Modeling and analyzing surgeries based on signals that are obtained automatically from the operating room (OR) is a field of recent interest. It can be valuable for analyzing and understanding surgical workflow, for skills evaluation and developing context-aware ORs. In minimally invasive surgery, laparoscopic video is easy to record but it is challenging to extract meaningful information from it. We propose a method that uses additional information about tool usage to perform a dimensionality reduction on image features. Using Canonical Correlation Analysis (CCA) a projection of a high-dimensional image feature space to a low dimensional space is obtained such that semantic information is extracted from the video. To model a surgery based on the signals in the reduced feature space two different statistical models are compared. The capability of segmenting a new surgery into phases only based on the video is evaluated. Dynamic Time Warping which strongly depends on the temporal order in combination with CCA shows the best results.