\end{tabular}
\end{table}
-\section{\gls{MFCC} Features}
+\section{\acrlong{MFCC} Features}
The waveforms in itself are not very suitable to be used as features due to the
high dimensionality and correlation. Therefore we use the often used
\glspl{MFCC} feature vectors which has shown to be
functions.
\end{enumerate}
-\section{\gls{ANN} Classifier}
-\todo{Spectrals might be enough, no decorrelation}
+The default number of \gls{MFCC} parameters is twelve. However, often a
+thirteenth value is added that represents the energy in the data.
+
+\section{Experimental setup}
+\subsection{Features}
+The thirteen \gls{MFCC} features are chosen to feed to the classifier. The
+parameters of the \gls{MFCC} features are varied in window step and window
+length. The default speech processing parameters are tested but also bigger
+window sizes since arguably the minimal size of a singing voice segment is a
+lot bigger than the minimal size of a subphone component on which the
+parameters are tuned. The parameters chosen are as follows:
+
+\begin{table}[H]
+ \centering
+ \begin{tabular}{lll}
+ \toprule
+ step (ms) & length (ms) & notes\\
+ \midrule
+ 10 & 25 & Standard speech processing\\
+ 40 & 100 &\\
+ 80 & 200 &\\
+ \bottomrule
+ \end{tabular}
+ \caption{\Gls{MFCC} parameter settings}
+\end{table}
-\section{Experiments}
\subsection{\emph{Singing} voice detection}
The first type of experiment conducted is \emph{Singing} voice detection. This
is the act of segmenting an audio signal into segments that are labeled either
as \emph{Singing} or as \emph{Instrumental}. The input of the classifier is a
feature vector and the output is the probability that singing is happening in
-the sample.
-
-\begin{figure}[H]
- \centering
- \includegraphics[width=.5\textwidth]{bcann}
- \caption{Binary classifier network architecture}\label{fig:bcann}
-\end{figure}
+the sample. This results in an \gls{ANN} of the shape described in
+Figure~\ref{fig:bcann}. The input dimension is thirteen and the output is one.
\subsection{\emph{Singer} voice detection}
The second type of experiment conducted is \emph{Singer} voice detection. This
is the act of segmenting an audio signal into segments that are labeled either
with the name of the singer or as \emph{Instrumental}. The input of the
classifier is a feature vector and the outputs are probabilities for each of
-the singers and a probability for the instrumental label.
+the singers and a probability for the instrumental label. This results in an
+\gls{ANN} of the shape described in Figure~\ref{fig:mcann}. The input dimension
+is yet again thirteen and the output dimension is the number of categories. The
+output is encoded in one-hot encoding. This means that the categories are
+labeled as \texttt{1000, 0100, 0010, 0001}.
+
+\subsection{\acrlong{ANN}}
+The data is classified using standard \gls{ANN} techniques, namely \glspl{MLP}.
+The classification problems are only binary and four-class so therefore it is
+interesting to see where the bottleneck lies. How abstract the abstraction can
+go. The \gls{ANN} is built with the Keras\footnote{\url{https://keras.io}}
+using the TensorFlow\footnote{\url{https://github.com/tensorflow/tensorflow}}
+backend that provides a high-level interface to the highly technical networks.
+
+The general architecture of the networks is show in Figure~\ref{fig:bcann} and
+Figure~\ref{fig:mcann} for respectively the binary classification and
+multiclass classification. The inputs are fully connected to the hidden layer
+which is fully connected too the output layer. The activation function used is
+a \gls{RELU}. The \gls{RELU} function is a monotonic symmetric one-sided
+function that is also known as the ramp function. The definition is given in
+Equation~\ref{eq:relu}. \gls{RELU} was chosen because of its symmetry and
+efficient computation. The activation function between the hidden layer and the
+output layer is the sigmoid function in the case of binary classification. Of
+which the definition is shown in Equation~\ref{eq:sigmoid}. The sigmoid is a
+monotonic function that is differentiable on all values of $x$ and always
+yields a non-negative derivative. For the multiclass classification the softmax
+function is used between the hidden layer and the output layer. Softmax is an
+activation function suitable for multiple output nodes. The definition is given
+in Equation~\ref{eq:softmax}.
+
+The data is shuffled before fed to the network to mitigate the risk of
+over fitting on one album. Every model was trained using $10$ epochs and a
+batch size of $32$.
+
+\begin{equation}\label{eq:relu}
+ f(x) = \left\{\begin{array}{rcl}
+ 0 & \text{for} & x<0\\
+ x & \text{for} & x \geq 0\\
+ \end{array}\right.
+\end{equation}
+
+\begin{equation}\label{eq:sigmoid}
+ f(x) = \frac{1}{1+e^{-x}}
+\end{equation}
+
+\begin{equation}\label{eq:softmax}
+ \delta{(\boldsymbol{z})}_j = \frac{e^{z_j}}{\sum\limits^{K}_{k=1}e^{z_k}}
+\end{equation}
+
+\begin{figure}[H]
+ \begin{subfigure}{.5\textwidth}
+ \centering
+ \includegraphics[width=.8\linewidth]{bcann}
+ \caption{Binary classifier network architecture}\label{fig:bcann}
+ \end{subfigure}%
+%
+ \begin{subfigure}{.5\textwidth}
+ \includegraphics[width=.8\linewidth]{mcann}
+ \caption{Multiclass classifier network architecture}\label{fig:mcann}
+ \end{subfigure}
+ \caption{\acrlong{ANN} architectures.}
+\end{figure}
\section{Results}
+\begin{table}[H]
+ \centering
+ \begin{tabular}{rccc}
+ \toprule
+ & \multicolumn{3}{c}{Parameters (step/length)}\\
+ & 10/25 & 40/100 & 80/200\\
+ \midrule
+ 3h & 0.86 (0.34) & 0.87 (0.32) & 0.85 (0.35)\\
+ 5h & 0.87 (0.31) & 0.88 (0.30) & 0.87 (0.32)\\
+ 8h & 0.88 (0.30) & 0.88 (0.31) & 0.88 (0.29)\\
+ 13h & 0.89 (0.28) & 0.89 (0.29) & 0.88 (0.30)\\
+ \bottomrule
+ \end{tabular}
+ \caption{Binary classification results (accuracy (loss))}
+\end{table}
+\begin{table}[H]
+ \centering
+ \begin{tabular}{rccc}
+ \toprule
+ & \multicolumn{3}{c}{Parameters (step/length)}\\
+ & 10/25 & 40/100 & 80/200\\
+ \midrule
+ 3h & 0.83 (0.48) & 0.82 (0.48) & 0.82 (0.48)\\
+ 5h & 0.85 (0.43) & 0.84 (0.44) & 0.84 (0.44)\\
+ 8h & 0.86 (0.41) & 0.86 (0.39) & 0.86 (0.40)\\
+ 13h & 0.87 (0.37) & 0.87 (0.38) & 0.86 (0.39)\\
+ \bottomrule
+ \end{tabular}
+ \caption{Multiclass classification results (accuracy (loss))}
+\end{table}
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