Recommender Systems Revisited
– From Items to Transactions
1
Laks V.S. Lakshmanan
University of British Columbia
Vancouver, Canada
http://www.cs.ubc.ca/~laks
Joint work with Zeinab Abbassi.
PersDB'09, Lyon.
3/12/2016
Why Recommendations?
2
 The Recommendation Paradigm

Suggest content (in most cases, items) to users based on her profile
and past activities.
 Why Recommendation?


Search queries can be generic: e.g., >90% of Yahoo! Travel queries
are general descriptions like family trip.
More so for Social Content Sites ...
PersDB'09, Lyon, August 2009.
Why Recommendations?
3
 Social Content Sites

Sites where users make friends and share contents


E.g., facebook, del.icio.us, Flickr, etc.
Content sites letting you share info with your social buddies

E.g., nytimes.com, indiatimes.com, youtube.com
 Recommendation is an indispensible information
exploration paradigm on social content sites.
 The rich activities and user connections provide lots
of opportunities for generating recommendations.
PersDB'09, Lyon, August 2009.
Overview of RecSys
4
 Item-Based Strategies
 Estimate the rating of an unrated item (i) by the user
(u) based on its similarity to items already rated and
how u rated those items.
 Collaborative Filtering Strategies
 Estimate the rating of i by u based on how u’s similarity
network (either explicit or implicit) rated i.
PersDB'09, Lyon, August 2009.
Overview of RecSys
5
U1
U2
…
X
Ui
…
Item-based.
I1
I2
…
Ij …
Overview of RecSys
6
U1
U2
…
X
Ui
…
User-based:
Collaborative
Filtering
I1
I2
…
Ij …
Overview of RecSys
7
 Fusion Strategies
 Model/Machine Leaning-based approaches.
 What’s common among all RecSys algorithms?
 Recommend items to users.
 What if we want to recommend transactions instead?
 Motivating Apps
 User exchanging items
Offline (one-shot) exchanges
 Asynchronous exchanges


Users buying/selling items for a price
Talk Outline
8
 Motivation
 Problem Definition
 Related Work
 Our Approach
 Experimental Results
 Summary & Future Work.
PersDB'09, Lyon, August 2009.
Motivation
9
 Online social networks – emergence and rapid
growth.
 Users spend more time on online social networks.
 MySpace and Facebook are among the top 10
websites:
Motivation – Exchange Markets
 There are exchange
10
markets around on the
Web today:
 OddShoe.org
 Peerflix.com (movie
exchange)
 ReadItSwapIt.co.uk
 JoeBarter.com
 Intervac
PersDB'09, Lyon, August 2009.
10
Motivation
11
 Need “Matching” Algorithms
 Enhance quality of user experience.
 Let more people be engaged in the system and more of the
time.

Monetization.
 Lack of comprehensive study of “matching”.
 Need efficient recommendation algorithms.
PersDB'09, Lyon, August 2009.
Some Related Problems
12
 Chinese Postman Problem:
 Collect mail from postal station (s).
 Deliver mail on all streets (edges).
 Minimize distance covered (fuel consumed).
Some Related Problems
13
 Cycle Covers:
?
 Let’s try again!
?
Some Related Problems
14
 Cycle Covers:
12
6
7
15
20
16
Can we cover all vertices with edge-disjoint cycles?
What is the minimum weight of such a cover?
Some Related Problems
15
 Cycle Covers:
12
6
7
15
20
16
Can we cover all vertices with edge-disjoint cycles?
What is the minimum weight of such a cover?
Vertex-disjoint, edge-disjoint, vertex/edge cover,
bounded length, etc. – variants.
Related Work
16
 Graphs – Cycle Cover Problem:
 Polytime algorithm for Chinese Postman problem on
undirected graphs [Edmonds & Johnson 73].
 CPP is NP-hard for mixed graphs [Papadimitriou 76] but
admits a 3/2-approx. [Raghavachari & Veerasamy 99].
 Cycle Cover -- cover given set of nodes/edges with set of
min. length cycles.
 Min. Weight Cycle Covers – a variant of CPP; NP-hard in
general [Thomassen 97].
 CC w/ bounds on cycle length (heuristic) [Hochbaum and
Olinick 01].
 Approximation algorithms when length is bounded
[Immorlica+ 05].
PersDB'09, Lyon, August 2009.
Related Work
17
 Recommender Systems:
 Management science perspective [Murthy & Sarkar 03].
 Collaborative filtering [Resnik+ 94, Shani+ 02].
 Survey of item-based, collaborative filtering, fusion-based,
and model-based [Adomavicius & Tuzhilin 05].
PersDB'09, Lyon, August 2009.
Related Work
18
 Kidney Exchange problem:
4,000 deaths/yr in US.
70,000 waiting for a cadaver kidney.
Related Work
19
 Kidney Exchange problem:
 In kidney transplants frequently the donor’s kidney is not
compatible with the patient’s.
 Example: A’ is willing to donate her kidney to A and B’ to B
but incompatible. However B’ kidney compatible with A and
A’ kidney with B.
 Motivation: Find feasible exchanges and save more
people’s lives.
 Medical constraints: no cycle
longer than 3!
PersDB'09, Lyon, August 2009.
Related Work
20
 Bi-cycles in this case: perfect matching,
therefore polynomial!
 Cycles of length 3 or more: NP-complete.
 In [Abraham+ 07] solved by Integer Linear
Programming for the problem of United States
kidney exchange with real data!
 We will look at a more general problem than KE.
 Incentivizing exchanges in P2P file-sharing
systems [Anagnostakis & Greenwald 04].
PersDB'09, Lyon, August 2009.
A Model
21
 Set of users U and a set of items I.
 Two lists for each user u in U – item list Su,
items u is willing to give away; wish list Wu,
items u is looking for.
 Network – nodes = users; u  v iff there is a
feasible transaction from u to v.
 Edges labeled with item.
i
v
u
j
PersDB'09, Lyon, August 2009.
Example
3/12/2016
22
PersDB'09, Lyon.
Different Models
23
 One-shot exchange Markets:
 Simple
exchange markets (swaps).
 Exchange markets through short
cycles.
 Probabilistic exchange markets.
 Wish List as Query List.
 Exchange markets over time.
PersDB'09, Lyon, August 2009.
Simple exchange markets
24
 Only one-by-one transactions.
i
 The problem is to find a set
of pairs:


[ (u,i) , (v,j)] where i Є Su, j Є
Wu, i Є Wv and j Є Sv.
form 2-cycles (swaps).
v
u
i
k
j
 Typically each user has one
instance of any item and also
wants one instance of an item
in his wish list  [ (u,i) , (*,*)]
should not appear more than
once for each user u, i.e.,
looking for a set of conflictfree cycles.
3/12/2016
w
PersDB'09, Lyon, August 2009.
24
Exchange markets through cycles.
25
 We look for cycles of
length more than 2 in
the system.
B7
Alice
Bob
 The goal is to find
cycles:
[ (u_1,i_1) , (u_2,i_2) ,
(u_3,i_3) , …, (u_k,i_k)
] where i_1 in S_u1, i_1
in W_u2, i_2 in S_u2,
i_2 in W_u2, ….
3/12/2016
B4
B8
PersDB'09, Lyon, August 2009.
Amy
25
Exchange markets through
short
cycles
26
 Note: A cycle can happen if and only if all the
participating edges are realized.
  discover short cycles and solve the short
cycle cover problem for cycles of length <= k,
where k = 3, 4, 5, …
PersDB'09, Lyon, August 2009.
Probabilistic Exchange Markets
27
 Each edge in the graph has a probability
indicating the likelihood of it being realized.
 The probability of realizing each edge is
independent of the other edges.
 Two kinds of probabilities are of interest:


Pu(v): what’s the probability u is willing to perform a
transaction with v?
Pu(i,j): what’s the probability u is willing to exchange item i
for j?
PersDB'09, Lyon, August 2009.
Query List as Wish List
28
 Wish list only contains “predicates” instead of
items.

E.g., horror movie, science fiction, eastern philosophy,
home hardware, …
 Item list as before.
 Users may rate/review items.
 Matchmaking has to factor in ratings, i.e.,
matching has to use RecSys technology.
-- Will focus on simple exchange, short cycles, and
prob. markets in this talk.
Goal
29
 Generate recommendations that maximize the
(expected) number of items exchanged through
the network.
 Each user u gets a reco.:


Gives = {(give i to v), …}
Gets = {(get j from w), …}
 Set of reco’s together constitute a set of
conflict-free cycles that maximize above metric.
SimpleMarket Problem
30
 Theorem: Even SimpleMarket problem is NP



complete.
(Contrast with one-by-one kidney exchange.)
Reduction from four-cycle partitioning of 4partite graphs to our problem.
Reduction from three-cycle partitioning of 3partite graphs to 4-cycle partitioning of 4-partite
graphs.
3-cycle partitionining of 3-partite graphs is NPcomplete [Holyer 81, Abraham+ 06].
PersDB'09, Lyon, August 2009.
ProbMarket
31
Lemma: The kidney exchange version of
ProbMarket can be solved in polynomial time.
Idea: Maximum weighted perfect matching
continues to work.
PersDB'09, Lyon, August 2009.
Algorithms
32
 Maximal set of Cycles
 Greedy.
 Local Search.
 Greedy/Local Search.
PersDB'09, Lyon, August 2009.
Maximal Algorithm
33
 Initialize the set of cycles CFSC=empty.
 At each step,




Find an exchange cycle C.
Add C to the set of cycles CFSC.
Remove all edges in G in conflict with this cycle.
Terminate if there is no remaining cycle.
 Find an exchange cycle C:


Run a DFS or BFS algorithm until you find a backward
edge.
BFS tends to find short cycles.
PersDB'09, Lyon, August 2009.
Greedy Algorithm
34
 Initialize the set of cycles CFSC=empty.
 At each step,




Find the best exchange cycle C.
Add C to the set of cycles CFSC.
Remove all edges in conflict with this cycle.
Terminate if there is no remaining cycle.
 Find the best exchange cycle C:

Try all short cycles and find the cycle with maximum
weight.
PersDB'09, Lyon, August 2009.
Intermediate Maximal/Greedy
35
 Improve Running Time.
 Find the best exchange cycle C:


Run BFS from each node v and find a cycle Cv.
Find the cycle Cv with the maximum weight and add it.
PersDB'09, Lyon, August 2009.
Local search algorithm
36
 Initialize the set of cycles CFSC=empty.
 At each step,
 Let the current set of cycles be CFSC.
 For any exchange cycle C that is not already picked,
Try to add C, and remove all cycles in CFSC in conflict
with C
 If the total weight of CFSC increases, add C to CFSC
and remove all conflicting cycles from CFSC.


If no local improvement is possible, output CFSC and
terminate.
PersDB'09, Lyon, August 2009.
Greedy/Local Search
37
 First, Run the greedy algorithm to find a set of
cycles CFSC.
 Then, Run the local search algorithm starting
from the set CFSC.
 How good are these algorithms?
PersDB'09, Lyon, August 2009.
Set Packing
38
 Our problem is a special case of weighted k-set
packing problem:
 Given a collection of sets, each of which has an
associated real weight and contains at most k
elements drawn from a finite base set, find a
collection of disjoint sets of maximum total
weight.
Output
Input
PersDB'09, Lyon, August 2009.
http://www.cs.sunysb.edu/~algorith/files/set-packing.shtml
Relation to set packing
39
 Elements  (User u gives item i) (User v gets
item j)
 Sets  Cycles of exchanges.
 Weights of sets:


Short cycle case: weight is 2k for k item exchanges.
Probabilistic: weight is [\pi_{e \in C} p(e)]*2k.
 Main difference: Sets are not given explicitly.
 Sets are cycles (given implicitly) and we have to
discover them.
PersDB'09, Lyon, August 2009.
Quality of Algorithms
40
 Maximal: No guaranteed quality: O((|V| + |E|)|B|)
time.
 Greedy: 2k-approximation [Chandra & Halldorsson
99]: O(|V|^2k |B|) time.
 Local Search: (2K-1)-approximation. [Arkin &Hassin
97]: O(|V|^2k|E|log OPT).
 Local Greedy: 2(2k+1)/3-approximation [Arkin &
Hassin 97].
 More details  [Abbassi & L 09].
PersDB'09, Lyon, August 2009.
Experiments
41
 Algorithms implemented in MATLAB and run on
2.16 GHz Intel Core 2 Duo CPU and 1 GBof RAM
under Windows XP.
 Goals:



Extent to which allowing cycles of length > 2 increases
coverage of users/items.
Quality of results of algorithms (Recall: Maximal has no
theoretical guarantees).
Scalability.
 Synthetic data: Structure as well as user
activities follow power law [Newman 03].
Takeaways: Allowing Larger Cycles
42
%Increase
23
34
45
Maximal
5.56
3.40
2.70
Greedy
7.33
3.81
3.12
Local Search
7.71
3.85
3.35
Experimental Results
43
43
44
44
45
45
Takeaways: Maximal vs Approximation
Algorithms
46
 Skew factor = 1.0, cycle length bound = 4,
#users = 25K.
Algorithm
#items exchanged
Maximal
60,000
Greedy, Local Search
65,000
 Skew factor = 1.5, cycle length bound = 4,
#users = 25K.
Algorithm
#items exchanged
Maximal
35,000
Greedy, Local Search
41,000
Summary & Future Work
47
 Market exchanges over online social nets – simple,






short cycles, probabilistic.
Related kidney exchange problem – polytime for
swaps and NP-complete for k > 2.
Even swaps NP-complete for market exchange.
Reduction to weighted k-set packing 
approximation algorithms and Maximal (heuristic).
Experiments: “Diminishing returns” as k goes up.
Maximal – more than one order of magnitude more
efficient and comparable quality!
More empirical analysis needed.
PersDB'09, Lyon, August 2009.
Summary & Future Work
48
 Experiments on Real data sets.
 More efficient approximation algorithms?
 Randomization?
 Exchange Markets over time?
 Many different objectives: e.g., #items exchanged,
fairness, average waiting time, …
 Market Price, Buy/Sell.
 Connection with game theory.
 Query List as Wish List (think movie in place of
kidney!)
PersDB'09, Lyon, August 2009.
Other Projects in Social Networks and A
Shameless Ad
49
 Mining/Analysis of Social Networks (e.g., for viral






marketing).
Network Evolution.
Diversification in RecSys.
Network-aware Search.
Social Search – SocialScope.
Opportunities for grad students and postdocs.
See http://www.cs.ubc.ca/~laks and UBC CS Grad
Programs
50
References Cited
51
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




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52
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



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




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