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\begin{document}

             \author[1]{D.  Malathi}

             \author[2]{S.  Valarmathy}

             \affil[1]{  Bannari Amman Institute of Technology, Anna University, India}

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\date{\small \em Received: 15 December 2013 Accepted: 4 January 2014 Published: 15 January 2014}

\maketitle


\begin{abstract}
        


Document Analysis represented in vector space model is often used in information retrieval, topic analysis, and automatic classification. However, it hardly deals with fuzzy information and decision-making problems. To account this, Intuitionistic partition based cosine similarity measure between topic/terms and correlation between document/topic are proposed for evaluation. Conceptual granulation is emphasized in the decision matrix expressed conventionally as tf-idf. A local clustering of topic-terms and document-topics results in comparing dependent terms with membership degree using cosine similarity measure and correlation. A preprocessing of documents with intuitionistic fuzzy sets results in efficient classification of large corpus. But it depends on the datasets chosen. The proposed method effectively works well with large sized categorized corpus.

\end{abstract}


\keywords{document analysis, intuitionistic fuzzy, topic modeling.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
ocument model in the information retrieval has three main components, namely Text Preprocessor, Topic Extractor and Corpus categoryzation. These components are integrated to deploy knowledge extraction in information system. In spite of this, the growing data and its knowledge recognition complications have considerably encouraging the extensions of machine learning algorithms. 
\section[{a) Document Model}]{a) Document Model}\par
The text document Modeling is observed as latent topics model. Various prominent approaches in machine learning are used to study the model. Document model is a mixture of topics \hyperref[b3]{[4]}. Topics are inferred by the collection of correlated words. But unsupervised learning perspective is the pulse of bubbling out the topics. By modeling, varieties of mining range can be established with various subjects. The models try to observe the likely documents and tend to focus on topics. But document models are discriminant because of random words due to linguistic factors such as synonym, hyponym, Polysemy, etc. 
\section[{b) Text Pre-processor}]{b) Text Pre-processor}\par
The functionalities essential for machine learning of document are document pre-processing and corpus representation. Stop words removal, word stemming, filtering to exclude certain words, are done within each document. This process is called preprocessing of documents. Obtained vocabulary is put up in the word-document matrix which is generally called as bag-of-words model. The document representations may be in binary (0, for nonoccurrence and 1 for occurrence of each term in a document), term frequency (tij -number of occurrence of ith word in jth document) and term frequency inverse document frequency (probable occurrence of tij' -distribution of ith word in jth document). Obtained data in this stage is huge in dimension, and lot of techniques \hyperref[b14]{[15]} have been proposed for dimension reduction. 
\section[{c) Topic Extractor}]{c) Topic Extractor}\par
A topic model is a probabilistic model that can be considered as a mixture of topics, represented by probability distributions of words in a document. The latent variables or topics are the inferring components of this model. The main objective is to learn from documents the distribution of the underlying topics in a given corpus. Topic model is Text corpora representation by a co-occurrence matrix of words and documents. The probabilistic latent semantic analysis (PLSA) model \hyperref[b9]{[10]} uses probability of words with given topics and probability of topics in a document, to build a topic model. The Latent Dirichlet Allocation (LDA) model \hyperref[b0]{[1]}, is another probabilistic approach which ties the parameters of all documents through hierarchical generative model. 
\section[{d) Corpus Categorization}]{d) Corpus Categorization}\par
Text Categorization is a classical application of Text Mining \hyperref[b18]{[19]}, and is used in email filters, social tagging and automatic labeling of documents in business libraries. Text mining applications in research and business intelligence include, latent semantic analysis techniques in bioinformatics automatic investigation of jurisdictions plagiarism detection in universities and publishing houses, cross-language information retrieval, spam filters learning, help desk inquiries, measuring customer preferences by analyzing qualitative interviews, automatic grading, fraud detection or parsing social network for ideas of new products \hyperref[b8]{[9]}. 
\section[{II.}]{II.} 
\section[{Literature Support}]{Literature Support}\par
The theory of fuzzy set is Consider as a degree of membership assigned to each element, where the degree of non-membership is just automatically equal to D its complement. However, human interpretation often does not express the corresponding degree of nonmembership as the complement to 1. So, Atanassov \hyperref[b0]{[1]}[2] \hyperref[b2]{[3]} introduced the concept of intuitionistic fuzzy set that is meant to reflect the fact that the degree of nonmembership is not always equal to 1 minus degree of membership, but there may be some hesitation degree.\par
Intuitionistic fuzzy set is a generalized constructive logic applied in fuzzy set. It is defined on a X of objects, with each object x is described by the degrees of membership and non-membership to a certain property, ( ) ( ) ( ) \{ \} X x x x x A A ? , , , ? µ (1) ( )( ) ( ) 1 0 ? + ? x x A A ? µ X x ? ? (2)\par
Therefore the degree of non determinacy of the object x with respect to the intuitionistic fuzzy set A is imposed as, ( ) ( ) ( )x x x A A A ? µ ? + = X x ? ? (3)\par
The model is well suited to represent a classification problem with high dimension. The confusion matrix of high dimension can be probably reduced to concept matrix of low dimension. The similarity measures \hyperref[b13]{[14]} and distance measures [21] \hyperref[b19]{[20]} between two intuitionistic fuzzy sets can be applied in pattern recognition.\par
In this paper, a Partition based approach \hyperref[b15]{[16]} inspired by Hierarchical segmentation \hyperref[b7]{[8]} and topic based segmentation \hyperref[b5]{[6]} are extended using Intuitionistic fuzzy set approach \hyperref[b21]{[23]} for local centralization of conceptual words. The intuitionistic fuzzy set theory is applied in conceptual term/topic detection. A cosine similarity and correlation are taken into for defining membership degree and the non-membership degree respectively. The results using this measure found better with respect to the dataset chosen. In literature a intuitionistic fuzzy representation of images for clustering \hyperref[b17]{[18]} [12] by utilizing a novel similarity metric are defined. But a minimal support is extended for text classification. So, a local centralization of conceptual terms using Intuitionistic logical clustering has been applied in the work. 
\section[{III.}]{III.} 
\section[{Proposed Model -Intuitionistic Partition based Concept Granulation (IPCG)}]{Proposed Model -Intuitionistic Partition based Concept Granulation (IPCG)}\par
Intuitionistic logic is a natural deduction system \hyperref[b12]{[13]},that have introduction rules µ and elimination rules ? for the logical connectives and quantifiers. The \{ \} ) ( ), ( , ij i ij i ij w w w A ? µ = where 1 0 < < ij w (4)\par
The similarity between words and on a topic is calculated by the cosine measure. Each document vector is normalized with the weight and length of terms in k partitions. Then the optimal term ij w \hyperref[b15]{[16]} should  The intuitionistic angular or cosine similarity \hyperref[b20]{[22]} measure between the m terms in a partitioned set is given as follows:( ) ? ? ? = = = = m i i B m i i A m i i B i A x x x x B A C 1 2 1 2 1 ) ( ) ( ) ( ) ( , µ µ µ µ (6)\par
The intuitionistic correlation \hyperref[b6]{[7]} of rows all fuzzy numbers are included from the samples of tf-idf (Partition Model). The crisp set is modified intuitionistically with the sample mean and variance of membership function as:( ) ( )( ) ( ) ( ) ? ? ? = = = ? ? ? ? ? ? ? ? ? ? = n i B i B n i A i A n i B i B A i A I x x x x B A CR 1 1 1 ) ( ) ( ) ( ) ( , µ µ µ µ µ µ µ µ (7)\par
The effectiveness of the intuitionistic classification of corpus is approximately studied and analyzed using the following entropy \hyperref[b20]{[22]} specifically used for Intuitionist Fuzzy Set 'A'.( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ? = + + = n i i A i A i A i A i A i A x x v x x x v x n E 1 , max , min 1 ? µ ? µ (8)\par
IV. 
\section[{Datasets a) Newspaper Article collection}]{Datasets a) Newspaper Article collection}\par
The newspaper articles under different topics are collected. The categories are marked. The training and testing documents are randomly chosen. The growing social media made essential to include newspaper article collection to include in this work. News are generally categorized by topic area ("politics," "business," etc.) written in clear, correct, "objective," and somewhat schematized language \hyperref[b4]{[5]}. This would pave way to extend the research towards social networking and marketing. The collection includes about 780 documents with 25 categories. All new social relevant topics ("mobile","opinion", etc.) are included for categorizing. 
\section[{b) Reuters-21578 Data Set}]{b) Reuters-21578 Data Set}\par
The Reuters-21578 Data Set collection provides a classification task with challenging properties. There are multiple categories, the categories are overlapping and non exhaustive, and there are relationships among the categories. There are interesting possibilities for the use of domain knowledge. There are many possible feature sets that can be extracted from the text, and most plausible feature/example matrices are large and sparse \hyperref[b10]{[11]}. 
\section[{c) Movie Review Dataset}]{c) Movie Review Dataset}\par
The Movie Review Dataset, Polarity dataset v0.9 with 900 positive and 900 negative reviews is used. Using movie reviews as data, the problem of classifying documents using standard machine learning techniques definitively outperform human-produced baselines processed reviews \hyperref[b16]{[17]}. The training cases are chosen randomly from each class about 100 documents. Which means about 500 cases are considered for training.\par
V. 
\section[{Results and Analysis}]{Results and Analysis}\par
The machine learning classification methods, such as Bayesian, Naïve Bayes, J48, Support Vector Machines, LMT are strong enough to support classifications.\par
In the case of concept granulation in document classification, the feature selection is fine tuned to achieve categories strictly connected to the human perception. Before imposing the features into the classifier, some form of selection must be chosen. The proposed method, selects the features according to the intuitionist logic. The features tf-idf matrix has been The proposed Concept Granulation Using Intuitionistic Partition Based Classification Model is implemented administered in the Java based system and analyzed for its significance. The intuitionistic correlation is applied to the specified datasets. In which the chosen dataset and the partitions play the very important role in finding the result of the model. The tfidf-IP is favorable for Reuter dataset than for Newspaper and Movies. This is represented in the Figures \hyperref[fig_5]{2(a} The perplexity is depicted in Figure 3 and Table1. So the analysis can be interpreted or inferred in the following ways:\par
Intuitionistic approach is in favor of the classified documents or corpus chosen Partition plays the important role in the proposed model. Out of four types of partition, k=8 plays a smoothened strong support for the proposed model k=16, the highest partition yield only a very moderate result and more confusions.\par
k=4, the least partition model yield the smooth but less significant support for all the datasets. k=8, yield the partially smooth but supportive significant for the movie dataset. (Than other partitions)\par
The results are focused to average training datasets and micro f-measure (Table \hyperref[tab_1]{2}) to show up the IPCG performs better with dimension reduction for categorization of corpus. Every datasets chosen for analysis behaves to the pull and push of various stages of the proposed model.   
\section[{Conclusions}]{Conclusions}\par
In this paper, we have proposed a intuitionistic partition based concept granulation topic-term model for a nominal tf-idf vector space model which is often used in information retrieval, topic analysis, and automatic classification. The cosine distance and correlation treatment to the tf-idf reduces the dimension and improves the efficiency of bag of words/terms in topics. However, it is priory treated using the intuitionistic partition for fitting the model into decision-making problems. To account this, Intuitionistic partition based cosine similarity measure between topic/terms and correlation between document/topic are included. The proposed fuzzy model is tailored with normal combinational approach to fetch intuitionistic fuzzy crisp set. Yet, it is observed the model is well behaving and promising for the categorized documents and not so bad support for the low inference corpus collections like movie review. So, this make us clear that the social media documents should be specially treated before introducing this model. It is felt that aggregation of social media topic-terms is needed. This is taken for future work or extension of the proposed work. \begin{figure}[htbp]
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\caption{\label{fig_1}?}\end{figure}
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\caption{\label{fig_2}}\end{figure}
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\noindent\textbf{1}\includegraphics[]{image-5.png}
\caption{\label{fig_3}Figure 1 :}\end{figure}
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\noindent\textbf{}\includegraphics[]{image-6.png}
\caption{\label{fig_4}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-7.png}
\caption{\label{fig_5}Figure 2 :}\end{figure}
  \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.08128415300546447\textwidth}P{0.21133879781420764\textwidth}P{0.14398907103825137\textwidth}P{0.14398907103825137\textwidth}P{0.10915300546448087\textwidth}P{0.09057377049180328\textwidth}P{0.06967213114754098\textwidth}}
\tabcellsep Training with 300 Doc\tabcellsep Dimension Reduction\tabcellsep \multicolumn{3}{l}{Perplexity Correlation}\tabcellsep \\
\tabcellsep Newspaper\tabcellsep 26\%\tabcellsep 0.231\tabcellsep 0.582\tabcellsep \tabcellsep \\
\tabcellsep Reuters\tabcellsep 22\%\tabcellsep 0.311\tabcellsep 0.520\tabcellsep \tabcellsep \\
\tabcellsep Movie\tabcellsep 16\%\tabcellsep 0.483\tabcellsep 0.480\tabcellsep \tabcellsep \\
Dataset\tabcellsep \tabcellsep tf-idf\tabcellsep \tabcellsep \tabcellsep IPCG\tabcellsep \\
Classifiers\tabcellsep \multicolumn{3}{l}{Reuters News Paper Movie}\tabcellsep Reuters\tabcellsep News Paper\tabcellsep Movie\\
SVM\tabcellsep 0.482\tabcellsep 0.422\tabcellsep 0.321\tabcellsep 0.844\tabcellsep 0.841\tabcellsep 0.799\\
NB\tabcellsep 0.401\tabcellsep 0.369\tabcellsep 0.297\tabcellsep 0.872\tabcellsep 0.834\tabcellsep 0.810\\
J48\tabcellsep 0.400\tabcellsep 0.399\tabcellsep 0.381\tabcellsep 0.798\tabcellsep 0.797\tabcellsep 0.784\\
Bayes'\tabcellsep 0.541\tabcellsep 0.411\tabcellsep 0.399\tabcellsep 0.831\tabcellsep 0.854\tabcellsep 0.829\\
LMT\tabcellsep 0.442\tabcellsep 0.541\tabcellsep 0.587\tabcellsep 0.878\tabcellsep 0.798\tabcellsep 0.722\end{longtable} \par
 
\caption{\label{tab_0}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_1}Table 2 :}\end{figure}
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