As the time goes on and on, digitization of text has been increasing enormously and the need to organize, categorize and classify text has become indispensable. Disorganization and very little categorization and classification of text may result in slower response time of text or information retrieval. Therefore it is very important and essential to organize, categorize and classify texts and digitized documents according to definitions proposed by text mining experts and computer scientists. Work has been done on Text Mining, Text Categorization and Automatic Text Classification by computer and information scientists, but obviously a lot of space for novel research in this domain is available. In this paper we have proposed the mathematical notation and graphical models for Text Mining, Text Categorization and Automatic Text Classification to get in depth understanding of these techniques and concepts. Introduction and proposal of mathematical and graphical models for Text Mining, Text Categorization and Automatic Text Classification will shorten the response time of text and information retrieval. Also the performance of web search engines can be improved so much by employing these mathematical and graphical models.

In this paper firstly I have compared Single Label Text Categorization with Multi Label Text Categorization in detail then I have compared Document Pivoted Categorization with Category Pivoted Categorization in detail. For this purpose I have given the general definition of Text Categorization with its mathematical notation for the purpose of its frugality and cost effectiveness. Then with the help of mathematical notation and set