Top-N%20Recommendation%20Algorithm%20Based%20on%20Item-Graph

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Top-N Recommendation Algorithm Based on Item-Graph

• Allen, Zhenjiang LIN
• CSE, CUHK
• June 7, 2007

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Outline

• 1. Top-N Recommendation Problem
• 2. Top-N Recommendation Algorithm
• 3. Item-Graph Model and GCP-based Method
• Item-Graph Model
• Generalized Conditional Probability(GCP)-based
  Recommendation Algorithm
• 4. Preliminary Experimental Results
• 5. Conclusion and Future Work

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1. Top-N Recommendation Problem

• The Top-N Recommendation Problem
• Given the preference information of users,
  recommend a set of N items to a certain user that
  he might be interested in, based on the items he
  has selected.
• E-commerce system example Amazon. COM,
  customers vs products.

Item 1 Item 2 Item 3 Item m
User 1 1 0 1 0
User 2 1 1 0 0

User n 0 1 0 1
New User 1 ? 1 ? ?
User-Item matrix
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Example the Amazon.com
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1. Top-N Recommendation Problem

• Challenges in E-commerce Systems
• Huge amounts of data millions of users and/or
  items
• Real-time return the results set
• Limited new users preference information
• Volatile users preference information.
• Contributions
• Propose the Item-Graph model.
• simple incremental
• to reflect the relationship among items
• Develop the Generalized Conditional
  Probability-based top-N recommendation algorithm.
• item-centric
• based-on the Item-Graph model

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2. Top-N Recommendation Algorithm

• Two main paradigms
• Content-based recommend items based on the
  content (textual information) of items.
• Fab system Balabanovic97, Syskill Webert
  system Pazzani97.
• Collaborative Filtering (CF) recommend items by
  collecting taste information from other users.
• Collaborative between users (link information).
• More popular than content-based recommendation,
  since in many domains (such as music,
  restaurants) it is hard to extract useful
  features from items.
• Tapestry system Goldberg92, Video Recommender
  Hill95, Ringo Shardanand95, GroupLens
  Konstan97, Jester system Goldberg01, Amazon
  Linden03.

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2. Top-N Recommendation Algorithm

• CF algorithms classified by strategy of using
  data
• Memory-based make recommendations based on the
  entire collection of references of the users.
• No pre-computing is needed, suffer serious
  scalability problem.
• E.g., Correlation-based Resnick94, Cosine-based
  Breese98.
• Model-based use the collection of user
  preferences to learn a model, which is then used
  to make recommendations.
• Building a model off-line, more scalable.
• E.g., Cluster models Ungar98, Bayesian network
  model Breese98, Association Rule Mining
  approach Lin00.

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2. Top-N Recommendation Algorithm

• CF algorithms classified by strategy of using
  objects
• User-centric look for similar (like-minded)
  users first and then make recommendation.
• Similarity between users is relatively dynamic.
• Pre-computing user neighborhood may lead to poor
  predictions.
• Item-centric look for similar (or related) items
  first and then make recommendation.
• Similarity between items is relatively static.
• Enables pre-computing of item-item similarity.
• Therefore, more scalable.
• The aim of our work
• Model-based Item-centric CF top-N recommendation
  algorithm.

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2. Top-N Recommendation Algorithm

• Notations
• Item set I I1, I2, , Im.
• User set U U1, U2, , Un.
• User-Item matrix D (Dn,m).
• Basket of the active user B ? I.
• Similarity score of x and y sim(x,y).
• Formal definition of top-N recommendation problem
• Given a user-item matrix D and a set of items B
  that have been purchased by the active user,
  identify an ordered set of items X such that
  X N, and X nB 0.

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2. Top-N Recommendation Algorithm

• Two classical item-item similarity measures
• Cosine-based (symmetric)
• sim(Ii, Ij) cos(D,i,
  D,j) (1)
• Conditional Probability(CP)-based (asymmetric)
• sim(Ii, Ij) P(Ij Ii) Freq(Ii
  Ij) / Freq(Ii) (2)
• Freq(X) the number of customers who have
  purchased the item set X.
• The ranking score for item x
• RS(x) ? b?B sim(b,x)
  (3)

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3. Item-Graph Model GCP-based Method

• Intuitions behind the Item-Graph
• The similarity between two items is proportional
  to the times of co-purchase of them.
• The similarity of item-pairs is transmissible.
• E.g.,
• Definition of the Item-Graph
• Given a dataset D (Dn,m), the Item-Graph is
  defined by a weighted undirected graph G(V, E,
  W), where
• V is the item set I.
• An edge (x, y)?E if and only if items x and y
  have been co-purchased.
• The weight of edge (x, y) is defined by the
  number of co-purchase of items x and y.

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3. Item-Graph Model GCP-based Method

• Updating the Item-Graph is easy
• Adding new users preference information T into
  the graph needs O(T2) operations, including
  adding edges and/or increasing weight of edges.
• E.g.,
• Potentially direct application of the Item-Graph
• Clustering the items.
• Measuring item-item similarity.
• Measuring importance of items.

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3. Item-Graph Model GCP-based Method

• Ideas in Generalized Conditional
  Probability-based method
• According to the definition of top-N
  recommendation problem, for any x in I-B, we
  just need to compute the basket-based
  conditional probability P(xB) Freq(xB) /
  Freq(B). However,
• Freq(xB) or Freq(B) may not exist, or
• Freq(xB) or Freq(B) are too small to make much
  sense.
• The CP-based method considers the sum of
  1-item-based conditional probabilities P(xy)
  instead, where x?I-B, y?B.
• However, the multi-item-based conditional
  probabilities may also contribute to the
  recommendation.
• E.g., suppose the ranking scores of x and y
  computed by the CP-based method are equal, and
  we also know P(xB)gtP(yB). Which one should be
  ranked higher, x or y?

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3. Item-Graph Model GCP-based Method

• The Generalized Conditional Probability
  (GCP)-based recommendation algorithm
• The ranking score of item x is defined by the sum
  of all possible multi-item-based conditional
  probabilities, that is,
• GCP(xB) ? S ? B P(xS) ? S ? B
  (Freq(xS) / Freq(S)). (4)
• However, the number of subsets of B is 2B.
• Use GCPd(xB) instead (set d2 in the following
  experiments)
• GCPd(xB) ? S ? B, S d P(xS).
  (5)
• Freq(xS) and Freq(S) can be extracted from the
  Item-Graph approximately.

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3. Item-Graph Model GCP-based Method

• Extracting Freq(A) from Item-Graph approximately
• For an item set A, obtaining the exact Freq(A)
  may not be possible from the Item-Graph.
• Extracting approximate Freq(A) from the
  Item-Graph instead.
• Find out the complete sub-graph of A (denoted by
  CSG(A)) in the Item-Graph, running time O(A2).
• Freq(A) minimal weight of edges in CSG(A).
• E.g.,
• for A a,b, Freq(A) 3.
• for B a,b,c, Freq(B) 1.
• P(cab) Freq(abc) / Freq(ab) 1 / 3.

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4. Preliminary Experimental Results

• Dataset
• The MovieLens (http//www.grouplens.org/data)
• A web-based movies recommender system
• Contains multi-valued ratings that indicate how
  much each user liked a particular movie or not
• Each user has rated at least 20 movies.
• We treat the ratings as an indication that the
  users have seen the movies (nonzero) or not
  (zero).

Table 1 The characteristics of the MovieLens
dataset
of Users of Items Density1 Average Basket Size
943 1682 6.31 106.04
1Density the percentage of nonzero entries in
the user-item matrix.
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4. Preliminary Experimental Results-1

• Evaluation Design
• Split the dataset into a training and test set by
• randomly selecting one rated movie of each user
  to be part of the test set,
• use the remaining rated movies for training.
• Cosine(COS)-based, CP-based, GCP-based methods,
  10-runs average.
• Evaluation Metrics
• Hit-Rate (HR)
• HR of hits /
  n (6)
• Average Reciprocal Hit-Rate (ARHR)
• ARHR (?i1,h1/pi) /
  n (7)
• of hits the number of items in the test set
  that were also in the top-N lists.
• h is the number of hits that occurred at
  positions p1, p2, , ph within the
• top-N lists (i.e., 1 pi N).

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4. Preliminary Experimental Results-1

• Performance of Top-N Recommendation Algorithms
• HR (left) x-axis top-N items, y-axis
  hit-rate of all users.
• ARHR (right) x-axis top-N items, y-axis
  average reciprocal hit-rate of all users.
• (For the GCP-based method, set d 2.)

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4. Preliminary Experimental Results-2

• Testing the Parameter d in GCP Method
• Testing the effect of d ( d 1, 2, 3 ).
• Evaluation Online Shopping Simulation
• Randomly selecting part of the user records to be
  the training set
• Use the remaining user records for training.
• STEP 0 Constructing the item-graph based on the
  training set
• STEP 1 for each user in the training set
• randomly moving one item out of the users basket
  and make recommendation based on the remaining
  items in the basket
• computing the order of this item in the
  recommendation list
• updating the item-graph.
• STEP 2 Computing HR and ARHR metrics.

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4. Preliminary Experimental Results-2

• Performance of Top-N Recommendation Algorithms
• HR (left) x-axis top-N items, y-axis
  hit-rate of all users.
• ARHR (right) x-axis top-N items, y-axis
  average reciprocal hit-rate of all users.

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5. Conclusion and Future Work

• Conclusion
• Top-N Recommendation Problem and item-centric
  Algorithms
• Cosine-based, conditional probability-based
• Item-Graph model
• Visualizing the relationship among items.
• Easy to update.
• Generalized Conditional Probability-based top-N
  recommendation algorithm
• Item-centric based on the Item-Graph model
• Future Work
• Clustering items and measuring item-item
  similarities based on the Item-Graph model
• Speeding up the GCP method.

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References

• Balabanovic97 M. Balabanovic and Y. Shoham.
  Fab Content-based, Collaborative Recommendation.
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• Breese98 J. S. Breese, D. Heckerman, David
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  Proceedings of the 14th Conference on Uncertainty
  in Artificial Intelligence (UAI-98), pages 43-52,
  San Francisco, 1998.
• Deshpande04 M. Deshpande and G. Karypis.
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  Trans. Inf. Syst., 22(1)143-177, 2004.
• Lin00 W. Lin. Association Rule Mining for
  Collaborative Recommender Systems. Thesis
  submitted for the Degree of M.S. in Computer
  Science.
• Linden03 G. Linden, B. Smith and J. York.
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• Resnick94 P. Resnick, N. Iacovou, M. Suchak, P.
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