Privacy Preserving ID3 over Horizontally, Vertically and Grid   Partitioned Data
  We consider privacy preserving decision tree induction via ID3 in the case where the training data is horizontally or vertically distributed. Furthermore, we consider the same problem in the case where the data is both horizontally and vertically distributed, a situation we refer to as grid partitioned data. We give an algorithm for privacy preserving ID3 over horizontally partitioned data involving more than two parties. For grid partitioned data, we discuss two different evaluation methods for preserving privacy ID3, namely, first merging horizontally and developing vertically or first merging vertically and next developing horizontally. Next to introducing privacy preserving data mining over grid-partitioned data, the main contribution of this paper is that we show, by means of a complexity analysis that the former evaluation method is the more efficient. 
Bart Kuijpers, Vanessa Lemmens, Bart Moelans and Karl Tuyls