phytoplankton_acoustic_data: Phytoplankton_acoustic_data
In RMBC: Robust Model Based Clustering

Description Usage Format References Examples

Data obtained by taking laboratory measurements of ultrasonic acoustic signals: a pulse is emitted by a transducer, this pulse interacts with phytoplankton suspended in the water and produces an acoustic dispersion (scattering), which is recorded by an electronic acquisition device. A filtering process of the signal is performed in a first stage. Portions of the signal belong o one of the two main cases:

(a) Signals corresponding to the acoustic response of phytoplankton
(b) Signals corresponding to spurious dispersers, such as bubbles or particles in suspension, whose intensity is greater than in case (a).

To classify a signal in one of these two groups biologists create a vector (X1, X2) defined as follows:

X1 = ratio of filtered to non-filtered signal power
X2 = filtered signal power expressed in dB.

The available data consists of 375 such measurements. These data is particularly useful to compare robust procedures because 20 to be outliers produced by a communication failure between the electronic device (digital oscilloscope) and the software for acquiring the acoustic signal. This failure occurs once every 5 microseconds, which allows the scientists to identify the outliers. The outliers appear as a separated group in the region X1 < 0.5 and X2 > 20.

1	phytoplankton_acoustic_data

a list of length 2, where its elements are

Y: A matrix of dimension 375 x 2, each row contains X1 and X2 values
outliers_index: An array with the outliers index-locations

[1] Cinquini, M., Bos, P., Prario, I and Blanc, S. (2016), “Advances on modelling, simulation and signal processing of ultrasonic scattering responses from phytoplankton cultures,” in Proceedings of Meetings on Acoustics 22ICA, 28, American Society of Acoustics.
[2] Gonzalez J.D, Maronna R., Yohai V., & and Zamar . (2021). Robust Model-Based Clustering. arXiv preprint <https://arxiv.org/abs/2102.06851>

################################
# upload matrix ################
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Y <- phytoplankton_acoustic_data$Y

outliers_index <- phytoplankton_acoustic_data$outliers_index

Yclean=Y[-outliers_index,]

trueOutliers=Y[outliers_index,]

################################
# plot results ################
################################

plot(Y, main = "Phytoplankton acoustic data", cex.main = 3, lwd = 1,pch = 19, cex = 1, 
     type = "n", xlab = "x1", ylab = "x2",  xlim = c(0,1.1), ylim = c(0,43)
     )
     
points(trueOutliers,lwd=2,cex=1,pch=4)

points(Yclean,col=1,lwd=1.5,pch=21, bg=4, cex=1)