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```"St. Petersburg National Research University of Information Technologies, Mechanics and
Optics"
Department of "Secure Information Technology"
Identification of the authors of short
messages portals on the Internet using
the methods of mathematical
linguistics.
Specialty 05.13.19
"Methods and systems of information protection, information security"
Supervisor: doctor of engineering science,
Lebedev I.S.
Purpose and objectives
The goal - a study of methods to identificate users.
Objectives:
study and development of scientific-methodical system
of identification of authorship of textual information
creation of the program layout, based on the proposed
approach
assessment of the performance and efficiency of the
developed prototyping implementation
Prospective directions of research
The use of naive Bayes classifier
Analysis based on the N - grams
Analysis based on latent Dirichlet allocation
Architecture of the proposed software
1
Users
Topic
1
*
*
*
*
Posts
Words
Vocabulary
Filters
Words
in
Posts
Naive Bayes classifier
Bayes theorem:
𝑃 𝑑 𝑐 𝑃(𝑐)
𝑃 𝑐𝑑 =
𝑃(𝑑)
𝑃 𝑐 𝑑 - probability that document 𝑑 belongs to the class 𝑐 ;
𝑃 𝑑 𝑐 - probability of finding document 𝑑 of any documents class 𝑐;
𝑃(𝑐) - unconditional probability of finding a document of class 𝑐 in the
case of documents;
𝑃(𝑑) - unconditional probability of a document 𝑑 in the case of
documents.
Naive Bayes classifier
Maximum a posteriori estimation:
𝑐𝑚𝑎𝑝 = argmax
𝑃 𝑑 𝑐 𝑃(𝑐)
𝑃(𝑑)
𝑐∈𝐶
𝑛
𝑃 𝑑 𝑐 ≈ 𝑃 𝜔1 𝑐 𝑃 𝜔2 𝑐 … 𝑃 𝜔𝑛 𝑐 ≈
𝑃(𝜔𝑖 |𝑐)
𝑖
𝑛
𝑐𝑚𝑎𝑝 = argmax 𝑃(𝑐)
𝑐∈𝐶
𝑃(𝜔𝑖 |𝑐)
𝑖
Naive Bayes classifier
The problem of arithmetic overflow:
𝑛
𝑐𝑚𝑎𝑝 = argmax log 𝑃(𝑐) +
𝑐∈𝐶
log 𝑃(𝜔𝑖 |𝑐)
𝑖
Estimation of parameters of the Bayes model:
𝐷𝑐
,
𝐷
•𝑃 𝑐 =
where 𝐷𝑐 - number of documents belong to class 𝑐, 𝐷 total number of documents in the training set;
• 𝑃 𝜔𝑖 𝑐 =
𝑊𝑖𝑐
,
𝑊
𝑖′ ∈𝑉 𝑖′ 𝑐
where 𝑊𝑖𝑐 - number of times as the i-th word
appears in the documents of class 𝑐, 𝑉 - dictionary of a set of
documents (a list of all unique words).
Naive Bayes classifier
The problem of unknown words:
𝑊𝑖𝑐 + 1
𝑊𝑖𝑐 + 1
𝑃 𝜔𝑖 𝑐 =
=
𝑉 + 𝑖 ′ ∈𝑉 𝑊𝑖 ′ 𝑐
𝑖 ′ ∈𝑉 (𝑊𝑖 ′ 𝑐 +1)
The final view of the formula:
𝑐𝑚𝑎𝑝
𝐷𝑐
= argmax log +
𝐷
𝑐∈𝐶
𝑛
𝑖
𝑊𝑖𝑐 + 1
log
𝑉 + 𝑖 ′ ∈𝑉 𝑊𝑖 ′ 𝑐
Naive Bayes classifier
Statistics used in the classification stage:
relative frequencies of the classes in the case of documents;
total number of words in each document class;
the relative frequencies of words within each class;
dictionary size (amount of unique words in training set).
𝐷𝑐
log +
𝐷
𝑛
𝑖𝜖𝑄
𝑊𝑖𝑐 + 1
log
𝑉 + 𝐿𝑐
𝐷𝑐 - number of documents belong to class 𝑐;
𝐷 - total number of documents in the training set;
𝑉 - dictionary of a set of documents (a list of all unique words);
𝐿𝑐 - the total number of words in documents of class c in the training set;
𝑊𝑖𝑐 - number of times as the i-th word appears in the documents of class 𝑐;
𝑄 - set of words of classified document (including repeats).
Results
1.00
𝑃 𝑐𝑑
0.80
0.79
0.81
0.76
0.72
0.64
0.60
0.54
0.40
0.20
0.00
75
100
125
150
Amount of training set
175
200
Conclusions
The implementation of the proposed solutions will identify
the authors of short message forums and blogs on the
Internet at various PR - actions to combat and control the
formation and manipulation of public opinion and other
manifestations of astroterfing.
```
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