An Energy-Efficient An Energy-Efficient Mobile Mobile

Recommender Recommender SystemsSystems

An Energy-Efficient An Energy-Efficient Mobile Mobile

Recommender Recommender SystemsSystems

Bingchun ZhuBingchun ZhuDung PhanDung Phan

Hien LeHien Le

February 22, 2011

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Agenda

• Introduction– Recommender System(RS)– Motivation– Problem formulation

• Algorithm• Experiment Results• Conclusion

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RS: What are they and Why are they

• RS: identify user interests and provide personalized suggestions.

• Enhance user experience– Assist users in finding information– Reduce search and navigation time

• Increase productivity • Increase credibility• Mutually beneficial proposition

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Types of RS

Three broad types:

1. Content based RS2. Collaborative RS3. Hybrid RS

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Types of RS – Content based RS

Content based RS highlights– Recommend items similar to those

users preferred in the past– User profiling is the key– Items/content usually denoted by

keywords– Matching “user preferences” with

“item characteristics” … works for textual information

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Types of RS – Collaborative RS

Collaborative RS highlights– Use other users recommendations

(ratings) to judge item’s utility– Key is to find users/user groups whose

interests match with the current user– More users, more ratings: better

results– Can account for items dissimilar to the

ones seen in the past too

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Types of RS: Hybrid

Hybrid model

The combination of two above models

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MOBILE Recommender System

IS widely studied before

BUT - Mostly based on user ratings - and is only exploratory in natureSOUnique features distinguishing mobile RS

remains open

The combination of two above models

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MotivationTaxi services are very popular and:

– Energy consumption counted;– Successful story of drivers are

different– Data related to individuals and objects

are rich – Mobile RS provides users access to

personalized recommendation anytime, anywhere

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To

• Provide more useful “local navigation” options

• High density of customer looking for the Cab

THEN:• Potential Travel Distance(PTD)• LCP• Skyroute algorithm

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Problem Definition

• Mobile sequential recommendation problem, which recommends sequential pickup points for Taxi driver to maximize his business success.

• Recommend a travel route for a Cab driver in a way such that the potential travel distance before having customer is minimized

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Problem Formulation

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Problem Formulation

• Assume a available set of N potential pick-up points:C = {C1, C2…Cn}

And • P={P(C1), P(C2)…, P(Cn)} is the

probability set, where P(Ci) is estimated probability at each pick-up point.

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Problem Formulation

is the set of directed sequences

is the number of all possible driving routes

where is the length of route

is the probabilities of all pick-up points containing in

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Mobile Sequential Recommendation(MRS) Problem

• is PTD function

• Driver current position

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Problem Formulation

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Computational Complexity

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Sequential Recommendation Algorithm

• Potential Travel Distance Function (PTD)– an objective function which is used to eval

uate condidate routes– property of PTD

• LCP algorithm– an algorithm which is used for pruning the

search space offline• SkyRoute algorithm

– an algorithm for seeking optimal recommendation routes

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Recommended Driving Route

• c1: a pick-up event happens with probability p(c1)

• c2: a pick-up event may happen with probabolity (1-p(c1))p(c2)– only when no pick-up event hap

pens at c1, this event happens.• ...• c4: a pick-up event happnes with pro

bability (1-p(c1))(1-p(c2))(1-p(c3))p(c4)

An exapmel of Recommended Driving Route with the length of suggensted driving route L = 4

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Potential Travel Distance Function

ii

L

iiR

L

iiLR

pp

where

DDDDD

pppppP

1

,...,,

,...,,

1211

1

1211

PTD is defined as the expected distance for a cab before picking up a customer in the route RL:

...)21(2)11(11 DDppDpDPPTD RR

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PTD Function Property

• Lemma. The Monotone Property of the PTD Function– the PTD function is strictly monotonically i

ncreaseing with each attribute of vector DP.• Vector DP is a vector combined by vector D

and vector P• With this property, it’s possible to

determine a candidate route is better than the other without computing PTDs.

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PTD Function Property

A recommended driving route R1 with a length L, associated with the vector DP1, dominates another route R2 with a length L, associated with vector DP2, iff the following two conditions hold:

• every element in DP1 is not worse than it peer in DP2

• at lease element in DP1 is better than its peer in DP2

By this definition, if a candidate route A is dominated by a candidate route B, A cannot be an optimal route.

element 2 B dominates A

B dominates C

element 1

A

B C

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Constrained Sub-route Dominance

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LCP Pruning Algorithm

• LCP Pruning algorithm– For two sub-routes A and B with a

length L , which includes only pick-up points, if sub-route A is dominated by sub-route B under Definition 2, the candidate routes with a length L which contain sub-route A will be dominated and can be pruned in advance.

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• LCP algorithm prunes the search space offline– LCP algorithm will enumerate all the L-len

gth sub-routes;– then prune the dominated sub-routes by

difinition 2 offline.• this pruning process can be done offline be

fore the position of a taxi driver is known

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SkyRoute and its Property

With lemma 4, if we can find skyline routes first, and then search the optimal driving routes from the set of skyline routes. This way can eliminate lots of candidates without computing the PTD function.

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Backward Pruning

C5 C6 C7PoCab

R1

R2

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SkyRoute Algorithm• Input

C: set of pick-up pointsP: probability set for all pick-up pointsDist: pairwise drive distance matrix of pick-up p

ointsL: the length of suggested drive routePoCab: current position

• Offline Processing (LCP)– Enumerate all sub-routes with length of L fro

m C– Prune and maintain dominated Constrained

Sub-routes with length L using sub-route dominance.

– Maintain the remained non-dmonated sub-routes with length L, denoted as

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• Online Processing– Enumate all candiate routes by connecting P

oCab with each sub-route of – for i = 2: L-1

• decide dominated sub-routes with i-th intermediate pick-up points and prune the corresponding candidates by using Backward pruning.

• update the candidate set by filtering the pruned candidates in above step.

– end for– Select the remained candidate routes with l

ength of L from the loop above– Final typical skyline query to get optimal sky

line routes

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Keywords

• PTD function: - a function to compute the Potential Travel

Distance before having a customer• LCP algorithm: - a route pruning algorithm. - can be done offline before the position of a

cab is known • SkyRoute algorithm: - a route pruning algorithm - SkyRoute includes: + LCP offline pruning + Online pruning when the position of

a cab is known

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Recommendation Process

• Obtaining the Optimal Driving Route: - Using LCP and SkyRoute for pruning

candidates - Compute PTD function for all remaining

candidates - Get the route with minimal PTD value• Other challenge: How to make the

recommendation for many cabs in the same area?

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Recommendation Process(cont.)

• Circulating mechanism - search k optimal drive routes - NO.1 route to the 1st coming empty

cab - NO.2 route to the 2nd coming empty cab - … - More than k empty cabs? Repeat from

NO.1

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Experimental Data

• Real world data: - GPS location traces of approximately 500

taxis collected around 30 days in San Francisco Bay area - Number of pick-up

points: 10 - Travelling distances

between pick-up points are measured with Google Map API

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Experimental Data(cont.)

• Synthetic data: - Randomly generate pick-up

points within a specific area - Generate pick up probability by a

standard uniform distribution - Using Euclidean distance instead

of driving distance - 3 sets: 10, 15, 20 pick-up points

respectively

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Optimal Routes with Real World Data

L=3: → C1 → C3 → C2 L=4: → C1 → C3 → C2 → C7

L=5: → C4 → C1 → C2 → C3 → C7

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Evaluated Algorithms

• BFS(Brute Force Search): - Compute the PTD value for all candidate routes - Find the minimum value as the optimal route • LCPS (LCP Search) - Use LCP algorithm for offline pruning - Compute PTD for remained candidate routes - Get the minimum value as the optimal route• SR(BNL)S: Sky Route + BNL (Block Nested Loop) - Using SkyRoute algorithm for pruning - Applying BNL for the remained candidates to get

skyline routes• SR(D&C)S: SkyRoute + D&C (Divide and Conquer ) - SkyRoute algorithm for pruning - D&C algorithm to get skyline routes

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Experiment Results

• A Comparison of Search Time - LCPS overperforms BFS and

SR(D&C)S

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Experiment Results(cont.)

• Comparison of Search Time(L=3) on Synthetic Data Set

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Experiment Results(cont.)

• The pruning effect

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Experiment Results(cont.)

• Comparison of Skyline Computing

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Multi Evaluation Functions

• Skyline computing is time consuming

• Given a cab and fixed potential pick-up points:

- Skylines are needed to compute only one time

- Search space is pruned drastically

=> Skyline computing will have advantage with multi evaluation criteria

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Multi Evaluation Functions(cont.)

• Using 5 different evaluations (including PTD)

• Select 5 corresponding optimal drive routes

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Conclusion

• This paper developes an energy-efficient mobile recommender system for Taxi drivers. This system is able to recommend a sequence of potential pick-up points for a driver such that the potential travel distance before having customer is minimized.

• This paper provides a Potential Travel Distance(PTD) function for evaluating candidate sequences and two recommendation algorithms LCP and SkyRoute.

• LCP algorithm outperforms BFS and SkyRoute when searching for one optimal route. However, SkyRoute has better performance than BFS and LCP when there is an online demand for different optimal driving routes.

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THANK YOU !!!

Questions??