360
M.F. Wilkins . L. ßoddy . G.ßJ. Dubelaar
pulse. The representation is also more compact. Typically only a few of the lowfrequency components have any significant amplitude, with the amplitude of the
remaining high-frequency components being close to zero. Thus, instead of using
all 33 sampie values to represent the pulse, the overall shape of the pulse can be
approximated with reasonable accuracy using relatively few cosine coefficients.
The square of the amplitude coefficients represents the power spectrum of the
pulse (the amount of energy contained in components of each frequency). The
position of the peak of the power spectrum can be used to define a "characteristic
length" for each pulse- this is the length scale of the most significant features
detected by the pulse. For example, a chain-forming diatom gives rise to a signal
with regularly-spaced peaks (Fig. 18.1a), leading to a peak in the power spectrum
at the spatial frequency corresponding to the length of the individual cells in the
chain (Fig. 18.1b).
18.2.4
Principal Component Analysis
Principal component analysis (Joliffe 1986) was used to investigate the extent to
which the variation between the normalised pulse shapes seen in the data set could
be explained by the combination of a small number of independent modes of
variation. The mean of the DCT transformed data was estimated and used to
generate a "mean pulse shape" for each parameter, the average of all the
normalised pulses over the data for all 36 species. The effect of variation from the
mean pulse shape along each of the first four principal component axes was
plotted (Fig. 18.2). The first mode was characterised primarily by a shift in the
position of the FLO peak (corresponding to the presence of phycoerythrin) with
respect to the peaks for the other signals. The second mode consisted of
simultaneous sharpening of the SSC and FLO peaks accompanied by the
development of a double peak in the FSC signal. The third mode consisted of a
shift in the position of the SSC peak, while the fourth mode was similar to the
second except that sharpening of the FLO peak was accompanied by flattening of
the SSC peak and vice versa. Higher modes showed more complex shape changes.
Several species showed pronounced bimodal distributions in the first mode of
variation, e.g. Cryptomonas maculata and Rhinomonas salina - this may be
caused not by the presence of two distinct subpopulations but rather be due to cells
with inherent asymmetry passing through the instrument in opposite orientations.
Supporting evidence for this conclusion comes from examining the between-class
variance as a percentage of the explained variance for each mode (Table 18.2),
showing that while the first mode accounts for the largest fraction (21.2%) of the
total variance, only 2.4% of this is due to between-class variance: there is thus
very little discriminatory information in this mode, implying that the cause of this
variation is common to cells of all species.
M.F. Wilkins . L. ßoddy . G.ßJ. Dubelaar
pulse. The representation is also more compact. Typically only a few of the lowfrequency components have any significant amplitude, with the amplitude of the
remaining high-frequency components being close to zero. Thus, instead of using
all 33 sampie values to represent the pulse, the overall shape of the pulse can be
approximated with reasonable accuracy using relatively few cosine coefficients.
The square of the amplitude coefficients represents the power spectrum of the
pulse (the amount of energy contained in components of each frequency). The
position of the peak of the power spectrum can be used to define a "characteristic
length" for each pulse- this is the length scale of the most significant features
detected by the pulse. For example, a chain-forming diatom gives rise to a signal
with regularly-spaced peaks (Fig. 18.1a), leading to a peak in the power spectrum
at the spatial frequency corresponding to the length of the individual cells in the
chain (Fig. 18.1b).
18.2.4
Principal Component Analysis
Principal component analysis (Joliffe 1986) was used to investigate the extent to
which the variation between the normalised pulse shapes seen in the data set could
be explained by the combination of a small number of independent modes of
variation. The mean of the DCT transformed data was estimated and used to
generate a "mean pulse shape" for each parameter, the average of all the
normalised pulses over the data for all 36 species. The effect of variation from the
mean pulse shape along each of the first four principal component axes was
plotted (Fig. 18.2). The first mode was characterised primarily by a shift in the
position of the FLO peak (corresponding to the presence of phycoerythrin) with
respect to the peaks for the other signals. The second mode consisted of
simultaneous sharpening of the SSC and FLO peaks accompanied by the
development of a double peak in the FSC signal. The third mode consisted of a
shift in the position of the SSC peak, while the fourth mode was similar to the
second except that sharpening of the FLO peak was accompanied by flattening of
the SSC peak and vice versa. Higher modes showed more complex shape changes.
Several species showed pronounced bimodal distributions in the first mode of
variation, e.g. Cryptomonas maculata and Rhinomonas salina - this may be
caused not by the presence of two distinct subpopulations but rather be due to cells
with inherent asymmetry passing through the instrument in opposite orientations.
Supporting evidence for this conclusion comes from examining the between-class
variance as a percentage of the explained variance for each mode (Table 18.2),
showing that while the first mode accounts for the largest fraction (21.2%) of the
total variance, only 2.4% of this is due to between-class variance: there is thus
very little discriminatory information in this mode, implying that the cause of this
variation is common to cells of all species.