Algorithms

1 files changed, 1 insertions, 1 deletions

diff --git a/algorithm.tex b/algorithm.tex
index 30ce77c..3045929 100644
--- a/algorithm.tex
+++ b/algorithm.tex
@@ -20,7 +20,7 @@ distribution of the model is given by:
   P(\bx, y) =  \cN(\bx | \bar{\bx}_y, \Sigma) P(y),
   \label{eq:mixture of Gaussians}
 \end{align}
-where $\bx$ denotes an observation, $y$ is a class, $P(y)$ is the probability of the class, and $\cN(\bx | \bar{\bx}_y, \Sigma)$ is the conditional probability of $\bx$ given $y$. The conditional is a multivariate normal distribution. Its mean is $\bar{\bx}_y$ and the variance of $\bx$ is captured by the covariance matrix $\Sigma$. The decision boundary between any two classes $y$ is linear when all conditionals $\cN(\bx | \bar{\bx}_y, \Sigma)$ have the same covariance matrix $\Sigma$ \cite{bishop06pattern}. In this scenario, the mixture of Gaussians model can be viewed as a probabilistic variant of the nearest-neighbor (NN) classifier in Section~\ref{sec:uniqueness}.
+where $\bx$ denotes an observation, $y$ is a class, $P(y)$ is the probability of the class, and $\cN(\bx | \bar{\bx}_y, \Sigma)$ is the conditional probability of $\bx$ given $y$. The conditional is a multivariate normal distribution. Its mean is $\bar{\bx}_y$ and the variance of $\bx$ is captured by the covariance matrix $\Sigma$. The decision boundary between two classes $y_1$ and $y_2$, $P(\bx, y_1) = P(\bx, y_2)$ for all $\bx$, is linear when all conditionals $\cN(\bx | \bar{\bx}_y, \Sigma)$ have the same covariance matrix $\Sigma$ \cite{bishop06pattern}. In this case, the mixture of Gaussians model can be viewed as a probabilistic variant of the nearest-neighbor (NN) classifier in Section~\ref{sec:uniqueness}.
 
 The mixture of Gaussians model has many advantages. First, the model can be
 easily learned using maximum-likelihood (ML) estimation \cite{bishop06pattern}.