refine.tex

隐马尔科夫模型工具箱

    TB thresh macroname itemlist
\end{verbatim}
Apart from the clustering mechanism, there are some other differences between
\texttt{TC} and \texttt{TB}.  Firstly, \texttt{TC} uses a distance metric between
states whereas \texttt{TB} uses a log likelihood criterion.  Thus, the threshold
values are not directly comparable.  Furthermore, \texttt{TC} supports any type
of output distribution whereas \texttt{TB} only supports single-Gaussian
continuous density output distributions.
Secondly, although the following describes only state clustering, 
the \texttt{TB} command\index{tb@\texttt{TB} command} can also be used to cluster whole
models.

A phonetic decision tree is a binary tree in which a yes/no phonetic 
question\index{phonetic questions}
is attached to each node.  
Initially all states in a given item list (typically a specific phone state position)
are placed at the
root node of a tree. Depending on each answer, the pool of states is
successively split and this continues until the states have trickled
down to leaf-nodes.  All states in the same leaf node are then tied. 
For example, Fig~\href{f:qstree} illustrates the case of tying the centre
states of all triphones of the phone /aw/ (as in ``out'').  All of the states trickle
down the tree and depending on the answer to the questions, they end up
at one of the shaded terminal nodes.   For example, in the illustrated
case, the centre state of \texttt{s-aw+n} would join the second leaf
node from the right since its right context is a central consonant,
and its right
context is a nasal  but its left context is not a central stop.

The question at each node is chosen to (locally) maximise the likelihood
of the training data given the final set of state tyings. 
Before any tree building can take place, all of the possible phonetic
questions must be loaded into \htool{HHEd} using \texttt{QS} 
commands\index{qs@\texttt{QS} command}.  Each
question takes the form ``Is the left or right context in the set P?'' where the
context is the model context as defined by its logical name.  The 
set P is
represented by an item list and
for convenience every question is given a name.  As an example, the
following command 
\begin{verbatim}
    QS "L_Nasal" { ng-*,n-*,m-* }
\end{verbatim}
defines the question ``Is the left context a nasal?''.

It is possible to calculate the log likelihood of the training
data given any pool of states (or models).  Furthermore, this 
can be done without reference to the
training data itself since for single Gaussian distributions the means, variances
and state occupation counts (input via a stats file) form sufficient statistics.
Splitting any pool into two will increase the log likelihood since it provides twice
as many parameters to model the same amount of data.  The increase obtained when
each possible question is used can thus be calculated and the question selected
which gives the biggest improvement.  

Trees are therefore built using a top-down sequential optimisation process.
Initially all states (or models) are placed in a single cluster at the root
of the tree.  The question is then found which gives the best split of the root
node.  This process is repeated until the increase in log likelihood falls
below the threshold specified in the \texttt{TB} command.
As a final stage, the decrease in log likelihood is calculated for merging
terminal nodes with differing parents.  Any pair of nodes for which this
decrease is less than the threshold used to stop splitting are then merged.
\index{tree optimisation}

As with the \texttt{TC} command, it is useful to prevent the creation of
clusters with very little associated training data.  The \texttt{RO} command
can therefore be used in tree clustering as well as in data-driven clustering.
When used with trees, any split which would result in a total occupation count
falling below the value specified is prohibited.  Note that the \texttt{RO}
command can also be used to load the required stats file.  Alternatively,
the stats file can be loaded using the \texttt{LS} command\index{ls@\texttt{LS} command}.

As with data-driven clustering, using the trace facilities provided by
\htool{HHEd} is recommended for monitoring and setting the appropriate thresholds.
Basic tracing provides the following summary data for each tree
\begin{verbatim}
    TB 350.00 aw_s3 {}
     Tree based clustering
      Start  aw[3] : 28  have  LogL=-86.899 occ=864.2
      Via    aw[3] : 5   gives LogL=-84.421 occ=864.2
      End    aw[3] : 5   gives LogL=-84.421 occ=864.2
    TB: Stats 28->5 [17.9%]  { 4537->285 [6.3%] total }
\end{verbatim}
This example corresponds to the case illustrated in Fig~\href{f:qstree}.
The \texttt{TB}
command has been invoked with a  threshold of 350.0 to cluster
the centre states of the triphones of the phone \textit{aw}.
At the start of clustering with all 28 states in a single pool, the average
log likelihood per unit of occupation is -86.9 and on completion with
5 clusters this has increased to -84.4.  The middle line labelled ``via'' gives
the position after the tree has been built but before terminal nodes have been
merged (none were merged in this case).  The last line summarises the overall
position.  After building this tree, a total of 4537 states were reduced
to 285 clusters.\index{clustering!tracing in}

As noted at the start of this section, an important advantage of tree-based clustering
is that it allows triphone models which have no training data to be synthesised.
This is done in \htool{HHEd} using the \texttt{AU} command\index{au@\texttt{AU} command} which has the form
\begin{verbatim}
    AU hmmlist
\end{verbatim}
Its effect is to scan the given \texttt{hmmlist} and any physical models listed
which are not in the currently loaded set are synthesised.  This is done 
by descending the previously constructed trees for that phone and answering the
questions at each node based on the new unseen context.  When each leaf node is
reached, the state representing that cluster is used for the corresponding state
in the unseen triphone\index{unseen triphones!synthesising}.

The \texttt{AU} command can be used within the same edit script as the tree building
commands.  However, it will often be the case that a new set of triphones is needed
at a later date, perhaps as a result of vocabulary changes.  To make this possible,
a complete set of trees can be saved using the \texttt{ST} 
command\index{st@\texttt{ST} command} and then later
reloaded using the \texttt{LT} command\index{lt@\texttt{LT} command}.
\index{decision trees!loading and storing}

\mysect{Mixture Incrementing}{upmix}

When building sub-word based continuous density systems, 
the final system will typically consist of multiple mixture component
context-dependent HMMs.  However, as indicated previously, the early
stages of triphone construction, particularly state tying, are best done
with single Gaussian models.  Indeed, if tree-based clustering is to be
used there is no option.\index{mixture incrementing}\index{up-mixing}

In \HTK\ therefore, the conversion from single Gaussian HMMs to multiple
mixture component HMMs is usually one of the final steps in building
a system.  The mechanism provided to do this is the \htool{HHEd} \texttt{MU} command
which will increase the number of components in a mixture by 
a process called \textit{mixture splitting}.
This approach to building a multiple
mixture component system is extremely
flexible since it allows the number of mixture components to be repeatedly increased
until the desired level of performance is achieved.\index{mixture splitting}

The \texttt{MU} command\index{mu@\texttt{MU} command} has the form
\begin{verbatim}
     MU n itemList
\end{verbatim}
where \texttt{n} gives the new number of mixture components required and
\texttt{itemList} defines the actual mixture distributions to modify.  This
command works by repeatedly splitting the mixture with the largest mixture
weight until the required number of components is obtained.  The actual
split is performed by copying the mixture, dividing the weights of both
copies by 2, and finally perturbing the means by plus or minus 0.2 standard
deviations.
For example, the command
\begin{verbatim}
     MU 3 {aa.state[2].mix}
\end{verbatim}
would increase the number of mixture components in the output distribution
for state 2 of model \texttt{aa} to 3.   Normally, however,  the number of
components in all mixture distributions will be increased at the same time.
Hence, a command of the form is more usual
\begin{verbatim}
     MU 3 {*.state[2-4].mix}
\end{verbatim}
It is usually a good idea to increment mixture components in
stages, for example, by incrementing by 1 or 2 then re-estimating, then
incrementing by 1 or 2 again and re-estimating, and so on until the
required number of components are obtained.  This also allows recognition performance
to be monitored to find the optimum.

One final point with regard to multiple mixture component distributions is that
all \HTK\ tools ignore mixture components whose weights fall below a threshold value
called \texttt{MINMIX} (defined in \texttt{HModel.h}).  Such mixture components
are called {\it defunct}.  Defunct mixture components can be
prevented by setting the \texttt{-w} option in \htool{HERest} so that all mixture
weights are floored to some level above 
\texttt{MINMIX}\index{minmix@\texttt{MINMIX}}.  If 
mixture weights\index{mixture weight floor}
are allowed to fall below \texttt{MINMIX} then the corresponding Gaussian
parameters will not be written out when the model containing that component
is saved.  It is possible to recover from this, however, since the \texttt{MU} command
will replace defunct mixtures\index{defunct mixtures} before performing any requested mixture
component increment.

\mysect{Regression Class Tree Construction}{hhedregtree}

In order to perform most model adaptation tasks (see
chapter~\ref{c:Adapt}), it will be neccesary to produce a binary regression
class tree\index{adaptation!regression tree}. 
This tree is stored in the MMF, along with a regression
base class identifier for each mixture component. An example
regression tree and how it may be used is shown in
subsection~\ref{s:reg_classes}. \htool{HHEd} provides the means to
construct a regression class tree for a given MMF, and is invoked
using the \texttt{RC} command\index{rc@\texttt{RC} command}. 
It is also necessary to supply a
statistics file, which is output using the \texttt{-s} option of
\texttt{HERest}. The statistics file can be loaded by invoking the
\texttt{LS}\index{ls@\texttt{LS} command} command.

A centroid-splitting algorithm using a Euclidean distance measure is
used to grow the binary regression class tree to cluster the model
set's  mixture components.  Each leaf node therefore specifies a 
particular mixture component cluster. This algorithm proceeds
as follows until the requested number of terminals has been achieved.
\begin{itemize}
\item Select a terminal node that is to be split.
\item Calculated the mean and variance from the mixture components clustered
at this node.
\item Create two children. Initialise their means to the parent mean 
perturbed in opposite directions (for each child) by a fraction of 
the variance.
\item For each component at the parent node assign the component 
to one of the children by using a Euclidean distance measure to 
ascertain which child mean the component is closest to.
\item Once all the components have been assigned, calculate the new
means for the children, based on the component assignments.
\item Keep re-assigning components to the children and re-estimating
the child means until there is no change in assignments from one
iteration to the next. Now finalise the split.
\end{itemize}

As an example, the following \htool{HHEd} script would produce a 
regression class tree with 32 terminal nodes, or regression base
classes:-
\begin{verbatim}
     LS "statsfile"
     RC 32 "rtree"
\end{verbatim}

A further optional argument is possible with the 
\texttt{RC} command. 
This argument allows the user to specify the non-speech class
mixture components using an \texttt{itemlist}, 
such as the silence mixture components. 
\begin{verbatim}
     LS "statsfile"
     RC 32 "rtree" {sil.state[2-4].mix}
\end{verbatim}
In this case the first split that will be made in the regression class tree
will be to split the speech and non-speech sounds, after which the
tree building continues as usual. 

\mysect{Miscellaneous Operations}{misedit}

The preceding sections have described the main \htool{HHEd} commands used for
building continuous density systems with tied parameters.  A further group
of commands (\texttt{JO}, \texttt{TI} and \texttt{HK}) are used to build
tied-mixture systems and these are described in Chapter~\ref{c:discmods}.
Those
remaining cover a miscellany of functions.  They are documented in the
reference entry for \htool{HHEd} and include commands to add and remove
state transitions\index{state transitions!adding/removing} 
(\texttt{AT}\index{at@\texttt{AT} command},
\texttt{RT}\index{rt@\texttt{RT} command}); synthesise triphones from
biphones (\texttt{MT}\index{mt@\texttt{MT} command}); 
change the parameter kind of a HMM (\texttt{SK}\index{sk@\texttt{SK} command});
modify stream dimensions (\texttt{SS}\index{ss@\texttt{SS} command},
\texttt{SU}\index{su@\texttt{SU} command},
\texttt{SW}\index{sw@\texttt{SW} command}); change/add an identifier name
to an MMF (\texttt{RN}\index{rn@\texttt{RN}} command); and expand
HMM sets by duplication, for example, as needed in making gender
dependent models (\texttt{DP}\index{dp@\texttt{DP} command}).


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