K nn cf a temporal social network
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k NN CF: A Temporal Social Network. Neal Lathia, Stephen Hailes, Licia Capra University College London RecSys ’ 08. Advisor: Hsin-Hsi Chen Reporter: Y.H Chang 2009/03/09. INTRODUCTION(1/4). Recommender System:

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K nn cf a temporal social network

kNN CF: A Temporal Social Network

Neal Lathia, Stephen Hailes, Licia Capra

University College London

RecSys’08

Advisor: Hsin-Hsi Chen

Reporter: Y.H Chang

2009/03/09

kNN CF: A Temporal

Social Network


Introduction 1 4

INTRODUCTION(1/4)

  • Recommender System:

    • It has been an important component, or even core technology, of online business.

    • EX: Amazon, Netflix (Netflix prize competition)

  • The process of computing recommendations is reduced to a problem of predicting the correct rating that users would apply to unrated items

kNN CF: A Temporal

Social Network


Introduction 2 4

INTRODUCTION(2/4)

  • k-Nearest Neighborhood Collaborative Filtering(kNN CF/ kNN) has surfaced amongst the most popular underlying algorithms of recommender systems.

    • Collaborative Filtering: using a set of user rating profiles to predict ratings of unrated items

kNN CF: A Temporal

Social Network


Introduction 3 4

INTRODUCTION(3/4)

  • In order to understand the effect of kNN, the algorithm can be viewed as a process that generates a social networkgraph, where nodes are users and edges connect k similar users.

  • In this work (1)we analyse user-user kNN graph from temporal perspective (2) we observe the emergent properties of the entire graph as algorithm parameters change.

kNN CF: A Temporal

Social Network


Introduction 4 4

INTRODUCTION(4/4)

The analysis is decomposed into four separate stages:

  • Individual Nodes

  • Node Pairs

  • Node Neighborhoods

  • Community Graphs

kNN CF: A Temporal

Social Network


I user profiles over time

I. USER PROFILES OVER TIME

kNN CF: A Temporal

Social Network


User profiles over time 1 2

USER PROFILES OVER TIME (1/2)

  • In this work we focus on the two MovieLens datasets

  • 100t MovieLens

    • 100, 000 ratings of 1682 movies by 943 users. (1997.09.20 to 1998.04.22)

  • 1000t MovieLens

    • About 1 million ratings of 3900 movies by 6040 users. (2000.04.25 to 2003.02.28)

kNN CF: A Temporal

Social Network


User profiles over time 2 2

USER PROFILES OVER TIME (2/2)

kNN CF: A Temporal

Social Network


Ii user pairs over time

II. USER PAIRS OVER TIME

kNN CF: A Temporal

Social Network


User pairs over time 1 6

user a, item i

b is a’s neighbor

:item i’s rating of neighbor b

:neighbor b’s mean rating

USER PAIRS OVER TIME(1/6)

  • Predictions are often computed as a weighted average of deviation from neighbor means:

Similarity between the

User a and its’ neighbor b

kNN CF: A Temporal

Social Network


User pairs over time 2 6 four highly cited methods of the similarity between users

USER PAIRS OVER TIME(2/6) - four highly cited methods of the similarity between users

Total n items

kNN CF: A Temporal

Social Network


User pairs over time 3 6 evolution of similarity

USER PAIRS OVER TIME(3/6) -evolution of similarity

kNN CF: A Temporal

Social Network


User pairs over time 4 6

USER PAIRS OVER TIME(4/6)

  • In this work we plot the similarity at time t, sim(t) against the similarity at the time of the next update, sim(t + 1).

  • The distance from points to the diagonal represents the changed from one update to the next.

kNN CF: A Temporal

Social Network


User pairs over time 5 6 sim t against sim t 1

COR

wPCC

Range:-1~+1

PCC

Range:-1~+1

VS

USER PAIRS OVER TIME(5/6)- sim(t) against sim(t+1)

sim(t + 1)

sim(t)

kNN CF: A Temporal

Social Network


User pairs over time 6 6

USER PAIRS OVER TIME(6/6)

We classified those similarity methods according to their temporal behavior—

  • Incremental:COR and wPCC

    • The differnce between (t) and (t+1) is small.

    • Growing

  • Corrective: VS method

    • Jumps from 0 to near-perfect

      then degrade

  • Near-random: PCC

    • near-random behavior

kNN CF: A Temporal

Social Network


Iii dynamic neighbourhoods

III. DYNAMIC NEIGHBOURHOODS

kNN CF: A Temporal

Social Network


Dynamic neighbourhoods 1 2

DYNAMIC NEIGHBOURHOODS(1/2)

  • The often-cited assumption of collaborative filtering is that users who have been like-minded in the past will continue sharing opinions in the future.

  • When applying user-user kNN CF, we would expect each user’s neighborhood to converge to a fixed set of neighbors over time

kNN CF: A Temporal

Social Network


Dynamic neighbourhoods 2 2

DYNAMIC NEIGHBOURHOODS(2/2)

(This experiment updated daily.)

The actual number of neighbors that a user will be connected to depends on:

  • similarity measure

  • neighborhood size k

The stepper they are,

the faster the user is

meeting other recommenders.

COR and wPCC

outperform the VS and PCC

(N.Lathia et al.,2008)

New recommend-ers Left

time

kNN CF: A Temporal

Social Network


Iv nearest neighbour graphs

IV. NEAREST-NEIGHBOUR GRAPHS

kNN CF: A Temporal

Social Network


Nearest neighbour graphs 1 5

NEAREST-NEIGHBOUR GRAPHS(1/5)

  • The last section, we focus on non-temporal characteristics of the dataset.(wPCC)

    • Path Length

    • Connectedness (using only positive sim)

    • Reciprocity: a characteristic of graphs explored in social network analysis; in this work, it is the proportion of users who are in other’s top-k

kNN CF: A Temporal

Social Network


Nearest neighbour graphs 2 5

NEAREST-NEIGHBOUR GRAPHS(2/5)

kNN CF: A Temporal

Social Network


Nearest neighbour graphs 3 5

NEAREST-NEIGHBOUR GRAPHS(3/5)

(1)There may be some users who are not in any other’s top-k. Their ratings are therefore inaccesible and will not be used in any prediction.

power law

kNN CF: A Temporal

Social Network


Nearest neighbour graphs 4 5

NEAREST-NEIGHBOUR GRAPHS(4/5)

(2)Some users will have incredible high in-degree. We call this group “power users”

kNN CF: A Temporal

Social Network


Nearest neighbour graphs 5 5

NEAREST-NEIGHBOUR GRAPHS(5/5)

  • More experiments about “power users”:

    • 1. remove the power users’ ability to prediction

    • 2. only the top power users are allow to contribute to the prediction

  • Results:

    • The remaining users can still make significant contribution to each user’s predictions

    • The 10 topmost power users hold access to over 50% of the dataset.

kNN CF: A Temporal

Social Network


Discussion

DISCUSSION

  • The evolution of similarity between any pair of users is dominated by the similarity method, and the four measures we explored can be classified into three categories (incremental, corrective, near-random) based on the temporal properties

  • Measures that are known to perform better display the same behavior: they are incremental, connect each user quicker, and offer broader access to the ratings in the training set.

kNN CF: A Temporal

Social Network


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