One-dimensional DVD maps (developmental histograms)
One-dimensional DVD-maps display changes in the values of a single feature, capturing the entire table (e.g., the whole song development) in a single image. Petr Janata was the first to suggest this idea, and showed that presenting the evolution of duration histograms during development has traceable structure. The plot shows the distribution of syllable durations during any one day in each raw using gray-scale and the entire matrix span that entire song development. SA+ uses a similar approach, except that the gray-scale is replaced by a 3D reconstruction.
Click the '1D developmental histograms' tab and open the table of bird109. Then select 'duration' for the X axis (Y axis selection has no effect - we only look at one feature) and click 'Histogram'. Computing the histogram takes about 30 seconds.
Each row in the 3D histogram shown below represents a single day of song development, and the height of the mountains represents the abundance (frequency) of a certain duration. The far side of the histogram represents the end of song development, and the 3 peaks stand for the 3 syllable types produced by this bird. As shown, it is very easy to trace the peaks backwards to the point of origin. The advantage of this representation is that it shows us the entire song development at a glance, based on the entire song development data. It is also making it obvious why is it so important to record and analyze the entire song development data - otherwise, computing such histograms won't be as robust and won't work on a short time scale. Note how one of the peaks 'takes a turn' during early song development (this is the vocal change of time-warping). You can see that the vocal change occurs within a few days, whereas thereafter, duration did not change much. As we shall discuss later on, vocal changes are often like this - they can take a few hours, a few days or several days, and then nothing happens during the next several days. Given this hectic nature of vocal change, DVD-maps give us an easy way of detecting critical moments in song development.
Finally, histograms can be computed for any features - not only duration - Try mean Wiener entropy and mean FM.
The range can be automatic or manual. When selecting a manual scale the minimum and maximum range is set by the user. The number of bins, however, is fixed and equals 100, so selecting a duration range of 0-500ms will give bins of 5ms. If you choose auto-scale, SA+ will scale the features based on the normalization of syllable features (see in options -> feature normalization).
Aliasing issues:never let the bin-size approach the encoding accuracy of a feature. The likely problem is with duration. The actual encoding is the window-step taken, which is about 1.4ms by default. Since we use 100 bins, the default definition is about 5ms when the range is set between 0-500ms. Setting it from, say 50-300ms is taking us down to 2.5ms - which is still fine, but going down to, say, 100-200 is taking us down to 1ms - which is below the critical (Nyquist) value - which will result in aliasing: a nasty, unresolvable artifact in the duration histogram.
Click 'open table', select 'bird109' and click 'DVD Play/Stop'. You should see and image
like the one presented below:
Only syllable with longer or shorter duration
than those thresholds are shown
File name containing the
current syllable
Date and time of
current syllable
Date and time of
current syllable
X-axis feature
presented
Y-axis feature
presented
Each red dot represents a syllable, the X axis is 'duration' by default, and the Y axis is
mean FM. Note that feature units are scaled, with median at 0 and with a spread of a
single MAD (median absolute deviation) unit. The beginning of the movie is also the
beginning of song development, when songs syllable are relatively unstructured.
Click at the long slider at the bottom, it should turn yellow, and move its thumb to the
right, about ¾ of the way. The movie should now look very different:
We can see 3 nice
clusters, which correspond to the 3 syllable types of the song
produced. To see other features of those clusters click on the Y-axis feature choice (you
can do this as the movie is playing). Clicking on the pitch shows different projections of
the clusters. Moving the mouse into the movie image will show a hand pointer, indicating
that you can move the image as desired. On the bottom right you will see a radio-group
with 3 choices: rotate, pan and zoom - try them all during the movie play.
At this point, our notion of clusters is informal, but in the next chapter you will learn how
to use SA+ to automatically identify the clusters. In this example, we already clustered
the data. To view the clusters select the 'color by cluster' from the color scheme. You can
now see those syllables that we did not cluster in grey color, and those that were
clustered by different colors. In the syllable table, each cluster is identified by a number,
and these numbers correspond to the following colors: