title: Estimating parameters in multivariate classification
body: <p>Newbie here typesetting my question, so excuse me if this don't work.</p>
  
  <p>I am trying to give a <em>bayesian classifier</em> for a multivariate classification problem where input is assumed to have <em>multivariate normal distribution</em>. I choose to use a discriminant function defined as <strong>log(likelihood * prior)</strong>. </p>
  
  <p>However, from the distribution,</p>
  
  <p>$${f(x \mid\mu,\Sigma) = (2\pi)^{-Nd/2}\det(\Sigma)^{-N/2}exp[(-1/2)(x-\mu)'\Sigma^{-1}(x-\mu)]}$$</p>
  
  <p>i encounter a term -log(det($S_i$)), where $S_i$ is my sample covariance matrix for a specific class i. Since my input actually represents a square image data, my $S_i$ discovers quite some correlation and resulting in det(S_i) being zero. Then my discriminant function all turn Inf, which is disastrous for me.</p>
  
  <p>I know there must be a lot of things go wrong here, anyone willling to help me out?</p>
  
  <hr>
  
  <p>UPDATE: Anyone can help how to get the formula working?</p>