Mercurial > hg > cip2012

Binary file draft.pdf has changed
--- a/draft.tex	Thu Mar 15 22:01:00 2012 +0000
+++ b/draft.tex	Fri Mar 16 12:13:52 2012 +0000
@@ -546,8 +546,11 @@
 		\label{eq:entro-rate}
 		h_\mu = H(X_t|\past{X}_t).
 	\end{equation}
-	The entropy rate gives a measure of the overall surprisingness
-	or unpredictability of the process.
+	The entropy rate is a measure of the overall surprisingness
+	or unpredictability of the process, and gives an indication of the average
+	level of surprise and uncertainty that would be experienced by an observer
+	processing a sequence sampled from the process using the methods of
+	\secrf{surprise-info-seq}.

 	The \emph{multi-information rate} $\rho_\mu$ (following Dubnov's \cite{Dubnov2006}
 	notation for what he called the `information rate') is the mutual
@@ -593,6 +596,8 @@
 	or \emph{erasure} \cite{VerduWeissman2006} entropy rate.
 	These relationships are illustrated in \Figrf{predinfo-bg}, along with
 	several of the information measures we have discussed so far.
+	The PIR gives an indication of the average IPI that would be experienced
+	by an observer processing a sequence sampled from this process.


 	James et al \cite{JamesEllisonCrutchfield2011} review several of these
@@ -758,11 +763,9 @@
 	 to the stochastic process.  %Dubnov, MacAdams, Reynolds (2006) %Bailes and
 	 Dean (2009)

-        \begin{itemize}
-            \item Continuous domain information
-                        \item Audio based music expectation modelling
-            \item Proposed model for Gaussian processes
-        \end{itemize}
+		[ Continuous domain information ]
+		[Audio based music expectation modelling]
+		[ Gaussian processes]


 \subsection{Beat Tracking}
@@ -805,7 +808,30 @@
     }
   \end{fig}

-The use of stochastic processes in music composition has been widespread for decades---for instance Iannis Xenakis applied probabilistic mathematical models to the creation of musical materials\cite{Xenakis:1992ul}.  Information dynamics can serve as a novel framework for the exploration of the possibilities of stochastic and algorithmic processes; outputs can be filtered to match a set of criteria defined in terms of the information dynamics model, this criteria thus becoming a means of interfacing with the generative processes.  This allows a composer to explore musical possibilities at the high and abstract level of expectation, randomness and predictability.
+The use of stochastic processes in music composition has been widespread for
+decades---for instance Iannis Xenakis applied probabilistic mathematical models
+to the creation of musical materials\cite{Xenakis:1992ul}.  Information dynamics
+can serve as a novel framework for the exploration of the possibilities of
+stochastic and algorithmic processes; outputs can be filtered to match a set of
+criteria defined in terms of information-dynamical characteristics, such as
+predictability vs unpredictability
+%s model, this criteria thus becoming a means of interfacing with the generative processes.
+This allows a composer to explore musical possibilities at the high and abstract level of
+expectation, randomness and predictability.
+In particular, the behaviour of the predictive information rate (PIR) defined in
+\secrf{process-info} make it interesting from a compositional point of view. The definition
+of the PIR is such that it is low both for extremely regular processes, such as constant
+or periodic sequences, \emph{and} low for extremely random processes, where each symbol
+is chosen independently of the others, in a kind of `white noise'. In the former case,
+the pattern, once established, is completely predictable and therefore there is no
+\emph{new} information in subsequent observations. In the latter case, all the observations
+are random and independent, and hence unpredictable, but also not informative about
+any other observation. Processes with high PIR maintain a certain kind of balance between
+predictability and unpredictability in such a way that the observer must be continually
+paying attention to each new observation as it occurs in order to make the best
+possible predictions about the evolution of the seqeunce. This balance between predictability
+and unpredictability is reminiscent of the Wundt curve (see \figrf{wundt}), which
+summarises the observations of Wundt [ref].. [etc \dots].


 %It is possible to apply information dynamics to the generation of content, such as to the composition of musical materials.
@@ -818,9 +844,8 @@

  \subsection{The Melody Triangle}

-\begin{figure}
-	\centering
-	\includegraphics[width=\linewidth]{figs/mtriscat}
+ \begin{fig}{mtriscat}
+	\colfig{mtriscat}
 	\caption{The population of transition matrices distributed along three axes of
 	redundancy, entropy rate and predictive information rate (all measured in bits).
 	The concentrations of points along the redundancy axis correspond
@@ -828,9 +853,8 @@
 	3, 4, \etc all the way to period 8 (redundancy 3 bits). The colour of each point
 	represents its PIR---note that the highest values are found at intermediate entropy
 	and redundancy, and that the distribution as a whole makes a curved triangle. Although
-	not visible in this plot, it is largely hollow in the middle.
-	\label{InfoDynEngine}}
-\end{figure}
+	not visible in this plot, it is largely hollow in the middle.}
+\end{fig}

 The Melody Triangle is an exploratory interface for the discovery of melodic
 content, where the input---positions within a triangle---directly map to information
@@ -845,7 +869,7 @@
 These are plotted in a 3D information space of $\rho_\mu$ (redundancy), $h_\mu$ (entropy rate) and
 $b_\mu$ (predictive information rate), as defined in \secrf{process-info}.
  In our case we generated thousands of transition matrices, representing first-order
- Markov chains, by a random sampling method.  In figure \ref{InfoDynEngine} we
+ Markov chains, by a random sampling method.  In figure \figrf{mtriscat} we
  see a representation of how these matrices are distributed in the 3D information
  space; each one of these points corresponds to a transition matrix.

@@ -855,8 +879,8 @@
 a flat triangle.  It is this triangular sheet that is our `Melody Triangle' and
 forms the interface by which the system is controlled.  Using this interface
 thus involves a mapping to information space; a user selects a position within
-the triangle, and a corresponding transition matrix is returned.  Figure
-\ref{TheTriangle} shows how the triangle maps to different measures of redundancy,
+the triangle, and a corresponding transition matrix is returned.
+\Figrf{TheTriangle} shows how the triangle maps to different measures of redundancy,
 entropy rate and predictive information rate.


@@ -871,11 +895,10 @@
 These melodies have some level of unpredictability, but are not completely random.
  Or, conversely, are predictable, but not entirely so.

- \begin{figure}
-\centering
-\includegraphics[width=0.9\linewidth]{figs/TheTriangle.pdf}
-\caption{The Melody Triangle\label{TheTriangle}}
-\end{figure}
+\begin{fig}{TheTriangle}
+	\colfig[0.9]{TheTriangle.pdf}
+	\caption{The Melody Triangle}
+\end{fig}

 %PERHAPS WE SHOULD FOREGO TALKING ABOUT THE
 %INSTALLATION VERSION OF THE TRIANGLE?
@@ -894,11 +917,17 @@
 space of the Melody Triangle.  A number of tokens, each representing a
 melody, can be dragged in and around the triangle.  For each token, a sequence of symbols with
 statistical properties that correspond to the token's position is generated.  These
-symbols are then mapped to notes of a scale\footnote{However they could just as well be mapped to any other property, such as intervals, chords, dynamics and timbres.  It is even possible to map the symbols to non-sonic outputs, such as colours.  The possibilities afforded by the Melody Triangle in these other domains remains to be investigated.}.
+symbols are then mapped to notes of a scale%
+\footnote{However they could just as well be mapped to any other property, such
+as intervals, chords, dynamics and timbres.  It is even possible to map the
+symbols to non-sonic outputs, such as colours.  The possibilities afforded by
+the Melody Triangle in these other domains remains to be investigated.}.
 Additionally keyboard commands give control over other musical parameters.

-The Melody Triangle can generate intricate musical textures when multiple tokens are in the triangle.
-Unlike other computer aided composition tools or programming environments, here the composer engages with music on a high and abstract level; the interface relating to subjective expectation and predictability.
+The Melody Triangle can generate intricate musical textures when multiple tokens
+are in the triangle.  Unlike other computer aided composition tools or programming
+environments, here the composer engages with music on a high and abstract level;
+the interface relating to subjective expectation and predictability.


@@ -976,16 +1005,30 @@


 \section{Conclusion}
-We outlined our information dynamics approach to the modelling of the perception of music.  This approach models the subjective assessments of an observer that updates its probabilistic model of a process dynamically as events unfold.  We outlined `time-varying' information measures, including a novel `predictive information rate' that characterises the surprisingness and predictability of musical patterns.
+We outlined our information dynamics approach to the modelling of the perception
+of music.  This approach models the subjective assessments of an observer that
+updates its probabilistic model of a process dynamically as events unfold.  We
+outlined `time-varying' information measures, including a novel `predictive
+information rate' that characterises the surprisingness and predictability of
+musical patterns.


-We have outlined how information dynamics can serve in three different forms of analysis; musicological analysis, sound categorisation and beat tracking.
+We have outlined how information dynamics can serve in three different forms of
+analysis; musicological analysis, sound categorisation and beat tracking.

-We have described the `Melody Triangle', a novel system that enables a user/composer to discover musical content in terms of the information theoretic properties of the output, and considered how information dynamics could be used to provide evaluative feedback on a composition or improvisation.  Finally we outline a pilot study that used the Melody Triangle as an experimental interface to help determine if there are any correlations between aesthetic preference and information dynamics measures.
+We have described the `Melody Triangle', a novel system that enables a user/composer
+to discover musical content in terms of the information theoretic properties of
+the output, and considered how information dynamics could be used to provide
+evaluative feedback on a composition or improvisation.  Finally we outline a
+pilot study that used the Melody Triangle as an experimental interface to help
+determine if there are any correlations between aesthetic preference and information
+dynamics measures.


 \section{acknowledgments}
-This work is supported by EPSRC Doctoral Training Centre EP/G03723X/1 (HE), GR/S82213/01 and EP/E045235/1(SA), an EPSRC Leadership Fellowship, EP/G007144/1 (MDP) and EPSRC IDyOM2 EP/H013059/1.
+This work is supported by EPSRC Doctoral Training Centre EP/G03723X/1 (HE),
+GR/S82213/01 and EP/E045235/1(SA), an EPSRC Leadership Fellowship, EP/G007144/1
+(MDP) and EPSRC IDyOM2 EP/H013059/1.

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