%Methodology

%Experiment(s) (set-up, data, results, discussion)
\section{Data \& Preprocessing}
To answer the research question, several experiments have been performed. Data
has been collected from several \gls{dm} and \gls{dom} albums. The exact data
used is available in Appendix~\ref{app:data}. The albums are extracted from the
audio CD and converted to a mono channel waveform with the correct samplerate
utilizing \emph{SoX}\footnote{\url{http://sox.sourceforge.net/}}. Every file
is annotated using Praat~\cite{boersma_praat_2002} where the lyrics are
manually aligned to the audio. Examples of utterances are shown in
Figure~\ref{fig:bloodstained} and Figure~\ref{fig:abominations} where the
waveform, $1-8000$Hz spectrals and annotations are shown. It is clearly visible
that within the genre of death metal there are different spectral patterns
visible over time.

\begin{figure}[ht]
	\centering
	\includegraphics[width=.7\linewidth]{cement}
	\caption{A vocal segment of the \acrlong{CC} song
		\emph{Bloodstained Cement}}\label{fig:bloodstained}
\end{figure}

\begin{figure}[ht]
	\centering
	\includegraphics[width=.7\linewidth]{abominations}
	\caption{A vocal segment of the \acrlong{DG} song
		\emph{Enthroned Abominations}}\label{fig:abominations}
\end{figure}

The data is collected from three studio albums. The first band is called
\gls{CC} and has been producing \gls{dm} for almost 25 years and has been
creating albums with a consistent style. The singer of \gls{CC} has a very
raspy growl and the lyrics are quite comprehensible. The vocals produced by
\gls{CC} are very close to regular shouting.

The second band is called \gls{DG} and makes even more violently
sounding music. The growls of the lead singer sound like a coffee grinder and
are sound less full. In the spectrals it is clearly visible that there are
overtones produced during some parts of the growling. The lyrics are completely
incomprehensible and therefore some parts were not annotated with the actual
lyrics because it was impossible to hear what was being sung.

The third band --- originating from Moscow --- is chosen bearing the name
\gls{WDISS}. This band is a little odd compared to the previous \gls{dm} bands
because they create \gls{dom}. \gls{dom} is characterized by the very slow
tempo and low tuned guitars. The vocalist has a very characteristic growl and
performs in several Muscovite bands. This band also stands out because it uses
piano's and synthesizers. The droning synthesizers often operate in the same
frequency as the vocals.

Additional detailss about the dataset are listed in Appendix~\ref{app:data}.
The data is labeled as singing and instrumental and labeled per band. The
distribution for this is shown in Table~\ref{tbl:distribution}.
\begin{table}[H]
	\centering
	\begin{tabular}{lcc}
		\toprule
		Instrumental & Singing\\
		\midrule
		0.59 & 0.41\\
		\bottomrule
	\end{tabular}
	\quad
	\begin{tabular}{lcccc}
		\toprule
		Instrumental & \gls{CC} & \gls{DG} & \gls{WDISS}\\
		\midrule
		0.59 & 0.16 & 0.19 & 0.06\\
		\bottomrule
	\end{tabular}
	\caption{Data distribution}\label{tbl:distribution}
\end{table}

\section{\acrlong{MFCC} Features}
The waveforms in itself are not very suitable to be used as features due to the
high dimensionality and correlation in the temporal domain. Therefore we use
the often used \glspl{MFCC} feature vectors which have shown to be suitable in
speech processing~\cite{rocamora_comparing_2007}. It has also been found that
altering the mel scale to better suit singing does not yield a better
performance~\cite{you_comparative_2015}. The actual conversion is done using
the \emph{python\_speech\_features}\footnote{\url{%
https://github.com/jameslyons/python_speech_features}} package.

\gls{MFCC} features are inspired by human auditory processing and are
created from a waveform incrementally using several steps:
\begin{enumerate}
	\item The first step in the process is converting the time representation
		of the signal to a spectral representation using a sliding analysis
		window with overlap. The width of the window and the step size are two
		important parameters in the system. In classical phonetic analysis
		window sizes of $25ms$ with a step of $10ms$ are often chosen because
		they are small enough to contain just one subphone event. Singing for
		$25ms$ is impossible so it might be necessary to increase the window
		size.
	\item The standard \gls{FT} gives a spectral representation that has
		linearly scaled frequencies. This scale is converted to the \gls{MS}
		using triangular overlapping windows to get a more tonotopic
		representation trying to match the actual representation of the cochlea
		in the human ear.
	\item The \emph{Weber-Fechner} law describes how humans perceive physical
		magnitudes\footnote{Fechner, Gustav Theodor (1860). Elemente der
		Psychophysik}. They found that energy is perceived in logarithmic
		increments. This means that twice the amount of energy does not mean
		twice the amount of perceived loudness. Therefore we take the log of
		the energy or amplitude of the \gls{MS} spectrum to closer match the
		human hearing.
	\item The amplitudes of the spectrum are highly correlated and therefore
		the last step is a decorrelation step. \Gls{DCT} is applied on the
		amplitudes interpreted as a signal. \Gls{DCT} is a technique of
		describing a signal as a combination of several primitive cosine
		functions.
\end{enumerate}

The default number of \gls{MFCC} parameters is twelve. However, often a
thirteenth value is added that represents the energy in the analysis window.
The $c_0$ is chosen is this example. $c_0$ is the zeroth \gls{MFCC}. It
represents the overall energy in the \gls{MS}. Another option would be
$\log{(E)}$ which is the logarithm of the raw energy of the sample.

\section{\acrlong{ANN}}
The data is classified using standard \gls{ANN} techniques, namely \glspl{MLP}.
The classification problems are only binary and four-class so it is
interesting to see where the bottleneck lies; how abstract can the abstraction
be made. 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
overfitting on one album. Every model was trained using $10$ epochs and a
batch size of $32$. The training set and test set are separated by taking a
$90\%$ slice of all the data.

\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}
		\centering
		\includegraphics[width=.8\linewidth]{mcann}
		\caption{Multiclass classifier network architecture}\label{fig:mcann}
	\end{subfigure}
	\caption{\acrlong{ANN} architectures.}
\end{figure}

\section{Experimental setup}
\subsection{Features}
The thirteen \gls{MFCC} features are used as the input.  Th 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}

\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. 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. 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}.
