The approach described here was to locate a vector that would have low or zero cosine similarity with PET scans of members of one diagnostic group, while maintaining a relatively
higher cosine similarity with the PET scans of members of another group. The ruxolitinib structure following is a description of the application of the method for discerning between subjects with AD and cognitively normal controls. Analogous methods were used for the MCI-c versus MCI-n comparisons. First, a set of AD PET scan right vectors were arranged in a matrix. The projections of a group of NC scan vectors onto the column space of this matrix were then computed. As mentioned above, this process is mathematically identical to Inhibitors,research,lifescience,medical finding the least squares approximation of the solution to a system of linear equations. Each of these projections was then subtracted from the corresponding NC scan vector, yielding a set of residual vectors—one for each NC subject (Fig. 1). These residual vectors were averaged to generate a single “prototypical” residual vector. Because the average residual Inhibitors,research,lifescience,medical was a linear combination of vectors orthogonal to the AD space, the average was also certain to be orthogonal to this space. As an orthogonal vector, it had zero cosine similarity with all of the AD scan vectors. This approach is similar to using subtraction of projections to accomplish a logical NOT for search engines (Widdows and Peters 2003; Widdows 2004). Measurements of similarity on the entire dataset
Inhibitors,research,lifescience,medical were generated using the following method. The scans were first “stratified” by assigning each one to one of 10 different groups, with each group containing comparable proportions of each type of scan (i.e., because the entire Inhibitors,research,lifescience,medical sample comprised 33% NC scans, 22% AD, 16% MCI-c, 29% MCI-n, each of the 10 groups was made
to approximate these proportions). Residual vectors were then computed using nine of the 10 groups and averaged together. For example, the NC scan vectors from these nine groups were projected onto the space defined by the AD scan vectors and residual vectors were obtained. Inhibitors,research,lifescience,medical The average of these residual vectors was then compared with cosine similarity to all scans in the group that was originally left out, regardless of type (i.e., diagnostic group). Thus, each scan in the left-out group received a cosine score reflecting its similarity to the residual vector Dacomitinib obtained when AD scans were regressed out of NC scans. The process was repeated 10 times, each time leaving out one group of scans and using the remaining nine groups to create a residual vector. This method is known as stratified 10-fold cross validation. Two sets of residual vectors were derived in this manner. The first set was derived using PET scans of cognitively normal controls and AD patients. This set consisted of two types of vectors: one created by projecting NC PET scan vectors onto a space defined by AD PET scans and one created by performing the opposite projection.