hence must be divided among these topics according to Equation 3. Score 29.087 becomes accorded to topic Algebra. Likewise, we get 14.543 for topic Pure, 4.848 for Mathematics, 1.212 for Science, and 0.303 for top element Books. These values are then used to build the profile vector of user ai. Success or failure of our approach largely depends upon taxonomy C used for clas￾sification. The more thoroughly crafted and fine-grained the latter taxonomy, the more meaningful our profile information becomes. Clearly, topic descriptors f(bk) for prod￾ucts bk must be chosen skillfully, too. By virtue of inference of fractional interest for super-topics, one may establish high user similarity for users which have not even rated one single product in common, as has been indicated before. According to our scheme, the more score two profiles have accumulated in same branches, the higher their com￾puted similarity