S-MSRRS5000: A Simulated Dataset Highlighting
the Challenges of Data Obtained From Multiple
Spatially Resolved Reflection Spectroscopy
Birk Martin Magnussen ∗, Maik Jessulat†, Claudius Stern‡and Bernhard Sick†
∗biozoom services GmbH
34121 Kassel, Germany
†Intelligent Embedded Systems
Universit¨
at Kassel
34121 Kassel, Germany
‡FOM Hochschule f¨
ur Oekonomie & Management
Hochschulzentrum Kassel
34117 Kassel, Germany
Abstract—Optical sensors based on spectroscopy are occasion-
ally used in consumer healthcare and wellness applications. This
includes applications such as measuring the concentration of
cutaneous carotenoids using sensors based on multiple spatially
resolved reflection spectroscopy (MSRRS). Processing the data
yielded from MSRRS-based sensors poses unique challenges.
When using machine learning for data processing, specialized
models such as continuous feature networks are required to
achieve good results. However, due to privacy issues of medical
data, data availability is low, hindering model development. In
this article, a simulated dataset is introduced, highlighting the
challenges of data from MSRRS-based sensors. Furthermore, the
underlying principles used for the simulation will be discussed.
Finally, several model architectures including continuous feature
networks are trained on the dataset, demonstrating the various
challenges.
Index Terms—dataset, simulated data, reflection spectroscopy
I. INTRODUCTION
Multiple spatially resolved reflection spectroscopy
(MSRRS) is a technology for analyzing biological tissue. One
common use-case for sensors based on MSRRS is measuring
the concentration of cutaneous carotenoids in humans [1].
MSRRS-based sensors consist of multiple light emitters
and light detectors. These emitters and detectors are then
arranged in a matrix. When a measuring sample is placed
on this detector matrix, the light emitted from an emitter
will pass through the sample before being detected by the
light detector. The measured brightness at the light detector
then depends on the wavelength of the light, the distance
between emitter and detector, as well as the optical properties
of the sample. By analyzing the brightness observed for all
Supported by the state Hessen through funding as part of the Distr@l
research grant 22 0041 2B.
emitter-detector pairs, it is possible to make predictions about
the measurement sample [2], such as the concentration of
cutaneous carotenoids.
This analysis of the observed brightness values can be per-
formed using machine learning. For this purpose, specialized
neural network architectures have been developed, such as
continuous feature networks [3], [4]. These continuous feature
networks are designed to tackle the difficulties of data yielded
by MSRRS-based sensors.
At the core of the difficulty of processing MSRRS-based
data is the irregularity of the data. The light emitters used
in MSRRS-based sensors have discrete wavelengths. As a
result, the observed spectrum is not sampled continuously, but
rather at discrete sampling points. Furthermore, these points
are not distributed equally but are at irregular intervals. A
Emitter wavelength (nm)
Emitter-Detector distance (mm)
450 520 590 660 730 800 870
0
3
6
9
12
15
Fig. 1. An example of the structure of data from MSRRS-based sensors [4].
similar situation is observed with the distance of emitter-
detector pairs. An example of this type of irregular data can
be seen in Figure 1.
In addition to the irregularity, any MSRRS-based sensor can
be afflicted by manufacturing inaccuracies. This can result in
the wavelengths of the light emitters shifting slightly between
individual sensors. Any machine learning model operating
on data from MSRRS-based sensors needs to be able to
compensate for these fluctuations.
When trying to predict properties or substances in human
tissue, the required training data is composed of medical
data. Due to privacy concerns, such data cannot be made
publicly available. Therefore, a simulated dataset called S-
MSRRS5000 is presented.
II. THE DATASET AND ITS CHALLENGES
For the creation of S-MSRRS5000, a virtual MSRRS-
based sensor with 8 detectors and 32 emitters is assumed.
S-MSRRS5000 is made up of four sets of 5000 simulated
measurements each. Each measurement consists of a series
of 256 data points. One data point always corresponds to
one emitter-detector pair of the virtual sensor. For each data
point, the observed brightness at the detector is listed. In
addition, the wavelength of the emitter and the emitter-detector
distance are listed. Together, the 256 data points make up one
measurement. For each such measurement, three ground truth
labels are available.
1) The concentration of cutaneous beta-carotene in the
simulated sample in milligrams per liter.
2) The concentration of hemoglobin in the blood of the
sample in grams per liter.
3) The oxygenation level of the blood in the sample as a
factor from 0 to 1.
The ground truth labels for each set are stored in a file
called dataset_meta.json. This JSON file contains a
single top-level array. Within are multiple JSON objects, each
representing one simulated measurement, with a key for each
label and a key called name containing the filename of the
measurement data itself. The file containing the measurement
data is a CSV file with a list of data points. Each data point
is listed with the wavelength of the emitted light, the emitter-
detector distance, and the measured intensity.
The four sets available in the dataset represent different
challenges of MSRRS-based data in ascending difficulty. The
challenges of the different sets are as follows:
1) 1_clean: Clean Data Only The first set represents
the ideal case. In this set, the virtual MSRRS-based
sensor is perfectly accurate. Similarly, the measurement
sample is simulated to have no noise or other factors
negatively impacting the data. The only factors with a
variable influence on the simulated brightness values
are substances with labels available as ground truth.
This set is thus useful to understand the structure of
MSRRS-based data and to establish a baseline for model
performance.
2) 2_noise: Noisy Samples The second set increases
the prediction difficulty by introducing measurement
noise. In addition to the substances with labels available
as ground truth, further randomized noise contributes to
the light absorption within the simulated sample. Fur-
thermore, the carotenoid concentration is simulated with
localized fluctuations and is no longer homogeneous
throughout the entirety of the sample.
3) 3_wavelength_shift: Inconsistent Emitter
Wavelengths The third set introduces production
inaccuracies of the sensor in addition to the noise of
the second set. In this set, the emitter wavelengths of
each measurement are no longer identical. Instead, they
are simulated to fluctuate in a small region around the
nominal target wavelength that is used in the previous
sets.
4) 4_missing_data: Missing Data From Detectors
The fourth set expands on the difficulty of the third
set. In addition to the sample noise and inconsistent
emitter wavelength, the fourth set allows for inoperable
detectors. As a result, it is no longer guaranteed that
all data points are available in a measurement. Instead,
some data points may be replaced by NaN-values. This
is to simulate detectors that might have to be disabled
due to them exceeding tolerances or being otherwise
defective.
III. SIMULATION BACKGROUND
The simulation of the brightness detected by the light
detectors is a highly simplified simulation. It does not aim to
accurately recreate the measurement values as when measuring
real human tissue but rather aims at recreating some of the core
challenges of real MSRRS-based data.
At its core, the simulation traces the light paths from every
light emitter to every light detector as semicircles. These
semicircles are split into equidistant segments. Figure 2 shows
an example of these light paths for two emitters and one
detector.
Starting from the light emitter, the light attenuation over
the light path segments is calculated. In this simulation,
attenuation is comprised of two components. First, since the
light emitter is not emitting a focused beam of light, the light
attenuates based on the distance to the emitter with the inverse-
square law. Given the distance to the light emitter dand the
length of the light path segment ls, the ratio between the
light intensity I0before the light path segment and the light
D
Fig. 2. Traced light paths split into equidistant segments of two emitters to
one light detector.
intensity Iafter the light path segment can be described as
follows:
I
I0
=d2
(d+ls)2(1)
The second component is the absorption of light by the
sample, calculated using the Beer-Lambert law. The Beer-
Lambert law describes the light attenuation due to the ab-
sorbance of light of the chemicals. Given the absorptivity a
of a chemical, optical beam length b, and the concentration
of the absorbing chemical c, the Beer-Lambert law allows to
calculate the logarithmic ratio between the light intensity I0
before the light path segment and the light intensity Iafter
the light path segment can be described as follows [5]:
−log (︃I
I0)︃=a·b·c(2)
The absorptivity ais a wavelength-dependent material con-
stant. The optical path length bcan be calculated as the product
of the light path segment length and the refractive index of
human skin (approximated as 1.37 [6]).
This dataset simulates the to-be-measured tissue as three
primary components. First, the tissue is assumed to consist of
a base of water. Additionally, the tissue contains hemoglobin
as found in blood, both oxygenated and not oxygenated.
Finally, a given concentration of carotenoids contributes to
the absorption of light.
For the base of water, the absorptivity used by the simulation
is based on the measurements of Kou, Labrie, and Chylek [7].
For the hemoglobin contained in the blood within the
simulated tissue, measurements compiled by Prahl [8] were
used as the absorptivity values in the simulation. The amount
of hemoglobin present for absorption is calculated as a com-
bination of the amount of hemoglobin per volume of blood,
and the ratio of volume of blood to volume of total tissue.
The volume of blood present in human limbs averages 5.6%
of the tissue volume [9]. For the concentration of hemoglobin
in human blood, values are sampled from a distribution based
on measurements from Kim et al. [10] and stored as labels in
the ground truth data. Similarly, for the ratio of oxygenated to
non-oxygenated blood, a value is sampled from a distribution
based on measurements from Epstein and Haghenbeck [11]
and similarly stored as a label in the ground truth data.
For the carotenoids to be predicted by a given machine
learning algorithm, a concentration is sampled from a distri-
bution of the beta-carotene concentrations in humans based
on measurements from Matsumoto et al. [12] and stored as a
label in the ground truth data. Data compiled by Prahl [13]
on the absorptivity spectrum of beta-carotene was used as the
basis for the simulation.
For the noise in set two and beyond, OpenSimplex-based
noise [14] is used. A three-dimensional noise map is used to
vary the localized concentration of carotenoids by up to ±15%.
A second, four-dimensional is used as well. The first three
dimensions represent the position in the simulated space while
the fourth dimension represents the current wavelength of
light. This noise map is used to add localized and wavelength-
dependent background absorptivity noise, representing other
substances present in the tissue.
The light emitter wavelength shift in the third and fourth
sets is sampled from a Gaussian distribution around the target
wavelength for the light emitter with a standard deviation of
2.5 nm.
In the fourth set, the chance that any single detector is
disabled for the simulation is fixed at 10%. This ratio is higher
than expected for real MSRRS-based sensors but serves as a
suitable worst-case scenario challenge for a prediction model.
IV. EXAMPLE USAGE AND RESULTS
For testing, three different machine learning models were
trained on each of the four sets within the S-MSRRS5000
dataset. The three models include a simple linear regres-
sion model, a multi-layer feed-forward neural network, and
a continuous feature network as proposed in Magnussen,
Stern, and Sick [3], [4]. For this experiment, each set of the
dataset was split into 3500 training measurements, and 1500
validation measurements. For both methods based on neural
networks, the 1500 validation measurements were further split
into 500 testing measurements and only 1000 final validation
measurements. The testing measurements were used to select
the best-performing model during training, while the validation
measurements are the basis for the final score of the model.
The training was repeated ten times for each model and each
set, with randomized training, testing, and validation data splits
for each repetition.
The linear regression model and the multi-layer feed-
forward network are not able to deal with missing input
data for the fourth set in S-MSRRS5000. Instead, the miss-
ing values were imputed by linearly interpolating values of
comparable wavelength and emitter-detector distances. The
continuous feature network is capable of handling missing
input data without imputation and was thus given the input
data of the fourth set unmodified.
The results shown in Table I include the root mean square
error (RMSE) and the coefficient of determination (r2) be-
tween the predicted results and the ground truth labels of
the dataset. The data is averaged over the ten runs, with the
respective standard deviation given for each quality metric.
It is to be noted that only training instances that yielded
a positive coefficient of determination contributed to the re-
spective quality metrics. Instead, the % fail metric indicates
the percentage of runs that yielded a negative coefficient of
determination, indicating models with an unusable training
result.
From the data in Table I, it can be observed that calculating
the concentration of carotenoids in a simplified simulation
such as used for S-MSRRS5000 is a simple task if no noise
is present. All models trained are able to achieve a very high
coefficient of determination. However, especially the introduc-
tion of fluctuations in the wavelength of the light emitters
has a significant impact on the linear regression model and
TABLE I
THE TRAINING ACCURACY OF DIFFERENT MODELS ON THE VARIOUS CHALLENGES OF THE S-MSRRS5000 DATASET.
linear regression multi-layer feed-forward network continuous feature network
RMSE r2% fail RMSE r2% fail RMSE r2% fail
clean data 0.0±0.01.0±0.0 0% 0.02±0.01.0±0.0 0% 0.03±0.0 0.99±0.0 0%
noisy data 0.03±0.00.99±0.0 0% 0.04±0.0 0.98±0.0 0% 0.05±0.01 0.97±0.01 0%
wavelength shift 0.26±0.0 0.29±0.01 40% - - 100% 0.11±0.01 0.85±0.03 0%
missing data 0.27±0.01 0.15±0.01 60% - - 100% 0.16±0.02 0.60±0.08 0%
the multi-layer feed-forward network. The multi-layer feed-
forward network was not able to achieve a positive coefficient
of determination for a single training repetition for the third
and fourth sets. The continuous feature network however is
capable of taking the exact wavelength and emitter-detector
distance for each input brightness into account. As a result, the
continuous feature network is able to keep a high coefficient of
determination and a low root mean square error for the third
set as well. A similar effect can be observed for the fourth
set, where the missing data significantly reduces the accuracy
of the linear regression model, whereas the continuous feature
network is able to deal with the missing data and still keeps
a comparatively high coefficient of determination.
These results, especially including the ability of the con-
tinuous feature network to achieve a high performance due to
being able to compensate for inconsistent wavelengths and for
missing data is consistent with recent findings on real data [3],
[4].
V. CONCLUSION
The S-MSRRS5000 dataset is a simulated dataset, op-
timized to show the structure and challenges of MSRRS-
based data. This article discusses the contents of the S-
MSRRS5000 dataset and the four challenge sets making up
the dataset. Furthermore, the relation of each challenge set to
the challenges of real data is highlighted.
This article also goes into detail on how the dataset is
simulated. This includes the underlying physical principles,
as well as the sources for the spectral data used.
Finally, the dataset is used to train different example models
on each of the challenge sets. The results from these experi-
ments are consistent with results on real data.
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