Data Mining Final Project Nick Foti Eric Kee. Topic: Author Identification Author Identification...
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Transcript of Data Mining Final Project Nick Foti Eric Kee. Topic: Author Identification Author Identification...
Data Mining Final Project
Nick Foti
Eric Kee
Topic: Author Identification• Author Identification
– Given writing samples, can we determine who wrote them?
– This is a well studied field• See also: “stylometry”
– This has been applied to works such as• The Bible• Shakespeare• Modern texts as well
Corpus Design• A corpus is:
– A body of text used for linguistic analysis
• Used Project Gutenberg to create corpus• The corpus was designed as follows
– Four authors of varying similarity• Anne Brontë• Charlotte Brontë• Charles Dickens• Upton Sinclair
– Multiple books per author
• Corpus size: 90,000 lines of text
Dataset Design• Extracted features common in literature
– Word Length– Frequency of “glue” words
• See Appendix A and [1,2] for list of glue words
• Note: corpus was processed using– C#, Matlab, Python
• Data set parameters are– Number of dimensions: 309
• Word length and 308 glue words
– Number of observations: ≈ 3,000• Each obervation ≈ 30 lines of text from a book
Classifier Testing and Analysis• Tested classifier with test data
– Used testing and training data sets • 70% for training, 30% for testing
– Used cross-validation
• Analyzed Classifier Performance– Used ROC plots– Used confusion matrices
• Used common plotting scheme (right)
Anne B.TP
Anne B.FP
Charlotte B.TP
Charlotte B.FP
78%
22%
55%
45%
E X A M P L E
Red Dots Indicate True-Positive Cases
Binary Classification
Word Length Classification• Calculated average word length for each
observation
• Computed gaussian kernel density from word length samples
• Used ROC curve to calculate cutoff– Optimized sensitivity and specificity with equal
importance
Word Length: Anne B. vs Upton S.
100%
0%
Anne B.T P
Anne B.F P
Upton SinclairT P
Upton SinclairF P
100%
0%
Anne BrontëCharlotte Brontë
Word Length: Brontë vs. Brontë
100%
0%
Anne B.T P
Anne B.F P
Charlotte B.T P
Charlotte B.F P
78.1%
21.9%
Anne BrontëCharlotte Brontë
Principal Component Analysis• Used PCA to find a better axis
• Notice: distribution similar to word length distribution
• Is word lengththe only usefuldimension?
Anne Brontë vs. Upton Sinclair
Word Length Density
PCA Density
Without word lengthPrincipal Component Analysis
• It appears that word length is the most useful axis
• We’ll come back to this…
Anne Brontë vs. Upton Sinclair
PCA Density
K-Means• Used K-means to find dominant patterns
– Unnormalized – Normalized
• Trained K-means on training set• To classify observations in test set
– Calculate distance of observation to each class mean
– Assign observation to the closest class
• Performed cross-validation to estimate performance
Unnormalized K-means Anne Brontë vs. Upton Sinclair
98.1%
1.9%
Anne B.T P
Anne B.F P
Upton SinclairT P
Upton SinclairF P
92.1%
7.9%
Unnormalized K-means Anne Brontë vs. Charlotte Brontë
95.7%
4.3%
Anne B.T P
Anne B.F P
Charlotte B.T P
Charlotte B.F P
74.7%
25.3%
Normalized K-means Anne Brontë vs. Upton Sinclair
53.3%
46.7%
Anne B.T P
Anne B.F P
Upton SinclairT P
Upton SinclairF P
49.4%50.6%
Normalized K-means Anne Brontë vs. Charlotte Brontë
15.8%
84.2%
Anne B.T P
Anne B.F P
Charlotte B.T P
Charlotte B.F P
86.7%
13.3 %
Discriminant Analysis• Peformed discriminant analysis
– Computed with equal covariance matrices• Used average Omega of class pairs
– Computed with unequal covariance matrices• Quadratic discrimination fails because covariance
matrices have 0 determinant (see equation below)
– Computed theoretical misclassification probability
• To perform quadratic discriminant analysis– Compute Equation 1 for each class– Choose class with minimum value
(1)
Discriminant Analysis
Anne Brontë vs. Upton Sinclair
92.2%
3.8%
Anne B.T P
Anne B.F P
Upton SinsclairT P
Upton SinclairF P
96.2%
7.8%
Theoretical P(err) = 0.149Empirical P(err) = 0.116
Discriminant Analysis
Anne Brontë vs. Charlotte Brontë
92.7%
7.3%
Anne B.T P
Anne B.F P
Charlotte B.T P
Charlotte B.F P
89.2%
10.8%
Theoretical P(err) = 0.181Empirical P(err) = 0.152
Logistic Regression• Fit linear model to training data on all dimensions• Threw out singular dimensions
– Left with ≈ 298 coefficients + intercept
• Projected training data onto synthetic variable– Found threshold by minimizing error of misclassification
• Projected testing data onto synthetic variable– Used threshold to classify points
Logistic Regression
Anne BTP
Anne BTP
Charlotte BTP
Charlotte BTP
Anne BrontëCharlotte Brontë
89.5%
10.5% 8%
92%
Anne Brontë vs Charlotte Brontë
Logistic Regression
Anne BTP
Anne BFP
Upton STP
Upton SFP
Anne BrontëUpton Sinclair
98%
2%
99%
2%
Anne Brontë vs Upton Sinclair
4-Class Classification
4-Class K-means• Used K-means to find patterns among all
classes– Unnormalized – Normalized
• Trained using a training set
• Tested performance as in 2-class K-means
• Performed cross-validation to estimate performance
Unnormalized K-Means
CD
TP
AB
FP
CB
FP
US
FP
CD
FP
AB
TP
CB
FP
US
FP
CD
FP
AB
FP
CB
TP
US
FP
CD
FP
AB
FP
CB
FP
US
FP
22%
54%
87%
34%
59%
88%
Anne Brontë Charlotte Brontë Upton SinclairCharles Dickens
4-Class Confusion Matrix
Normalized K-Means
CD
TP
AB
FP
CB
FP
US
FP
CD
FP
AB
TP
CB
FP
US
FP
CD
FP
AB
FP
CB
TP
US
FP
CD
FP
AB
FP
CB
FP
US
FP
20%
67%
26%
67%70% 67%
27%
Anne Brontë Charlotte Brontë Upton SinclairCharles Dickens
4-Class Confusion Matrix
Additional K-means testing• Also tested K-means without word length
– Recall that we had perfect classification with 1D word length (see plot below)
– Is K-means using only 1 dimension to classify?
Note: perfect classification only occurs between Anne B. and Sinclair
Anne Brontë vs. Upton Sinclair
CD
TP
AB
FP
CB
FP
US
FP
CD
FP
AB
TP
CB
FP
US
FP
CD
FP
AB
FP
CB
TP
US
FP
CD
FP
AB
FP
CB
FP
US
FP
35%
29%
44%
33%35%
43%
72%
Anne Brontë Charlotte Brontë Upton SinclairCharles Dickens4-Class Confusion Matrix
Unnormalized K-Means (No Word Length)
• K-means can classify without word length
Multinomial Regression• Multinomial distribution
– Extension of binomial distribution• Random variable is allowed to take on n values
• Used multinom(…) to fit log-linear model for training– Used 248 dimensions (max limit on computer)– Returns 3 coefficients per dimension and 3
intercepts
• Found probability that observations belongs to each class
Multinomial Regression• Multinomial Logit Function is
where j are the coefficients and cj are the intercepts
• To classify– Compute probabilities
• Pr(yi = Dickens), Pr(yi = Anne B.), …
– Choose class with maximum probability
Multinomial Regression
CD
TP
AB
FP
CB
FP
US
FP
CD
FP
AB
TP
CB
FP
CB
FP
CD
FP
AB
FP
CB
TP
US
FP
CD
FP
AB
FP
CB
FP
US
FP
78% 86% 83% 93%
Anne Brontë Charlotte Brontë Upton SinclairCharles Dickens
4-Class Confusion Matrix
CD
TP
AB
FP
CB
FP
US
FP
CD
FP
AB
TP
CB
FP
CB
FP
CD
FP
AB
FP
CB
TP
US
FP
CD
FP
AB
FP
CB
FP
US
FP
76% 79% 79% 91%
Upton SinclairCharles Dickens Anne Brontë Charlotte Brontë
(Without Word Length)
4-Class Confusion Matrix
Multinomial Regression
• Multinomial regression does not require word length
Appendix A: Glue WordsI a aboard about above across after again against ago ahead all almost along alongside already also although always am amid amidst among amongst an and another any anybody anyone anything anywhere apart are aren't around as aside at away back backward backwards be because been before beforehand behind being below between beyond both but by can can't cannot could couldn't dare daren't despite did didn't directly do does doesn't doing don't done down during each either else elsewhere enough even ever evermore every everybody everyone everything everywhere except fairly farther few fewer for forever forward from further furthermore had hadn't half hardly has hasn't have haven't having he hence her here hers herself him himself his how however if in indeed inner inside instead into is isn't it its itself just keep kept later least less lest like likewise little low lower many may mayn't me might mightn't mine minus more moreover most much must mustn't my myself near need needn't neither never nevertheless next no no-one nobody none nor not nothing notwithstanding now nowhere of off often on once one ones only onto opposite or other others otherwise ought oughtn't our ours ourselves out outside over own past per perhaps please plus provided quite rather really round same self selves several shall shan't she should shouldn't since so some somebody someday someone something sometimes somewhat still such than that the their theirs them themselves then there therefore these they thing things this those though through throughout thus till to together too towards under underneath undoing unless unlike until up upon upwards us versus very via was wasn't way we well were weren't what whatever when whence whenever where whereas whereby wherein wherever whether which whichever while whilst whither who whoever whom with whose within why without will won't would wouldn't yet you your yours yourself yourselves
Conclusions• Authors can be identified by their word usage frequencies• Word length may be used to distingush between the Brontë
sisters– Word length does not, however, extend to all authors (See Appendix C)
• The glue words describe genuine differences between all four authors– K-means distinguishes the same patterns that multinomial regression
classifies• This indicates that supervised training finds legitimate patterns, rather than
artifacts
• The Brontë sisters are the most similar authors• Upton Sinclair is the most different author
Appendix B: Code• See Attached .R files
Appendix C: Single Dimension 4-Author Classification
CD
TP
AB
FP
CB
FP
US
FP
CD
FP
AB
TP
CB
FP
US
FP
CD
FP
AB
FP
CB
TP
US
FP
CD
FP
AB
FP
CB
FP
US
FP
22%
46%
94%
6%
11%
54%
96%
Anne Brontë Charlotte Brontë Upton SinclairCharles Dickens4-Class Confusion Matrix
3%
Classification using Multinomial Regression
References
[1] Argamon, Saric, Stein, “Style Mining of Electronic Messages for Multiple Authorship Discrimination: First Results,” SIGKDD 2003.
[2] Mitton, “Spelling checkers, spelling correctors and the misspellings of poor spellers,” Information Processing and Management, 1987.
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