Compressed Fisher Linear Discriminant Analysis: Classification of Randomly Projected Data

author: Robert J. Durrant, School of Computer Science, University of Birmingham
published: Oct. 1, 2010,   recorded: July 2010,   views: 3753

Related Open Educational Resources

Related content

Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Lecture popularity: You need to login to cast your vote.


We consider random projections in conjunction with classification, specifically the analysis of Fisher's Linear Discriminant (FLD) classifier in randomly projected data spaces. Unlike previous analyses of other classifiers in this setting, we avoid the unnatural effects that arise when one insists that all pairwise distances are approximately preserved under projection. We impose no sparsity or underlying low-dimensional structure constraints on the data; we instead take advantage of the class structure inherent in the problem. We obtain a reasonably tight upper bound on the estimated misclassification error on average over the random choice of the projection, which, in contrast to early distance preserving approaches, tightens in a natural way as the number of training examples increases. It follows that, for good generalisation of FLD, the required projection dimension grows logarithmically with the number of classes. We also show that the error contribution of a covariance misspecification is always no worse in the low-dimensional space than in the initial high-dimensional space. We contrast our findings to previous related work, and discuss our insights.

Link this page

Would you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !

Write your own review or comment:

make sure you have javascript enabled or clear this field: