From afe44781966d3a18e96d19759dfa182ebf64100e Mon Sep 17 00:00:00 2001
From: Jon Whiteaker <jbw@berkeley.edu>
Date: Thu, 20 Sep 2012 19:51:48 -0700
Subject: small fixes to algorithms

---
 algorithm.tex | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

(limited to 'algorithm.tex')

diff --git a/algorithm.tex b/algorithm.tex
index ff396eb..faadd9a 100644
--- a/algorithm.tex
+++ b/algorithm.tex
@@ -56,7 +56,7 @@ observation $\bx$, the model predicts $\hat{y} = \arg\max_y P(y | \bx)$, where:
     \Sigma)P(y)}
 \end{equation}
 In this setting, the decision boundary between two classes $y_1$ and $y_2$:
-$\set{\bx | P(\bx, y_1) = P(\bx, y_2)}$ is an hyperplane \cite{bishop06pattern}
+$\set{\bx | P(\bx, y_1) = P(\bx, y_2)}$ is a hyperplane \cite{bishop06pattern}
 and the mixture of Gaussians model can be viewed as a probabilistic variant of
 the nearest-neighbor (NN) classifier in Section~\ref{sec:uniqueness}.
 
@@ -79,14 +79,14 @@ and the higher the precision.
 \subsection{Sequential hypothesis testing}
 \label{sec:SHT}
 
-In our setting (see \xref{sec:experiment-design}), skeletons measurements
+In our setting (see \xref{sec:experiment-design}), skeleton measurements
 are not isolated. On the contrary, everytime a person walks in front of the
 camera we get a set of time-indexed measurements belonging to the same
 individual that we want to classify. The mixture of Gaussians model can be
 extended to temporal inference through through the Sequential hypothesis
 testing \cite{wald47sequential} framework. In this framework, a subject is
-sequentially tested for belonging to one of several class, by assuming that
-conditioned on the class, the measurements are independent realisations of the
+sequentially tested for belonging to one of several classes, by assuming that
+conditioned on the class, the measurements are independent realizations of the
 same random variable. In our case, the probability that the sequence of data
 $\bx^{(1)}, \dots, \bx^{(t)}$ belongs to the class $y$ at time $t$ is given by:
 \begin{equation}\label{eq:SHT}
@@ -104,5 +104,5 @@ prediction is accepted when the classifier is confident, that is $P(\hat{y}
 Sequential hypothesis testing is a common technique for smoothing temporal
 predictions. In particular, note that the prediction at time $t$ depends on all
 data up to time $t$. This reduces the variance of predictions, especially when
-input data are noisy, such as in the domain of skeleton recognition.
+input data is noisy, such as in the domain of skeleton recognition.
 
-- 
cgit v1.2.3-70-g09d2

