Tolerance Rough Set Model Approach to Document Clustering

1 A tolerance rough set model Denote the set of M full text documents by D, and the set of N terms from D by T. The method generates a hierarchical structure of D in two phases. The rst phase extracts and maps each document dj 2 D into a list of terms ti each of which is assigned a weight that re BLOCKINects its importance in the document, then enriches documents with their approximations by the proposed tolerance rough set model. The second phase groups documents by an agglomerative clustering method using the document approximations. The key issue in formulating the tolerance rough set model (TRSM) to represent documents is the identica-tion of tolerance classes of index terms. We employ the co-occurrence of index terms in all documents from D to determine a tolerance relation and tolerance classes. Denote by f d j (t i) the number of occurrences of term t i in d j , and by f D (t i) the number of documents in D that term t i occurs in, and by f D (t i ; t j) the number of documents in D in which two index terms t i and t j co-occur. We dene an uncertainty function I depending on a threshold as I(ti) = ftj j fD(ti; tj) g [ ftig (1) It is clear that the function I dened above sat-ises the condition of t i 2 I (t i) and t j 2 I (t i) i t i 2 I (t j) for any t i ; t j 2 T , and so I is both re BLOCKINexive and symmetric. This function corresponds to a tolerance relation I T 2 T that t i It j i t j 2 I (t i), and I (ti) is the tolerance class of index term ti. A vague inclusion function , which determines how much X is included in Y , is dened as (X; Y) = jX\Y j=jXj. Using this the membership function for t i 2 T ; X T can be dened as (t i ; X) = (I (t i); X) = jI (t i) \ Xj=jI (t i)j. With these denitions we can dene a tolerance space as R = (T ; I ; ; P) in which the lower approximation L(R; X) and the upper approximation U(R; X) in R of …