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diff --git a/algorithm.tex b/algorithm.tex index c7d22ae..fbe2dc8 100644 --- a/algorithm.tex +++ b/algorithm.tex @@ -23,13 +23,13 @@ The mixture of Gaussians model has many advantages. First, the model can be easi \end{align} In practice, the prediction $\hat{y}$ is accepted when the classifier is confident. In other words, $P(\hat{y} | \bx) \! > \! \delta$, where $\delta \in (0, 1)$ is a threshold that controls the precision and recall of the classifier. In general, the higher the threshold $\delta$, the lower the recall and the higher the precision. -In this work, we use the mixture of Gaussians model for skeleton recognition. Skeleton measurements are represented by a vector $\bx$ and each person is assigned to one class $y$. To verify that our approach is suitable for skeleton recognition, we plot for each skeleton feature $x_k$ (Section~\ref{sec:experiment}) the histogram of differences between the feature and its expectation $(\bar{\bx}_y)_k$ in the corresponding class $y$ (Figure~\ref{fig:marginals}). All histograms look approximately normal. This indicates that all class conditionals $P(\bx | y)$ are multivariate normal and our generative model, although very simple, may be nearly optimal \cite{bishop06pattern}. +In this work, we use the mixture of Gaussians model for skeleton recognition. Skeleton measurements are represented by a vector $\bx$ and each person is assigned to one class $y$. In particlar, our dataset $\cD = \set{(\bx_1, y_1), \dots, (\bx_n, y_n)}$ consists of $n$ pairs $(\bx_i, y_i)$, where $y_i$ is the label of the skeleton $\bx_i$. To verify that our method is suitable for skeleton recognition, we plot for each skeleton feature $x_k$ (Section~\ref{sec:experiment}) the histogram of differences between all measurements and the expectation given the class $(\bx_i)_k - \E{}{x_k | y_i}$ (Figure~\ref{fig:error marginals}). All histograms look approximately normal. This indicates that all class conditionals $P(\bx | y)$ are multivariate normal and our generative model, although very simple, may be nearly optimal \cite{bishop06pattern}. \begin{figure}[t] \centering - \includegraphics[height=4.4in, angle=90, bb=4.5in 1.5in 6.5in 7in]{graphics/Marginals} - \caption{Histograms of differences between 9 skeleton measurements $x_k$ (Section~\ref{sec:experiment}) and their expected value $(\bar{\bx}_y)_k$ in the corresponding class $y$.} - \label{fig:marginals} + \includegraphics[height=4.4in, angle=90, bb=4.5in 1.5in 6.5in 7in]{graphics/ErrorMarginals} + \caption{Histograms of differences between 9 skeleton measurements $x_k$ (Section~\ref{sec:experiment}) and their expectation given the class $y$.} + \label{fig:error marginals} \end{figure} diff --git a/graphics/ErrorMarginals.pdf b/graphics/ErrorMarginals.pdf Binary files differnew file mode 100644 index 0000000..7271d17 --- /dev/null +++ b/graphics/ErrorMarginals.pdf diff --git a/graphics/Marginals.pdf b/graphics/Marginals.pdf Binary files differdeleted file mode 100644 index 682c994..0000000 --- a/graphics/Marginals.pdf +++ /dev/null |