General Framework for
Sentiment Analysis of Twitter Data
with Special Attention Towards
Improving Health Awareness
B. J. Gunasekara
Supervisor - Dr R. D. Nawarathna
Introduction
Social networking
encourages users to
express their ideas &
views on
their day-to-day life
style
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
2
Social Media Analytics
• The practice of gathering data from web
resources like blogs and social media and
analyzing that data
• Applications
 Big Data Analysis
 Survey & Marketing
 Decision Making
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
3
Twitter
“To give everyone the
power to create and
share ideas and
information instantly,
without barriers”
4
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
288 Million Monthly Active Users
500 Million Tweets Sent Per Day
152,000+ Tweets by Healthcare
professionals per Day
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
5
Tell your story with
140 characters
 Textual content
 User mentions
 Hashtags
 URLs
 Location
Content of a tweet
6
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
Most of the tweets contain a less
informational value!!!
but a collection of tweets can
provide a
valuable insight into a
population
7
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
One voice can make a difference…
But a million can change the world!
#LetDoctorsBeDoctors #ChildhoodCancer
#BreastCancer
#digitalhealth
#ObesityCareWeek
# Parkinsons#Lyphoma
#Migraine
8
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
Importance of Improving Health
Literacy
• Maintain personal health & wellbeing
• Save on your medical costs
• Avoid Misinterpretations
 chemo isn't so nice. Bad dreams 
 I really am surprised at how bad the side-effects are from
#chemo this time. It's taken me by surprise a bit. Not good.
 hospitals are the worst!! hate the medicine like
smell lingering in the air why did my life become
so bad  hate #chemo ahhh
 Don't let chemotherapy take away your 'you‘ !!!
find your fab again with @Baldlybeautiful
 My dads experimental chemo has officially stopped
his tumors from growing for an entire year now 
9
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
Natural Language Processing
• NLP is the platform built to understand the linguistic
interaction between humans and computers.
• Main Tasks –
 Information Extraction
 Semantic Parsing
 Text To 3D Scene Generation
 Sentiment And Social Meaning
 Machine Translation
 Dialog And Speech Processing
 Automatic Summarization
 Text Segmentation
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
10
• Sentiment analysis is the extraction of
subjective information in a document using
NLP, text analysis and computer linguistics.
• Basic Tasks
 Polarity classification
 Subjectivity/objectivity identification
 Feature/aspect-based sentiment analysis
Sentiment Analysis (Opinion Mining)
11
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
Related Work
• Language feature analysis
• Special frameworks
 Autoregressive Moving Average (ARMA)
 Latent Dirichlet allocation(LDA)
 Ailment Topic Aspect Model (ATAM)
• Derivations from existing models
 BioCaster Ontology,
an extant knowledge model of laymen’s terms
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
12
Problem Statement
• Perform a sentiment analysis which concerns
on improving health awareness,
by analyzing the typical public reaction to
common illnesses and treatments in Twitter
community.
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
13
Methodology
• The proposed method is based on POS Tagged
Bigrams with Naïve Bayes Classifier
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
14
15
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
Feature Extraction
• “200 lives were lost, coz of this massive
dengue outbreak “Tweet
• ['lives', 'lost', 'coz', 'massive', 'dengue',
'outbreak']Unigrams
• ['lives_lost', 'lost_coz', 'coz_massive',
'massive_dengue', 'dengue_outbreak']Bigrams
• [('lives', 'NNS'), ('were', 'VBD'), ('lost',
'VBN'), ('coz', 'NN'), ('of', 'IN'), ('this', 'DT'),
('massive', 'JJ'), ('dengue', 'NN'),
('outbreak', 'NN')]
POS tagging
16
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
Bigram vs. Unigram
• The frequency distribution of bigrams in a
string is used for simple statistical analysis of
text.
• Unlike unigrams, bigrams suggest another
word (increased long-tail specificity )
• Classifier has more contexts to predict the
label than relying on single word.
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
17
POS Tagging
• The process of labeling the particular part of
speech of a word with respect to its definition,
as well as its context.
• Mainly nouns & adjectives were considered.
• Adjectives can modify a noun to add value, to
add better sense.
 Penn Treebank
 Brown Corpus
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
18
• Based on Bayes Theorem
• It assumes that the probability of each attribute
belonging to a given class value is independent
of all other attributes and probabilities of each
attribute belonging to each class.
• Ideal for categorical data – easy to calculate
using ratios.
Naïve Bayes classifier
19
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
System Implementation
• Python 3.4
 Operator - Functional interface to built-in operators.
 Itertools - Numeric and Mathematical Modules
 Re - Searching within and changing text using formal
patterns.
• NLTK
 Probability - Classes for representing and processing
probabilistic information
 Classify - Classifiers
 Metrics - Testing & validation
• Matplotlib & Pylab
• Tkinter
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
20
Experimental Setup
• Specific health topics, illnesses and treatments
were selected using WebMD and Mayo Clinic
• Tweets related to those issues were collected
using NodeXL tool.
• Data was collected over a period of time to
ensure that it does not contain any strange
outliers.
• Training sets
– the datasets were distributed within groups with 10
people in each and the label of a tweet was
assigned according to the tag chosen by
the majority.
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
21
• Both Naïve Bayes and Maximum Entropy
classifiers were used.
• Experiments were carried trying out for
different combinations of bigram/unigram,
with part-of-speech (POS) tagging.
• The performance was evaluated with
cross validation.
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
22
Datasets
23
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
Name
Content
(keywords)
# From To Classified
Polarity Ratio
(Negative:Positive)
Dengue Dengue 472
27/04/2015
20:29
1/7/2015
15:14
Yes 323:149
H1N1 H1N1, Influenza 548
24/06/15
1:45
30/06/15
14:57
Yes 314 : 234
Chemo-I Chemotherapy 170
12/10/15
7:12
22/10/15
14:37
Yes 72 : 98
Chemo-II Chemotherapy 734
12/10/2015
12:04
22/10/15
14:37
No -
Experiment 1: Dengue Dataset
Dengue, Dengue Vaccine
Naïve Bayes MaxEnt
Uni
grams
Bi
grams
POS-
Tagged
Bigrams
Uni
grams
Bi
grams
POS-
Tagged
Bigrams
Accuracy 72.52 75.50 81.82 68.68 70.32 76.06
Weighted
Precision
74.26 74.40 81.69 72.42 65.91 61.28
Weighted
Recall
70.70 73.77 82.26 67.30 70.82 57.70
Weighted
F-measure
70.90 71.00 79.84 67.55 60.57 58.72
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
24
Accuracy
25
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
60.00
65.00
70.00
75.00
80.00
85.00
Naïve Bayes Maximum Entropy
Unigrams
Bigrams
POS-Tagged Bigrams
Weighted F-measure
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
Naïve Bayes Maximum Entropy
Unigrams
Bigrams
POS-Tagged Bigrams
26
Experiment 2: H1N1 Dataset
H1N1,Influenza
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
27
Naïve Bayes
Unigrams Bigrams POS-Tagged Bigrams
Accuracy
67.43 70.59 76.04
Weighted Precision 67.52 70.62 76.09
Weighted Recall 67.95 70.44 76.05
Weighted F-measure 65.69 70.08 75.78
Experiment 3: Chemo-I Dataset
Chemotherapy
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
28
Naïve Bayes
Unigrams Bigrams POS-Tagged Bigrams
Accuracy 75.88 76.47 78.24
Weighted Precision 78.23 78.66 79.96
Weighted Recall 75.10 75.60 77.16
Weighted F-measure 75.69 76.25 77.93
Polarity Checker : Dataset Analysis
29
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
Polarity Checker : Top Stories
Positive Negative
1
#Dengue News: Scientists identify the
skin immune cells targeted by the
dengue virus
United Nations News Centre - At least
3,000 suspected Dengue fever cases
reported in Yemen – UN health agency:
2
Co-ordination meet of BBMP Health and
edu. dept. regarding control and
prevention of Dengue and Chikungunya
fever spread by Mosquito bite. (1/5)
#MyiTimes Country faces largest dengue
epidemic ever - KUALA LUMPUR: The
country is probably facing the largest
dengue problem
3
Well that's a 1st! Malaysia Dept of Health
officials doing house to house calls
looking for dengue hot spots!!
Clean bill of health here!
#Dengue News: Country faces largest
dengue epidemic ever - Free Malaysia
Today
4
@PascalBarollier Fantastic! Thanks for
helping our tribe put a face to dengue
global leaders won't forget.
Country faces largest dengue epidemic
ever: The number of deaths has doubled
this year compared to the same period…
5
@DengueInfo Thank you for helping us
get the word out on Dengue Tribe! To
help put a face to dengue, join here
#Yemen Yemen: At least 3,000 suspected
Dengue fever cases reported in Yemen –
UN health agency says 30
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
Polarity Checker : Text Analysis
31
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
Buzzmeter
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
32
Buzzmeter : Unigram vs. Bigram
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
33
Buzzmeter : Unigram vs. Bigram
• Chemo radiation
• Breast cancer
• Last chemo
• Cancer awareness
34
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
Conclusion
• This research presents a sentiment analysis with
special attention towards improving health
awareness.
 automatic classification of a given tweet
 generate the general attitude from a given set of
tweets, with top stories.
 track most commonly used words/phrases in health
related tweets
• POS-tagged bigrams using nouns + adjectives
with Naive Bayes method produced the
best overall performance.
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
35
Future Recommendations
• Real-time Twitter data analyzing
• Web plug-ins
• Mobile apps
• Identifying pattern of spreading of a disease,
threatened areas & age groups
• Health alerts/warnings system
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
36
Questions?
37
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya
Thank You!!!
38
Department of Stat. & Comp. Sc., Faculty of
Science, University of Peradeniya

General Framework for Sentiment Analysis of Twitter Data, with Special Attention towards Improving Health Awareness - Final Year Research Project

  • 1.
    General Framework for SentimentAnalysis of Twitter Data with Special Attention Towards Improving Health Awareness B. J. Gunasekara Supervisor - Dr R. D. Nawarathna
  • 2.
    Introduction Social networking encourages usersto express their ideas & views on their day-to-day life style Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 2
  • 3.
    Social Media Analytics •The practice of gathering data from web resources like blogs and social media and analyzing that data • Applications  Big Data Analysis  Survey & Marketing  Decision Making Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 3
  • 4.
    Twitter “To give everyonethe power to create and share ideas and information instantly, without barriers” 4 Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya
  • 5.
    288 Million MonthlyActive Users 500 Million Tweets Sent Per Day 152,000+ Tweets by Healthcare professionals per Day Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 5
  • 6.
    Tell your storywith 140 characters  Textual content  User mentions  Hashtags  URLs  Location Content of a tweet 6 Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya
  • 7.
    Most of thetweets contain a less informational value!!! but a collection of tweets can provide a valuable insight into a population 7 Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya
  • 8.
    One voice canmake a difference… But a million can change the world! #LetDoctorsBeDoctors #ChildhoodCancer #BreastCancer #digitalhealth #ObesityCareWeek # Parkinsons#Lyphoma #Migraine 8 Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya
  • 9.
    Importance of ImprovingHealth Literacy • Maintain personal health & wellbeing • Save on your medical costs • Avoid Misinterpretations  chemo isn't so nice. Bad dreams   I really am surprised at how bad the side-effects are from #chemo this time. It's taken me by surprise a bit. Not good.  hospitals are the worst!! hate the medicine like smell lingering in the air why did my life become so bad  hate #chemo ahhh  Don't let chemotherapy take away your 'you‘ !!! find your fab again with @Baldlybeautiful  My dads experimental chemo has officially stopped his tumors from growing for an entire year now  9 Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya
  • 10.
    Natural Language Processing •NLP is the platform built to understand the linguistic interaction between humans and computers. • Main Tasks –  Information Extraction  Semantic Parsing  Text To 3D Scene Generation  Sentiment And Social Meaning  Machine Translation  Dialog And Speech Processing  Automatic Summarization  Text Segmentation Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 10
  • 11.
    • Sentiment analysisis the extraction of subjective information in a document using NLP, text analysis and computer linguistics. • Basic Tasks  Polarity classification  Subjectivity/objectivity identification  Feature/aspect-based sentiment analysis Sentiment Analysis (Opinion Mining) 11 Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya
  • 12.
    Related Work • Languagefeature analysis • Special frameworks  Autoregressive Moving Average (ARMA)  Latent Dirichlet allocation(LDA)  Ailment Topic Aspect Model (ATAM) • Derivations from existing models  BioCaster Ontology, an extant knowledge model of laymen’s terms Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 12
  • 13.
    Problem Statement • Performa sentiment analysis which concerns on improving health awareness, by analyzing the typical public reaction to common illnesses and treatments in Twitter community. Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 13
  • 14.
    Methodology • The proposedmethod is based on POS Tagged Bigrams with Naïve Bayes Classifier Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 14
  • 15.
    15 Department of Stat.& Comp. Sc., Faculty of Science, University of Peradeniya
  • 16.
    Feature Extraction • “200lives were lost, coz of this massive dengue outbreak “Tweet • ['lives', 'lost', 'coz', 'massive', 'dengue', 'outbreak']Unigrams • ['lives_lost', 'lost_coz', 'coz_massive', 'massive_dengue', 'dengue_outbreak']Bigrams • [('lives', 'NNS'), ('were', 'VBD'), ('lost', 'VBN'), ('coz', 'NN'), ('of', 'IN'), ('this', 'DT'), ('massive', 'JJ'), ('dengue', 'NN'), ('outbreak', 'NN')] POS tagging 16 Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya
  • 17.
    Bigram vs. Unigram •The frequency distribution of bigrams in a string is used for simple statistical analysis of text. • Unlike unigrams, bigrams suggest another word (increased long-tail specificity ) • Classifier has more contexts to predict the label than relying on single word. Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 17
  • 18.
    POS Tagging • Theprocess of labeling the particular part of speech of a word with respect to its definition, as well as its context. • Mainly nouns & adjectives were considered. • Adjectives can modify a noun to add value, to add better sense.  Penn Treebank  Brown Corpus Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 18
  • 19.
    • Based onBayes Theorem • It assumes that the probability of each attribute belonging to a given class value is independent of all other attributes and probabilities of each attribute belonging to each class. • Ideal for categorical data – easy to calculate using ratios. Naïve Bayes classifier 19 Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya
  • 20.
    System Implementation • Python3.4  Operator - Functional interface to built-in operators.  Itertools - Numeric and Mathematical Modules  Re - Searching within and changing text using formal patterns. • NLTK  Probability - Classes for representing and processing probabilistic information  Classify - Classifiers  Metrics - Testing & validation • Matplotlib & Pylab • Tkinter Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 20
  • 21.
    Experimental Setup • Specifichealth topics, illnesses and treatments were selected using WebMD and Mayo Clinic • Tweets related to those issues were collected using NodeXL tool. • Data was collected over a period of time to ensure that it does not contain any strange outliers. • Training sets – the datasets were distributed within groups with 10 people in each and the label of a tweet was assigned according to the tag chosen by the majority. Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 21
  • 22.
    • Both NaïveBayes and Maximum Entropy classifiers were used. • Experiments were carried trying out for different combinations of bigram/unigram, with part-of-speech (POS) tagging. • The performance was evaluated with cross validation. Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 22
  • 23.
    Datasets 23 Department of Stat.& Comp. Sc., Faculty of Science, University of Peradeniya Name Content (keywords) # From To Classified Polarity Ratio (Negative:Positive) Dengue Dengue 472 27/04/2015 20:29 1/7/2015 15:14 Yes 323:149 H1N1 H1N1, Influenza 548 24/06/15 1:45 30/06/15 14:57 Yes 314 : 234 Chemo-I Chemotherapy 170 12/10/15 7:12 22/10/15 14:37 Yes 72 : 98 Chemo-II Chemotherapy 734 12/10/2015 12:04 22/10/15 14:37 No -
  • 24.
    Experiment 1: DengueDataset Dengue, Dengue Vaccine Naïve Bayes MaxEnt Uni grams Bi grams POS- Tagged Bigrams Uni grams Bi grams POS- Tagged Bigrams Accuracy 72.52 75.50 81.82 68.68 70.32 76.06 Weighted Precision 74.26 74.40 81.69 72.42 65.91 61.28 Weighted Recall 70.70 73.77 82.26 67.30 70.82 57.70 Weighted F-measure 70.90 71.00 79.84 67.55 60.57 58.72 Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 24
  • 25.
    Accuracy 25 Department of Stat.& Comp. Sc., Faculty of Science, University of Peradeniya 60.00 65.00 70.00 75.00 80.00 85.00 Naïve Bayes Maximum Entropy Unigrams Bigrams POS-Tagged Bigrams
  • 26.
    Weighted F-measure Department ofStat. & Comp. Sc., Faculty of Science, University of Peradeniya 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 Naïve Bayes Maximum Entropy Unigrams Bigrams POS-Tagged Bigrams 26
  • 27.
    Experiment 2: H1N1Dataset H1N1,Influenza Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 27 Naïve Bayes Unigrams Bigrams POS-Tagged Bigrams Accuracy 67.43 70.59 76.04 Weighted Precision 67.52 70.62 76.09 Weighted Recall 67.95 70.44 76.05 Weighted F-measure 65.69 70.08 75.78
  • 28.
    Experiment 3: Chemo-IDataset Chemotherapy Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 28 Naïve Bayes Unigrams Bigrams POS-Tagged Bigrams Accuracy 75.88 76.47 78.24 Weighted Precision 78.23 78.66 79.96 Weighted Recall 75.10 75.60 77.16 Weighted F-measure 75.69 76.25 77.93
  • 29.
    Polarity Checker :Dataset Analysis 29 Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya
  • 30.
    Polarity Checker :Top Stories Positive Negative 1 #Dengue News: Scientists identify the skin immune cells targeted by the dengue virus United Nations News Centre - At least 3,000 suspected Dengue fever cases reported in Yemen – UN health agency: 2 Co-ordination meet of BBMP Health and edu. dept. regarding control and prevention of Dengue and Chikungunya fever spread by Mosquito bite. (1/5) #MyiTimes Country faces largest dengue epidemic ever - KUALA LUMPUR: The country is probably facing the largest dengue problem 3 Well that's a 1st! Malaysia Dept of Health officials doing house to house calls looking for dengue hot spots!! Clean bill of health here! #Dengue News: Country faces largest dengue epidemic ever - Free Malaysia Today 4 @PascalBarollier Fantastic! Thanks for helping our tribe put a face to dengue global leaders won't forget. Country faces largest dengue epidemic ever: The number of deaths has doubled this year compared to the same period… 5 @DengueInfo Thank you for helping us get the word out on Dengue Tribe! To help put a face to dengue, join here #Yemen Yemen: At least 3,000 suspected Dengue fever cases reported in Yemen – UN health agency says 30 Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya
  • 31.
    Polarity Checker :Text Analysis 31 Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya
  • 32.
    Buzzmeter Department of Stat.& Comp. Sc., Faculty of Science, University of Peradeniya 32
  • 33.
    Buzzmeter : Unigramvs. Bigram Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 33
  • 34.
    Buzzmeter : Unigramvs. Bigram • Chemo radiation • Breast cancer • Last chemo • Cancer awareness 34 Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya
  • 35.
    Conclusion • This researchpresents a sentiment analysis with special attention towards improving health awareness.  automatic classification of a given tweet  generate the general attitude from a given set of tweets, with top stories.  track most commonly used words/phrases in health related tweets • POS-tagged bigrams using nouns + adjectives with Naive Bayes method produced the best overall performance. Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 35
  • 36.
    Future Recommendations • Real-timeTwitter data analyzing • Web plug-ins • Mobile apps • Identifying pattern of spreading of a disease, threatened areas & age groups • Health alerts/warnings system Department of Stat. & Comp. Sc., Faculty of Science, University of Peradeniya 36
  • 37.
    Questions? 37 Department of Stat.& Comp. Sc., Faculty of Science, University of Peradeniya
  • 38.
    Thank You!!! 38 Department ofStat. & Comp. Sc., Faculty of Science, University of Peradeniya