link prediction 방법의 개념 및 활용

Link Prediction방법의개념및활용

Kyunghoon Kim

UNIST Mathematical Sciences

[email protected]

2015. 9. 3.

Kyunghoon Kim (UNIST) Network Link Prediction 2015. 9. 3. 1 / 86

http://www.math.unist.ac.kr/

About me

Speaker

Kyunghoon Kim (Graduate Student)

UNIST (Ulsan National Institute of Science and Technology)

Mathematical Sciences, School of Natural Sciences

Lab

Adviser : Bongsoo Jang

Homepage : http://amath.unist.ac.kr

“Be the light that shines the world with science and technology.”


https://www.linkedin.com/pub/kyunghoon-kim/44/889/69a

http://math.unist.ac.kr

https://www.linkedin.com/pub/bongsoo-jang/63/829/197

http://amath.unist.ac.kr

목차

1 Social Network

2 Link Prediction

Research Trend

Definition

Framework

Example

Theory

3 Link Prediction with Python

4 데모


Social Network

A social network is a social structure made up of

a set of social actors (such as individuals or organizations)

and a set of the dyadic ties (or interactions, relations) between these actors.


Social Network : Internet

Ref: http://supraliminalsolutions.com/


Social Network : Information exchange

Ref: https://niftynotcool.files.wordpress.com/2013/12/internet-wallpaper-hd.jpg


Social Network : Degree Centrality


Social Network : Betweenness Centrality


Social Network : IoT (Internet of Things)

Ref: http://www-01.ibm.com/common/ssi/cgi-bin/ssialias?subtype=XB&infotype=PM&appname=GBSE_GB_TI_

USEN&htmlfid=GBE03620USEN&attachment=GBE03620USEN.PDF


http://www-01.ibm.com/common/ssi/cgi-bin/ssialias?subtype=XB&infotype=PM&appname=GBSE_GB_TI_USEN&htmlfid=GBE03620USEN&attachment=GBE03620USEN.PDF

http://www-01.ibm.com/common/ssi/cgi-bin/ssialias?subtype=XB&infotype=PM&appname=GBSE_GB_TI_USEN&htmlfid=GBE03620USEN&attachment=GBE03620USEN.PDF

Social Network : Problem

Non-trivial taskincompletion

dynamic


Research Trend of Link Prediction

Keyword “link prediction social network”

Wang, Peng, et al. ”Link prediction in social networks: the state-of-the-art.” Science China Information Sciences 58.1 (2015):

1-38.Kyunghoon Kim (UNIST) Network Link Prediction 2015. 9. 3. 11 / 86

Application of Link Prediction

1 추천시스템 (links)

친구추천 (12’)

공동저자추천 (07’)

온라인쇼핑몰의상품추천 (11’)

특허추천 (13’)

타분야협력자추천 (12’)

연락처추천 (11’)


http://dl.acm.org/citation.cfm?id=2180866

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=5996005

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6009562

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.297.3100


http://arxiv.org/abs/1102.1753


2 복잡계연구 (links)

네트워크진화연구 (02’)

웹사이트링크예측 (02’)


http://arxiv.org/abs/cond-mat/0104162



3 다양한분야에적용 (links)

헬스케어 (12’)

단백질네트워크 (12’)

비정상적커뮤니케이션확인 (09’)


http://link.springer.com/article/10.1007%2Fs13721-012-0005-7

http://link.springer.com/article/10.1007%2Fs13721-012-0005-7



Wang, Peng, et al. ”Link prediction in social networks: the state-of-the-art.” Science China Information Sciences 58.1 (2015)


Definition of Link Prediction

사회망(social networks)에서링크예측이란

지금의네트워크에서빠진링크를예측하는것

미래의네트워크에서새롭게나타나거나사라질링크를예측하는것



사회망

G (V ,E ) at t

에대해,

링크가생기거나사라지는것을 (t ′ > t)

빠진링크나관찰되지않은링크가있는것을 (at t)

찾아내는것.


Framework of Link Prediction

Wang, Peng, et al. ”Link prediction in social networks: the state-of-the-art.”

Science China Information Sciences 58.1 (2015): 1-38.


Link Prediction Example : Terrorist Networks



Problems of criminal network analysis

1 Incompleteness - the inevitability of missing nodes and links that the

investigators will not uncover.

2 Fuzzy boundaries - the difficulty in deciding who to include and who

not to include.

3 Dynamic - these networks are not static, they are always changing.

http://pear.accc.uic.edu/ojs/index.php/fm/article/view/941/863


http://pear.accc.uic.edu/ojs/index.php/fm/article/view/941/863


Several summaries of data about hijackers in major newspaper

Sydney Morning Herald, 2001

Washington Post, 2001

From 2 to 6 weeks after the event, it appeared that a new relationship

or node was added to the network on a daily basis.


링크예측의이론

https://www.cs.umd.edu/class/spring2008/cmsc828g/

Slides/link-prediction.pdf

Liben‐Nowell, David, and Jon Kleinberg. “The link‐prediction problem

for social networks.” Journal of the American society for information

science and technology 58.7 (2007): 1019-1031.


https://www.cs.umd.edu/class/spring2008/cmsc828g/Slides/link-prediction.pdf

https://www.cs.umd.edu/class/spring2008/cmsc828g/Slides/link-prediction.pdf

http://www.cs.cornell.edu/home/kleinber/link-pred.pdf



링크예측의세분화

Wang, Peng, et al. ”Link prediction in social networks: the state-of-the-art.”


링크예측의세분화


Link Prediction with Python

Contents

Scikit-learn

Large-scale Matrix

Books

NumPy & Pandas

Morpheme Analyzer

NetworkX

IPython & D3.js


K-means Algorithm


K-means Algorithm

1 from sklearn import cluster

2

3 k = 2

4 kmeans = cluster.KMeans(n_clusters=k)

5 kmeans.fit(data)


K-means Algorithm

http://cjauvin.blogspot.kr/2014/03/k-means-vs-louvain.html


http://cjauvin.blogspot.kr/2014/03/k-means-vs-louvain.html

얼마나큰행렬을다룰수있나요?

NetworkX는기본네트워크구조로 “dictionary of dictionaries of

dictionaries”를사용

dict-of-dicts-of-dicts 자료 구조의 장점:Find edges and remove edges with two dictionary look-ups.

Prefer to “lists” because of fast lookup with sparse storage.

Prefer to “sets” since data can be attached to edge.

G[u][v] returns the edge attribute dictionary.

n in G tests if node n is in graph G.

for n in G: iterates through the graph.

for nbr in G[n]: iterates through neighbors.

https://networkx.github.io/documentation/latest/reference/introduction.html


https://networkx.github.io/documentation/latest/reference/introduction.html


Million-scale Graphs Analytic Frameworks

SNAP : http://snap.stanford.edu/snappy/index.html

Billion-scale Graphs Analytic Frameworks

Apache Hama : https://hama.apache.org/ (소개글)

Pegasus : http://www.cs.cmu.edu/~pegasus/

s2graph : https://github.com/daumkakao/s2graph (슬라이드)

Graph Database

Neo4j : http://neo4j.com/

OrientDB : http://orientdb.com/


http://snap.stanford.edu/snappy/index.html

https://hama.apache.org/

http://www.hadoopsphere.com/2015/06/large-scale-graph-processing-with.html

http://www.cs.cmu.edu/~pegasus/

https://github.com/daumkakao/s2graph

http://www.slideshare.net/HBaseCon/use-cases-session-5

http://neo4j.com/

http://orientdb.com/

네트워크공부를위한기본서적

1 Networks: An Introduction by Mark Newman

2 링크 : 21세기를지배하는네트워크과학 LINKED The New Science of Networks


링크를예측하기위한준비운동

1 NumPy :계산속도에최적화된모듈

2 Pandas :데이터구조


NumPy: Numerical Python

다차원배열

1 근접메모리를사용하고, C언어로구성됨

2 하나의데이터타입

3 연산이한번에배열내의모든요소에적용됨

http://www.numpy.org/


http://www.numpy.org/


1 tic = timeit.default_timer()

2 for index, value in enumerate(b):

3 b[index] = value*1.1

4 toc = timeit.default_timer()

5 print toc-tic

6 1.82178592682



1 import numpy as np

2 import timeit

3 a = np.arange(1e7)

4 b = list(a)

5 tic = timeit.default_timer()

6 a = a*1.1

7 toc = timeit.default_timer()

8 print toc-tic

9 0.029629945755

사용방법에따라, ndarray의연산속도는 list()보다훨씬빠름.


Pandas: Python Data Analysis Library


Pandas / get data yahoo

1 %pylab inline

2 import pandas as pd

3 import pandas.io.data

4 import datetime

5 start=datetime.datetime(2015,1,1); end=datetime.datetime(2015,8,26)

6 text = """A, AAPL, AMCC, AMD, AMGN, AMKR, AMNT.OB, AMZN, APC, ASOG.PK, AULO.OB, BAC, BBD-A.TO, BBD-B.TO, BEEI.OB, BKSD.OB, BP.BA, BPMI.PK, C, CAJT.PK, CAT, CGFI.OB, CHINA, CHKP, CIEN, CL, CLEC, CLNE, CNLG, COKE, CPAH.OB, CPHD, CPRT, CRDN, CRGN, CSCO, CSRVE.OB, CTS, CTXS, CVM, CVX, DE, DELL, DLTR, DO, DOG, DSCM, DVNNF.OB, DYN, EGN, ELNK, ELX, EP, ERJ, ETFC, EVEH.OB, FARO, FDO, FILE, FLIR, FNLY.OB, FNPR.OB, FORC.OB, FPP, GAGO.PK, GBVS.OB, GCAP.PK, GDKI.PK, GDTI.OB, GE, GEPT.PK, GERN, GFCI.PK, GILD, GLW, GOOG, GRDB.OB, GRMN, GS, GTXO.OB, GWGI.PK, HAL, HAST, HCKT, HD, HK, HPQ, HRAL.PK, IBM, IMDS.OB, IMGM.OB, INFY, INTC, IOC, IRF, JAVA, JCP, JDSU, JNJ, JNPR, JYHW.OB, K, KDSM.OB, KKD, KLDO.OB, KO, LEG, LOW, LRCX, LU, medx, MINI, MKC, MLNK, MNLU.OB, MO, MON, MOT, MRK, MSFT, MVBY.PK, MYL, NGEN, NGLS, NOIZ, NOK, NOVL, NOVOE.OB, NTGR, NVDA, NVS, NXRA.PK, OMI, ORCL, OSTK, PDLI, PEGA, PEP, PFE, PG, PHLI.OB, PNM, PPBV.OB, PWER, PYTO.OB, PZE, PZZA, Q, QCOM, QPCIE.OB, RIG, RIO, S, SBR, SCMR, SCON, SGAL.OB, SGP, SHRPQ.PK, SIFY, SIRI, SLB, smd, SUN, SVA, T, TAMO.OB, TASR, TEF, TNEN.OB, TRXAQ.PK, TWX, TXN, UTVG.OB, VOD, VRTL.PK, VSCI, VTSS.PK, VZ, WAG, WCYO.OB, WFC, WLL, WMT"""

7 text = text.replace(’ ’, ’’).split(’,’)

8 corps = []

9 for t in text:

10 if ’.’ not in t:

11 corps.append(t)

Code : https://goo.gl/8ddrnSKyunghoon Kim (UNIST) Network Link Prediction 2015. 9. 3. 50 / 86

https://goo.gl/8ddrnS

Pandas / get data yahoo

1 df = pd.io.data.get_data_yahoo(corps, start=start, end=end)

2 df[’Adj Close’].head()


Pandas / Return Value

1 returns = df[’Adj Close’].pct_change()

2 corr = returns.corr()

3 corr


Pandas / Correlation

1 bm = corr>0.5

2 bm.astype(int)


Pandas / Convert to array

1 mat = bm.astype(int).values

2 mat


NetworkX / from numpy matrix

1 import networkx as nx

2 graph = nx.from_numpy_matrix(mat)

3 graph = nx.relabel_nodes(graph, dict(enumerate(bm.columns)))

4 nx.draw(graph, with_labels=True)


NetworkX / figsize

1 plt.figure(figsize=(20, 20))

2 nx.draw_spring(graph, with_labels=True)


NetworkX / figsize

1 first = sorted(nx.connected_components(graph),

2 key=len, reverse=True)[0]

3 G = graph.subgraph(first)

4 nx.draw(G, with_labels=True)


NetworkX /결국 Gephi에서작업?

1 nx.write_gexf(G, ’graph.gexf’)

Gephi에서 gexf열기


http://gephi.org

KoNLPy


mecab-ko

은전한닢 프로젝트( http://eunjeon.blogspot.kr/ )

검색에서쓸만한오픈소스한국어형태소분석기를만들자! by이용운,유영호

1 $ sudo docker pull koorukuroo/mecab-ko

2 $ sudo docker run -i -t koorukuroo/mecab-ko:0.1

3 안녕하세요

4 안녕 NNG,*,T,안녕,*,*,*,*

5 하 XSV,*,F,하,*,*,*,*

6 세요 EP+EF,*,F,세요,Inflect,EP,EF,시/EP/*+어요/EF/*

7 EOS

https://github.com/koorukuroo/mecab-ko


http://eunjeon.blogspot.kr/

https://github.com/koorukuroo/mecab-ko

mecab-ko


mecab-ko-web

1 $ sudo docker pull koorukuroo/mecab-ko-web

2 $ sudo docker run -i -t koorukuroo/mecab-ko-web:0.1

3 172.17.0.43 (Docker Container IP)

4 127.0.0.1

5 * Running on http://0.0.0.0:5000/ (Press CTRL+C to quit)

1 >>> import urllib2

2 >>> response = urllib2.urlopen(’http://172.17.0.43:5000/?text=안녕’)

3 >>> text = response.read()

4 >>> print text

5 안녕 NNG,*,T,안녕,*,*,*,*

6 EOS

https://github.com/koorukuroo/mecab-ko-web


https://github.com/koorukuroo/mecab-ko-web

mecab api

1 http://information.center/api/korean?sc=APIKEY&s=안녕하세요

http://information.center/korean


http://information.center/korean

mecab api

1 import Umorpheme.morpheme as um

2 from collections import OrderedDict

3

4 s = ’유니스트는 울산에 있습니다’

5 server = ’http://information.center/api/korean’

6 apikey = ’’ # Register at http://information.center/korean

7 data = um.analyzer(s, server, apikey, ’유니스트,UNIST’, 1)

8

9 temp =

10 for key, value in data.items():

11 temp[int(key)] = value

12 data = OrderedDict(sorted(temp.items()))

13

14 for i, j in data.iteritems():

15 print i, j[’data’], j[’feature’]

0 유니스트 CUSTOM

1 는 JX

2 울산 NNP

3 에 JKB

4 있 VV

5 습니다 EC


Pandas에대한자세한내용은..


링크예측의기본정의

Γ (x) :점 x의이웃들의집합

|Γ (x)| :점 x의이웃들의개수


공통이웃들

공통 이웃들(Common Neighbors):

CN(u, v) = |Γ (u) ∩ Γ (v)|

본 그래프는 실제가 아닌 가상으로 설정된 상황임을 알려드립니다


리소스할당지수

리소스 할당 지수(Resource Allocation Index):∑w∈Γ (u)∩Γ (v)

1|Γ (w)|



리소스 할당 지수(Resource Allocation Index):∑w∈Γ (u)∩Γ (v)

1|Γ (w)|

preds = nx.resource_allocation_index(G)

for u, v, p in preds:

print ’(%s, %s) -> %.8f’ % (u, v, p)



(수지, 혜리) -> 0.33333333

(수지, 경훈) -> 0.83333333

(아이유, 민호) -> 1.00000000

(혜리, 민호) -> 0.00000000

(혜리, 경훈) -> 0.33333333



∑w∈Γ (u)∩Γ (v)

1|Γ (w)|

(수지, 혜리) -> 0.33333333

(수지, 경훈) -> 0.83333333

(아이유, 민호) -> 1.00000000

(혜리, 민호) -> 0.00000000

(혜리, 경훈) -> 0.33333333


한국어표시하기

1 pip install --upgrade

2 git+https://github.com/koorukuroo/networkx_for_unicode

1 import matplotlib.font_manager as fm

2 fp1 = fm.FontProperties(fname="./NotoSansKR-Regular.otf")

3 nx.set_fontproperties(fp1)

4 G = nx.Graph()

5 G.add_edge(u’한국어’,u’영어’)

6 nx.draw(G, with_labels=True)


선호적연결

선호적 연결(Preferential attachment):

|Γ (u)||Γ (v)|


선호적연결

nx.draw_networkx_nodes(G, pos, node_size=500, node_color=’yellow’)

nx.draw_networkx_edges(G, pos, alpha=0.2)

nx.draw_networkx_labels(G, pos, font_size=20);

selected_lines = []

for u in G.nodes_iter():

preds = nx.preferential_attachment(G, [(u, v) for v in nx.non_neighbors(G, u)])

largest = heapq.nlargest(5, preds, key = lambda x: x[2])

for l in largest:

selected_lines.append(l)

subG = nx.Graph()

for line in selected_lines:

print line[0], line[1], line[2]

if line[2]>1:

subG.add_edge(line[0], line[1])

pos_subG = dict()

for s in subG.nodes():

pos_subG[s] = pos[s]

nx.draw_networkx_edges(subG, pos_subG, edge_color=’red’)


선호적연결


선호적연결

1 degree = nx.degree_centrality(G)

2

3 nx.draw_networkx_nodes(G, pos, node_color=’yellow’, nodelist=degree.keys(),

4 node_size=np.array(degree.values())*10000)

5 nx.draw_networkx_edges(G, pos, alpha=0.2)

6 nx.draw_networkx_labels(G, pos, font_size=20);

7

8 selected_lines = []

9 for u in G.nodes_iter():

10 preds = nx.preferential_attachment(G, [(u, v) for v in nx.non_neighbors(G, u)])

11 largest = heapq.nlargest(5, preds, key = lambda x: x[2])

12 for l in largest:

13 selected_lines.append(l)

14 subG = nx.Graph()

15 for line in selected_lines:

16 print line[0], line[1], line[2]

17 if line[2]>1:

18 subG.add_edge(line[0], line[1])

19 pos_subG = dict()

20 for s in subG.nodes():

21 pos_subG[s] = pos[s]

22 nx.draw_networkx_edges(subG, pos_subG, edge_color=’red’)


선호적연결


NetworkX의 Link Prediction함수들


http://networkx.github.io/documentation/development/reference/algorithms.link_prediction.html

LPmade

https://github.com/rlichtenwalter/LPmade


https://github.com/rlichtenwalter/LPmade

데모

matplotlib

ipython과 d3.js


ipython과 d3.js

1 from IPython.display import display, HTML


d3.js (Data-Driven Documents)


http://d3js.org

ipython에서파일쓰기


ipython에서 d3.js가동하기

코드 https://goo.gl/LpxsKc


https://goo.gl/LpxsKc

ipython과 d3.js

1 edges = d3_graph(G)

2 make_html_graph(edges, 1000, 500) # make_html_graph(edges)

3

4 %%HTML

5 <iframe src="d3.html" width=100% height=500 frameborder=0></iframe>

Demo 화면 : http://i.imgur.com/FeQ9kii.gif


http://i.imgur.com/FeQ9kii.gif

The End


link prediction 방법의 개념 및 활용

Education