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03-07-01-ACA-Input-Post-Processing.tex
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03-07-01-ACA-Input-Post-Processing.tex
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% move all configuration stuff into includes file so we can focus on the content
\input{include}
\subtitle{module 3.7.1: feature post-processing}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
% generate title page
\input{include/titlepage}
\section[overview]{lecture overview}
\begin{frame}{introduction}{overview}
\begin{block}{corresponding textbook section}
%\href{http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6331120}{Chapter 3~---~Instantaneous Features}: pp.~63--66
sections~3.7.1--3.7.3
\end{block}
\begin{itemize}
\item \textbf{lecture content}
\begin{itemize}
\item derived features
\item feature aggregation
\item feature normalization
\end{itemize}
\bigskip
\item<2-> \textbf{learning objectives}
\begin{itemize}
\item discuss the advantages of specific derived features
\item summarize the principles of feature aggregation
\item list two forms of feature normalization and explain their usefulness
\end{itemize}
\end{itemize}
\inserticon{directions}
\end{frame}
\section[intro]{introduction}
\begin{frame}{feature post-processing}{introduction 1/2}
\begin{itemize}
\item extracting multiple instantaneous features leads to
\begin{itemize}
\item[$\rightarrow$] one feature vector per block, or
\item[$\rightarrow$] one feature matrix per audio file
\end{itemize}
\end{itemize}
\bigskip
\begin{eqnarray*}
\mat{V} &=& \left[\vec{v}(0)\; \vec{v}(1)\; \ldots\; \vec{v}(\mathcal{N}-1)\right] \nonumber\\
&=&
\left[
\begin{array}{cccc}
v_0(0) & v_0(1) & \ldots & v_0(\mathcal{N}-1)\\
v_1(0) & v_1(1) & \ldots & v_1(\mathcal{N}-1)\\
\vdots & \vdots & \ddots & \vdots \\
v_{\mathcal{F}-1}(0) & v_{\mathcal{F}-1}(1) & \ldots & v_{\mathcal{F}-1}(\mathcal{N}-1)\\
\end{array}
\right]
\end{eqnarray*}
\bigskip
\begin{footnotesize}
dimensions: $\mathcal{F}\times \mathcal{N}$ (number of features and number of blocks, resp.)
\end{footnotesize}
\end{frame}
\begin{frame}{feature post-processing}{introduction 2/2}
multiple options for feature matrix processing:
\begin{enumerate}
\item derive additional features
\item aggregate existing features (e.g., one feature vector per file)
\item ensure similar scale and distribution
\end{enumerate}
\end{frame}
\section[derived]{derived features}
\begin{frame}{feature post-processing}{examples of derived features}
%\begin{columns}
%\column{.5\linewidth}
\begin{itemize}
\item \textbf{diff}: use the change in value
\begin{equation*}
v_{j,\Delta}(n) = v_j(n) - v_j(n-1)
\end{equation*}
\smallskip
\item<2-> \textbf{smoothed}: remove high frequency content by low-pass filtering
\begin{itemize}
\item (anticausal) single-pole
\begin{equation*}
v_{j,\mathrm{LP}}(n) = (1-\alpha)\cdot v_j(n) - \alpha\cdot v_{j,\mathrm{LP}}(n-1)
\end{equation*}
\item moving average
\end{itemize}
\end{itemize}
%\column{.5\linewidth}
%\vspace{-10mm}
%\begin{figure}%
%\includegraphics{DerivedFeatures}%
%\end{figure}
%\end{columns}
%\addreference{matlab source: \href{https://github.com/alexanderlerch/ACA-Slides/blob/master/matlab/displayDerivedFeatures.m}{matlab/displayDerivedFeatures.m}}
\end{frame}
\section[normalization]{feature normalization}
\begin{frame}{feature post-processing}{feature normalization}
\vspace{-3mm}
\begin{columns}
\column{.5\linewidth}
\begin{itemize}
\item \textbf{reasons}
\begin{itemize}
\item features have different ranges and distributions
\item ensure that one feature does not have outsized impact
\end{itemize}
\smallskip
\item \textbf{z-score normalization}
\begin{equation*}\label{eq:featnorm_zscore}
v_{j,\mathrm{N}}(n) = \frac{v_j(n) - \mu_{v_j}}{\sigma_{v_j}}.
\end{equation*}
\item \textbf{min-max normalization}
\begin{equation*}\label{eq:featnorm_minmax}
v_{j,\mathrm{N}}(n) = \frac{v_j(n) - \min(v_j)}{\max(v_j) - \min(v_j)}.
\end{equation*}
\end{itemize}
\column{.5\linewidth}
\begin{block}{normalization}
The normalization constants $\mu_{v_j},\sigma_{v_j},\max(v_j),\min(v_j)$ have to be estimated from the \emph{{Training Set}}. The same (training) constants are then applied during inference. Extracting constants from the \emph{Test Set} is meaningless as the system has to infer with exactly the same parameters as during training.
\end{block}
\end{columns}
\end{frame}
\section[aggregation]{feature aggregation}
\begin{frame}{feature post-processing}{feature aggregation}
feature aggregation:\footnote{also compare \textit{pooling} operation in machine learning} compute \textit{summary features} from feature series $\Rightarrow$ \textbf{subfeatures}
\bigskip
\begin{itemize}
\item \textbf{reasons}
\begin{itemize}
\item only one feature vector required per file
\item data reduction
\item characteristics of distribution or change over time contain additional info
\end{itemize}
\smallskip
\item \textbf{examples}
\begin{itemize}
\item \textit{statistical descriptors}
\begin{itemize}
\item mean, median, max, standard deviation
\end{itemize}
\item \textit{hand crafted }
\begin{itemize}
\item anything that might be meaningful --- periodicity, slope, \ldots
\end{itemize}
\end{itemize}
\end{itemize}
\end{frame}
\begin{frame}{feature post-processing}{feature aggregation}
\begin{columns}
\column{.4\linewidth}
\begin{itemize}
\item could be for whole file or \textbf{texture window}:\\ split feature series in overlapping blocks of a few seconds length
\bigskip
\item<2-> could be \textbf{hierarchical} process:
\begin{enumerate}
\item compute subfeatures per window
\item compute subfeatures of subfeature series
\item (go to 1.)
\end{enumerate}
\end{itemize}
%\begin{footnotesize}
%\begin{align}
%%\mat{V} &=&
%\left[
%\begin{array}{ccccc}
%v_0(0) & v_0(1) & v_0(2) & v_0(3) & v_0(4) \\
%v_1(0) & v_1(1) & v_1(2) & v_1(3) & v_1(4) \\
%\vdots & \vdots & \vdots & \vdots & \vdots \\
%\undermat{\left[\begin{array}{c}
%\mu_0(0)\\
%\sigma_0(0)\\
%\mu_1(0)\\
%\sigma_1(0)\\
%\vdots\\
%\mu_{\mathcal{F}-1}(0)\\
%\sigma_{\mathcal{F}-1}(0)
%\end{array}\right] }{v_{\mathcal{F}-1}(0) & v_{\mathcal{F}-1}(1) & v_{\mathcal{F}-1}(2)& v_{\mathcal{F}-1}(3)} & v_{\mathcal{F}-1}(4)\\
%\end{array}
%\right]
%\end{align}
%\end{footnotesize}
%\vspace{8\baselineskip}
%\caption[Feature Aggregation]{Example aggregation with a texture window length of $4$ with the arithmetic mean $\mu$ and the standard deviation $\sigma$}
%\label{fig:feature_aggregation}
\column{.6\linewidth}
\figwithmatlab{TextureWindow}
\end{columns}
\end{frame}
\section{summary}
\begin{frame}{summary}{lecture content}
\begin{itemize}
\item \textbf{feature matrix should be processed to adapt to task and classifier}
\begin{itemize}
\item derive additional features
\item aggregate features
\item normalize features
\end{itemize}
\bigskip
\item \textbf{derived features}
\begin{itemize}
\item take existing features and ``create'' new ones
\end{itemize}
\bigskip
\item \textbf{feature normalization}
\begin{itemize}
\item avoid different value ranges might impacting classifier
\item handle different feature distributions
\end{itemize}
\bigskip
\item \textbf{aggregate features: subfeatures}
\begin{itemize}
\item combine blocks of features by computing, e.g., statistical features from them (mean, standard deviation, \ldots)
\item subfeature vector is used as classifier input or as intermediate feature series
\end{itemize}
\end{itemize}
\inserticon{summary}
\end{frame}
\end{document}