being $N$ the number of Hermite functions used, $W$ the window size in seconds and
$f_{s}$\ the sampling frequency.
$\phi _{n}[l,\sigma )$ is the $n$-Hermite function, ${c_{n}}$\ are the coefficients of the linear combination, $e[l]$ is the error between $x[l]$ and the Hermite representation, and $\sigma $ controls the width of the Hermite function enabling it to adjust to the width of the QRS. The Hermite functions $\phi
_{n}[l,\sigma )$ , $0\leq n<N$,\ are defined as:
\begin{equation}
\phi _{n}[l,\sigma )=\frac{1}{\sqrt{\sigma 2^{n}n!\sqrt{\pi }}}% e^{-(l\cdot T_{s})^{2}/2\sigma ^{2}}H_{n}(l\cdot T_{s}/\sigma )
\end{equation}%
been $ T_{s}$ the inverse of the sampling frequency.
The Hermite polynomial $H_{n}(x)$ can be obtained recursively: …show more content…
For example $H_{2}(x)=4x^{2}-2$, $%
H_{3}(x)=8x^{3}-12x$, and so on.

Each QRS complex is represented by the N coefficients of the linear combination of the Hermite functions using $c_{n}(\sigma )$, $0 \leq n<N$, and by $\sigma$. Fig. \ref%
{fig:OriginalBeat} illustrates that the higher the order of the Hermite functions used, the more accurate the approximation of the beat is. However, using many functions has the risk of modeling noise in the signal, and not the actual shape of the QRS …show more content…
Gain Ratio is based on
Information Gain, but it applies a correction to penalize decisions with a high branching factor. Chi-square feature evaluation ranks features by computing the value of the chi-squared statistic with respect to the class
\cite{Mantel1963}.

To apply these techniques we used the entire MIT-BIH database. We considered that the beats were labeled with the beat type to which they belong according to the database annotations. Feature selection was performed for each record (patient) separately and over the set of all the beats from all recordings together, in order to compare the results from these two approaches. The feature selection results were not encouraging. The most relevant features selected by the three feature selection techniques varied considerably between patients, and the features selected for each patient varied considerably from those selected in the set made of all the beats of the database. Despite many attempts, we had to dismiss the possibility of gaining information about the relevance of the features that could be used for all patients. While our results suggest that it is possible to reduce the feature space for a particular patient, the features that are