EM in high-dimensional spaces.
This paper considers fitting a mixture of Gaussians model to high-dimensional data in scenarios where there are fewer data samples than feature dimensions. Issues that arise when using principal component analysis (PCA) to represent Gaussian distributions inside Expectation-Maximization (EM) are addressed, and a practical algorithm results. Unlike other algorithms that have been proposed, this algorithm does not try to compress the data to fit low-dimensional models. Instead, it models Gaussian distributions in the (N - 1)-dimensional space spanned by the N data samples. We are able to show that this algorithm converges on data sets where low-dimensional techniques do not.
Draper
Bruce A
BA
Elliott
Daniel L
DL
Hayes
Jeremy
J
Baek
Kyungim
K
D000465:Algorithms; D001185:Artificial Intelligence; D016000:Cluster Analysis; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D016013:Likelihood Functions; D008954:Models, Biological; D015233:Models, Statistical; D010363:Pattern Recognition, Automated / Q000379:methods*; D025341:Principal Component Analysis; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013382:Subtraction Technique