Let be the text collection composed by the texts whose terms have been obtained by applying of TP method and including terms closer to from each original text. Let be the vocabulary of and the average of for terms that belong to but not to . value is linked to the similarity among the texts. Clearly lowest value of is 1, and it means the new terms added to are not shared by the texts of . In our experiments it was observed that a decreasing of ( ) contributed to change instances from an incorrect cluster to a correct one. Therefore, terms with low help to distribute texts into the clusters; the decreasing of , the decreasing of similarity between texts. Now, we can define an indicator of the goodness of a selection .

Whenever the number of clusters () decreases after apply clustering to , a lower value means that new terms added to vocabulary will provide rising of similarity between texts in . In such conditions indicates a good selection. A way to express the above description is to say that a good clustering supposes that be greater than and be greater than . We define the goodness of selection as:

(7) |

In Table 3 a neighbour of maximum value of is shown. Row 1 is , the number of terms selected by TP method, row 2 the size of vocabulary of , row 3 normalized values of , and in row 4 the measure.

i |
20 | 21 | 22 | 23 | 24 |

1,572 | 1,619 | 1,661 | 1,706 | 1,744 | |

0.573 | 0.621 | 1.027 | 0.584 | 0.990 | |

0.637 | 0.6411 | 0.6415 | 0.636 | 0.551 |