On a warm day in April 2013, I was sitting in a friend's kitchen in Paris, trying to engineer serendipity. I was trying to get my computer to write music on its own. I wanted to be able to turn it on and have it spit out not just any goofy little algorithmic tune but beautiful, compelling, mysterious music; something I'd be proud to have written myself. The kitchen window was open, and as I listened to the sounds of children playing in the courtyard below, I thought about how the melodies of their voices made serendipitous counterpoint with the songs of nearby birds and the intermittent drone of traffic on the rue d'Alésia. In response to these daydreams, I was making a few tweaks to my software--a chaotic, seat-of-the-pants affair that betrayed my intuitive, self-taught approach to programming--when I saw that Bill Seaman had just uploaded a new batch of audio files to our shared Dropbox folder. I had been collaborating with Bill, a media artist, on various aspects of computational creativity over the past few years. I loaded Bill's folder of sound files along with some of my own into the software and set it rolling. I was thrilled and astonished.

On a warm day in April 2013, I was sitting in a friend's kitchen in Paris, trying to engineer serendipity. I was trying to get my computer to write music on its own. I wanted to be able to turn it on and have it spit out not just any goofy little algorithmic tune but beautiful, compelling, mysterious music; something I'd be proud to have written myself. The kitchen window was open, and as I listened to the sounds of children playing in the courtyard below, I thought about how the melodies of their voices made serendipitous counterpoint with the songs of nearby birds and the intermittent drone of traffic on the rue d'Alésia. In response to these daydreams, I was making a few tweaks to my software--a chaotic, seat-of-the-pants affair that betrayed my intuitive, self-taught approach to programming--when I saw that Bill Seaman had just uploaded a new batch of audio files to our shared Dropbox folder. I had been collaborating with Bill, a media artist, on various aspects of computational creativity over the past few years. I loaded Bill's folder of sound files along with some of my own into the software and set it rolling. I was thrilled and astonished.

Subspace models play an important role in a wide range of signal processing tasks, and this paper explores how the pairwise geometry of subspaces influences the probability of misclassification. When the mismatch between the signal and the model is vanishingly small, the probability of misclassification is determined by the product of the sines of the principal angles between subspaces. When the mismatch is more significant, the probability of misclassification is determined by the sum of the squares of the sines of the principal angles. Reliability of classification is derived in terms of the distribution of signal energy across principal vectors. Larger principal angles lead to smaller classification error, motivating a linear transform that optimizes principal angles. The transform presented here (TRAIT) preserves some specific characteristic of each individual class, and this approach is shown to be complementary to a previously developed transform (LRT) that enlarges inter-class distance while suppressing intra-class dispersion. Theoretical results are supported by demonstration of superior classification accuracy on synthetic and measured data even in the presence of significant model mismatch.