DE102023122800B3 - Method for determining a binary classifier and method for assigning a sample to one of two possible classes based on spectroscopic data of the sample - Google Patents

Abstract

The invention relates to a computer-implemented method for determining a binary classifier, wherein the classifier is designed to assign a sample to one of two possible classes (P ₁ , P ₂ ) on the basis of spectroscopic data of this sample, comprising the steps:
- receiving two-dimensional spectroscopic data of the sample, the data comprising discrete values in a wavelength dimension (12) and a time dimension (14),
- determining features F1 to F5 formed along the time dimension (14) of the data for several wavelengths and/or for several wavelength ranges (16),
- determining linear combinations of the features F1 to F5 for the plurality of wavelengths and/or for the plurality of wavelength ranges (16) by analyzing the features with regard to their separation strength for the two classes (P ₁ , P ₂ ), and
- Determining a subset of the determined linear combinations by analyzing the linear combinations with regard to their discrimination power for the two classes (P ₁ , P ₂ ).
The invention further relates to a computer-implemented method for assigning a sample to one of two possible classes based on spectroscopic data of the sample.
The invention also relates to a device for data processing, a computer program product, and a computer-readable data carrier.

Description

The invention relates to a computer-implemented method for determining a binary classifier.

The invention further relates to a computer-implemented method for assigning a sample to one of two possible classes based on spectroscopic data of the sample.

The invention also relates to a device for data processing, a computer program product, and a computer-readable data carrier.

There is currently an effort to be able to determine the sex of a future chick while the egg is still fertilized.

In the course of development, different fluorophores are formed in male and female chicks in the bird egg. Due to their complex structure, the corresponding molecules have an unpredictable fluorescence capacity. During fluorescence, energetic transitions from the excited state to the ground state of the molecule are observed. This process is time-dependent.

The document WO 2021 / 144 420 A1 describes a device and a method for optical in-ovo sex determination in a fertilized bird's egg. The device comprises a light source for emitting excitation radiation for exciting fluorescence in an area inside the bird's egg, a spectroscopic device for time- and/or spectrally resolved analysis of fluorescence radiation emitted from the area inside the bird's egg, and an evaluation unit for sex determination from the data determined by means of the spectroscopic device.

The document WO 2023 / 161 532 A1 relates to a method and apparatus for detecting and/or classifying particles of organic compounds from a fingerprint of backscattered light in a liquid dispersion sample. The method uses an electronic data processor to detect and/or classify particles in the sample, the method comprising using the electronic data processor to pre-train a machine learning classifier with a plurality of sample particles.

The publication of Nipuna Rajapaksha et al. “Supervised machine learning algorithm selection for condition monitoring of induction motors” from Proceedings: 2021 IEEE southern power electronics conference (SPEC), 06-09 December 2021 - ISBN 978-1-6654-3623-6 describes supervised machine learning (ML) algorithms that can be used for condition monitoring of three-phase induction motors and their advantages and disadvantages. It also discusses how to select the dominant features from raw data by time domain and frequency domain analysis using the acoustic data collected from a three-phase induction motor. The paper further describes the classification accuracy of each ML algorithm and a method for selecting an algorithm based on experimental results.

Based on this, it is the object of the invention to provide means to increase the accuracy of in-ovo sex determination and/or to improve the robustness of the method.

The object is achieved according to the invention by the features of the independent claims. Preferred embodiments of the invention are specified in the subclaims, which can each represent an aspect of the invention individually or in combination.

• - Empfangen von zweidimensionalen spektroskopischen Daten der Probe, wobei die Daten diskrete Werte in einer Wellenlängendimension und einer Zeitdimension umfassen,
• - Bestimmen von entlang der Zeitdimension der Daten gebildeten Merkmale F1 bis F5 für mehrere Wellenlängen und/oder für mehrere Wellenlängenbereiche, wobei die Merkmale
  • • F1: statistische Momente der 2. bis 4. Ordnung der Daten in der Zeitdimension,
  • • F2: Koeffizienten einer Ausgleichsgerade der Daten in der Zeitdimension,
  • • F3: Reelle Koeffizienten einer Fouriertransformation der Daten in der Zeitdimension,
  • • F4: Koeffizienten einer Ausgleichsgerade durch die für Merkmal F3 bestimmten reellen Koeffizienten der Fouriertransformation, und
  • • F5: Entropie der Daten in der Zeitdimension
  umfassen,
• - Ermitteln von Linearkombinationen der Merkmale F1 bis F5 für die mehreren Wellenlängen und/oder für die mehreren Wellenlängenbereiche durch Analysieren der Merkmale im Hinblick auf ihre Trennstärke für die zwei Klassen, und
• - Ermitteln von einer Untermenge der ermittelten Linearkombinationen durch Analysieren der Linearkombinationen im Hinblick auf ihre Trennstärke für die zwei Klassen.

According to the invention, a computer-implemented method for determining a binary classifier is provided, wherein the classifier is designed to assign a sample to one of two possible classes on the basis of spectroscopic data of this sample, comprising the steps

• - receiving two-dimensional spectroscopic data of the sample, the data comprising discrete values in a wavelength dimension and a time dimension,
• - Determining features F1 to F5 formed along the time dimension of the data for several wavelengths and/or for several wavelength ranges, wherein the features
  • • F1: statistical moments of the 2nd to 4th order of the data in the time dimension,
  • • F2: coefficients of a best fit line of the data in the time dimension,
  • • F3: Real coefficients of a Fourier transform of the data in the time dimension,
  • • F4: coefficients of a regression line through the real coefficients of the Fourier transform determined for feature F3, and
  • • F5: Entropy of the data in the time dimension
  include,
• - determining linear combinations of the features F1 to F5 for the multiple wavelengths and/or for the multiple wavelength ranges by analyzing the features with regard to their discriminatory power for the two classes, and
• - Determining a subset of the determined linear combinations by analyzing the linear combinations with regard to their discrimination power for the two classes.

• - Empfangen von zweidimensionalen spektroskopischen Daten der Probe, wobei die Daten diskrete Werte in einer Wellenlängendimension und einer Zeitdimension umfassen, und
• - Anwenden eines Klassifikators auf die empfangenen Daten, wobei der Klassifikator mit obigen Verfahren ermittelt wurde.

Furthermore, the invention relates to a computer-implemented method for assigning a sample based on spectroscopic data of the sample to one of two possible classes, and in particular for assigning a fertilized bird egg to one of two possible sexes, comprising the steps

• - receiving two-dimensional spectroscopic data of the sample, the data comprising discrete values in a wavelength dimension and a time dimension, and
• - Applying a classifier to the received data, where the classifier was determined using the above methods.

Furthermore, the invention relates to a device for data processing comprising means for carrying out one of the two above methods or means for carrying out both methods.

Furthermore, the invention relates to a computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out one of the two above methods or both of the above methods.

Furthermore, the invention relates to a computer-readable data carrier on which the above computer program product is stored.

One aspect of the invention is that it has been found that when assigning a sample to one of two possible classes based on spectroscopic data of the sample, an improved hit rate is achieved if not only statistical features of the spectroscopic data are considered to determine the classifier in the training phase.

A further aspect of the invention is that a two-stage method is used to determine the classifier. It has been found that a classifier which is created by determining the linear combinations of the features F1 to F5 for the multiple wavelengths and/or for the multiple wavelength ranges by analyzing the features with regard to their discriminatory strength for the two classes, and by determining a subset of the determined linear combinations by analyzing the linear combinations with regard to their discriminatory strength for the two classes, achieves a higher hit rate when assigning the sample. In other words, a model is built using the training data in a two-stage method.

In addition, a classifier determined according to the method according to the invention can also provide a far more robust method for assignment, in which samples whose spectroscopic data were not measured under ideal conditions and have an increased signal-to-noise ratio can still be assigned to the two possible classes with a high hit rate. It is preferably provided that the classifier is a linear classifier. A linear classifier separates the classes along a linear hyperplane.

The two-dimensional spectroscopic data of the sample are preferably present in a two-dimensional data matrix, with one row of the data matrix preferably comprising the time response and in particular the decay curves for individual singular wavelengths or an averaged time response and in particular averaged decay curves for several directly adjacent singular wavelengths. In the second case, one row of the data matrix corresponds to the time response of a wavelength range. The wavelength The wavelength range preferably has a bandwidth which comprises no more than 4 nm, preferably no more than 3 nm. It is further preferred that the number of adjacent singular wavelengths which are averaged for the wavelength range is no more than eight singular wavelengths and preferably no more than six singular wavelengths.

In the first stage of the method for determining the binary classifier, the features F1 to F5 are first determined for the rows of the matrix. Preferably, the features F1 to F5 are determined for each row of the matrix. In other words, the features F1 to F5 are preferably formed from singular wavelengths and/or from the wavelength ranges.

With regard to the feature F1, the statistical moments of the 2nd to 4th order are preferably the central moments, i.e. the central moment of the 2nd order (standard deviation), the central moment of the 3rd order (skewness) and the central moment of the 4th order (kurtosis).

With respect to feature F2, the coefficients of the best-fit line are preferably the coefficients of a normal equation g(x) = ax + b through the data in the time dimension.

With respect to feature F3, the real coefficients are preferably the real coefficients of the fast Fourier transform of the data in the time dimension.

For feature F4, the coefficients of the best-fit line are preferably the coefficients of a normal equation f(x) = sx + t divided by the real coefficients of the fast Fourier transform determined for feature F3.

With respect to feature F5, the entropy of the data in the time dimension is preferably the Shannon entropy according to E = - Σ _z p _z log ₂ p _z , with p _z as the probability for the measured value z.

The features are then analyzed in terms of their discrimination strength in order to eliminate features with weak discrimination strength. In other words, linear combinations are determined from the features for each wavelength and/or for each wavelength range, whereby the eliminated features in the linear combination have a coefficient of zero and are therefore not taken into account. After this step, a linear combination of the features F1 to F5 specific to this row is therefore preferably available for each row of the data matrix.

In the subsequent step of the method, in the second stage, a subset of the linear combinations is determined from the linear combinations formed. This is done by analyzing the linear combinations with regard to their separation strength in order to preferentially eliminate linear combinations with weak separation strength. In other words, certain linear combinations that have particularly high separation strengths are preferentially identified.

In other words, it is preferred that the classifier is determined by means of feature selection and/or selection of linear combinations based on training data. In particular, it has been shown that the two-stage process can be used to determine a binary classifier that has a particularly high hit rate. The classifier is also particularly robust because it also enables spectroscopic data from the sample to be reliably classified with a high signal-to-noise ratio.

According to a preferred development of the invention, the sample is a fertilized bird's egg and the two classes represent a male sex and a female sex of the fertilized bird's egg. The method for determining the classifier has proven to be particularly suitable for determining a classifier for determining the sex of the fertilized bird's egg. In particular, hit rates of 100% were achieved with the classifier determined according to the present method when classifying the fertilized bird's egg.

According to a further preferred development of the invention, it is provided that the received two-dimensional spectroscopic data are intrinsic fluorescence data of the sample and in particular intrinsic fluorescence data of the sample, in particular of the fertilized bird's egg, recorded by means of time-resolved laser-induced fluorescence spectroscopy (zLIF) and/or by means of time-correlated single photon counting (TCSPC). In other words, in relation to determining a binary classifier, which is preferably used for in-ovo sex determination in a fertilized bird's egg, knowledge of the lifetime and the decay profile of excited molecular states (time dimension of the two-dimensional data) in addition to the energy of the emitted photons (wavelength dimension of the two-dimensional data) are relevant for the identification of the sex of the fertilized bird egg.

In order to detect the autofluorescence radiation, the spectroscopic data can be recorded using laser-induced fluorescence methods. This method is based on the fluorescence excitation of the sample by an excitation pulse from a light source such as a laser or an LED. The fluorophores in the sample and preferably in the bird's egg are excited by the laser. After some time, usually in the order of a few nanoseconds to microseconds, the excited fluorophores will lose their excitation and emit light with a wavelength that is longer than the excitation wavelength. This fluorescence light is typically recorded with a photomultiplier tube (PMT) or by means of a multi-channel detector designed as an ICCD camera.

In some methods - also known as boxcar methods - the complete spectrum is recorded at different times after an excitation pulse using an ICCD camera.

It is also possible to use time-correlated single photon counting (TCSPC) to record the self-fluorescence radiation. With TCSPC, the complete spectrum is not recorded after each excitation pulse. Instead, individual photons of a periodic light signal - in this case the self-fluorescence radiation - are detected and the respective times between the excitation pulse of the pulsed excitation radiation and the arrival of the photon in the detection device are determined. In other words, the time measurement is started by the excitation pulse and the photon emitted during the transition from the excited state to the ground state stops the measurement. The measurement is repeated many times and the individual time-correlated photons (in relation to the excitation pulse) are sorted into a so-called TCSPC histogram according to their measured time. The TCSPC histogram represents the temporal progression of the self-fluorescence radiation after excitation. Preferably, the TCSPC histogram generated by means of the detection device has a class width, also called bin width or container width, for the histogram classes from 1 ps to 50 ps, preferably from 10 ps to 20 ps. Preferably, the class width of the TCSPC histogram can be adapted to the device and/or sample to be examined. Further preferably, when adapting the class width of the TCSPC histogram, a temporal resolution of the entire device - and particularly preferably a full width at half maximum (FWHM) of the instrument response function (IRF) - is taken into account. The FWHM of the IRF depends essentially on the light source and a pulse length generated by the light source and/or on a detector element of the detection device.

According to a preferred development of the invention, it is provided that in order to determine the features F2 to F5, the data in the time dimension are present as normalized data, such that a mean value of the data in the time dimension is zero. It can also preferably be provided that in order to determine one or more of the features F2 to F5, the data are also normalized such that a standard deviation of the data in the time dimension is one. It has been shown that better results for classification are achieved if the raw data provided by the measurement are not used directly to determine the features F2 to F5. Instead, it is advantageous if the time dimension of the data is present in normalized form, in which the mean value µ = 0 and, preferably, for some or all of the features F2 to F5, the standard deviation σ = 1.

In contrast, in this context, according to a further preferred development of the invention, it is provided that the data in the time dimension are available as non-standardized data for determining the feature F1. In other words, the non-standardized raw data are preferably used to determine the standard deviation, the skewness and the curvature.

In connection with the features F3 and F4, according to a further development of the invention, it is provided that the real coefficients of the Fourier transformation of the data in the time dimension of the feature F3 are ordered in ascending order and/or that the coefficients of the best fit line are determined by the real coefficients of the Fourier transformation determined for feature F3 on the basis of real coefficients of the Fourier transformation ordered in ascending order. In other words, the real coefficients of the Fourier transformation for feature F3 are therefore sorted - namely ordered in ascending order. Furthermore, in connection with the feature F4, the best fit line f(x) = sx + t is preferably formed by the real coefficients of the Fourier transformation ordered in ascending order.

wobei c_i der jeweilige Koeffizient des Merkmals F_i ist. Die Koeffizienten c_i können beliebige Werte annehmen. Wird durch Analyse der Merkmale im Hinblick auf ihre Trennstärke ermittelt, dass ein Merkmal keine hohe Trennstärke aufweist, ist bevorzugt vorgesehen, dass der entsprechende Koeffizient des Merkmals in der Linearkombination 0 ist, und das Merkmal entsprechend eliminiert wird. In diesem Zusammenhang ist bevorzugt vorgesehen, dass der Schritt Ermitteln von Linearkombinationen der Merkmale F1 bis F5 für die mehreren Wellenlängen und/oder für die mehreren Wellenlängenbereiche ein Definieren eines Koeffizienten der Linearkombination als Null für Merkmale, deren Trennstärke unter einem vordefinierten Schwellwert liegt, umfasst.In connection with the determination of linear combinations, according to a further development of the method, the determination of linear combinations of the features F1 to F5 is a Determining coefficients of the linear combinations. The linear combinations are preferably linear combinations according to ${\displaystyle \sum {}_{i=1}^{i=5}{c}_i{F}_i},$

where c _i is the respective coefficient of the feature F _i . The coefficients c _i can assume any values. If it is determined by analysis of the features with regard to their separation strength that a feature does not have a high separation strength, it is preferably provided that the corresponding coefficient of the feature in the linear combination is 0 and the feature is eliminated accordingly. In this context, it is preferably provided that the step of determining linear combinations of the features F1 to F5 for the multiple wavelengths and/or for the multiple wavelength ranges comprises defining a coefficient of the linear combination as zero for features whose separation strength is below a predefined threshold value.

According to a further preferred development of the invention, it is provided that the step of determining the linear combinations of the features F1 to F5 for the multiple wavelengths and/or for the multiple wavelength ranges by analyzing the features with regard to their separating strength for the two classes; and/or that the step of determining the subset of the determined linear combinations by analyzing the linear combinations with regard to their separating strength for the two classes comprises an analysis using linear discriminant analysis. In other words, the measured spectroscopic data are preferably processed using feature engineering to determine the classifier, with features and linear combinations formed from the features with weak separating strength being eliminated. It has been shown that a classifier that was determined without eliminating features and/or without eliminating linear combinations has a lower hit rate than with eliminating features and/or eliminating linear combinations.

In this context, according to a further preferred development, a discriminant function and preferably the Fisher discriminant function and/or a hit rate of the determined classifier are used as a metric for the discrimination strength during the analysis.

• - Empfangen von zweidimensionalen spektroskopischen Daten der Probe, wobei die Daten diskrete Werte in einer Wellenlängendimension und einer Zeitdimension umfassen, und
• - Anwenden eines Klassifikators auf die empfangenen Daten, wobei der Klassifikator mit dem oben beschriebenen Verfahren ermittelt wurde.

As already mentioned, the invention also relates to a method for assigning a sample based on spectroscopic data of the sample to one of two possible classes, and in particular for assigning a fertilized bird egg to one of two possible sexes, comprising the steps

• - receiving two-dimensional spectroscopic data of the sample, the data comprising discrete values in a wavelength dimension and a time dimension, and
• - Applying a classifier to the received data, where the classifier was determined using the method described above.

Preferably, the sample is a fertilized bird's egg. With regard to the method, the sex determination of the bird's egg is preferably carried out by prioritizing specific linear combinations, whereby the linear combinations were formed from the features F1 to F5 formed from the time dimension of the data.

The person skilled in the art will derive further technical aspects and advantages of the method for assigning a sample to one of two possible classes based on spectroscopic data of the sample from the above description of the method for determining the binary classifier.

• 1 in a) eine schematische Darstellung von zweidimensionalen spektroskopischen Daten einer Probe, die im Rahmen eines Verfahrens zum Ermitteln eines binären Klassifikators gemäß einem bevorzugten Ausführungsbeispiel der Erfindung empfangen werden, sowie in b) eine schematische Darstellung einer Trennstärke von entlang der Zeitdimension der Daten gebildeten Merkmalen im Merkmalsraum, und
• 2 eine schematische Darstellung einer linearen Diskriminanzfunktion, die im Rahmen eines Verfahrens zum Ermitteln eines binären Klassifikators gemäß einer bevorzugten Ausgestaltung der Erfindung, Linearkombinationen der entlang der Zeitdimension der Daten gebildeten Merkmalen voneinander in zwei Klassen trennt.

The invention is explained below by way of example with reference to the accompanying drawings using preferred embodiments, wherein the features shown below can represent an aspect of the invention both individually and in combination. They show:

• 1 in a) a schematic representation of two-dimensional spectroscopic data of a sample received as part of a method for determining a binary classifier according to a preferred embodiment of the invention, and in b) a schematic representation of a separation strength of features formed along the time dimension of the data in the feature space, and
• 2 a schematic representation of a linear discriminant function which, in the context of a method for determining a binary classifier according to a preferred embodiment of the invention, separates linear combinations of the features formed along the time dimension of the data into two classes.

1 shows left in 1a) a schematic representation of two-dimensional spectroscopic data of a sample received as part of a method for determining a binary classifier according to a preferred embodiment of the invention.

The measured spectroscopic data are time-resolved fluorescence emissions measured on hatching eggs on the third day of incubation. The sex of the hatching eggs was determined using PCR.

• Emissionsparameter: τ_min = 0 ns; τ_max = 30 ns (Diskreditierung = 1 ns);
• λ_min = 340,14 nm; λ_max = 720,60 nm (Diskreditierung 0,5 nm).

The time-resolved fluorescence emissions were recorded at a fluorescence excitation of 266 nm with the following parameters using the Boxcar measurement method:

• Emission parameters: τ _min = 0 ns; τ _max = 30 ns (discreditation = 1 ns);
• λ _min = 340.14 nm; λ _max = 720.60 nm (discreditation 0.5 nm).

The two-dimensional spectroscopic data of the sample received for determining the classifier are present in a two-dimensional data matrix A, wherein a row (a _j1 , ..., a _jn ), j = 1, ... ,m of the data matrix comprises the time behavior and in particular the decay curves 10a for individual singular wavelengths or an averaged decay curve 10b for several directly adjacent singular wavelengths. $$\text{A}=\left(\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \dots & a_{2n}\\ ⋮& ⋮& \cdots & ⋮\\ a_{m1}& a_{m2}& \cdots & a_{mn}\end{array}\right),$$

If the data matrix A is represented graphically, this results in 1 a) shown image, where the y-axis 12 corresponds to the wavelength dimension and the x-axis 14 to the time dimension. On the one hand, the decay curves 10a of individual singular wavelengths are shown, as well as decay curves 10b averaged over the wavelength range 16.

In the preferred embodiment of the method for determining the binary classifier described below, after the two-dimensional data have been received, features F1 to F5 formed along the time dimension of the data are determined for several wavelengths and/or for several wavelength ranges.

• • F1: statistische Momente der 2. bis 4. Ordnung der Daten in der Zeitdimension,
• • F2: Koeffizienten einer Ausgleichsgerade der Daten in der Zeitdimension,
• • F3: Reelle Koeffizienten einer Fouriertransformation der Daten in der Zeitdimension,
• • F4: Koeffizienten einer Ausgleichsgerade durch die für Merkmal F3 bestimmten reellen Koeffizienten der Fouriertransformation, und
• • F5: Entropie der Daten in der Zeitdimension

The characteristics F1 to F5 are the following characteristics:

• • F1: statistical moments of the 2nd to 4th order of the data in the time dimension,
• • F2: coefficients of a best fit line of the data in the time dimension,
• • F3: Real coefficients of a Fourier transform of the data in the time dimension,
• • F4: coefficients of a regression line through the real coefficients of the Fourier transform determined for feature F3, and
• • F5: Entropy of the data in the time dimension

Since the decay curves 10 are a function of time, they are also referred to as S(τ) in the following. The decay curves 10 are received in an original non-normalized form.

The feature F1 is thus the standard deviation σ, skewness γ and kurtosis ω calculated for S(τ).

To determine the features F2 to F5, the decay curves are brought into a normalized form S _N (τ), where S(τ) has the mean µ = 0 and the standard deviation σ = 1.

The feature F2 is the coefficients a, b of the normal equation g(x) = ax + b for S _N (τ).

The feature F3 is the ascending ordered real coefficients of the fast Fourier transform FFT[S _N (τ)].

The feature F4 is the coefficients s, t of the normal equation f(x) = sx + t for the ascending real coefficients of the fast Fourier transform FFT[S _N (τ)].

The feature F5 is the entropy E [S _N (τ)].

gebildet, wobei c_i der jeweilige Koeffizient des Merkmals F_i ist.Subsequently, linear combinations of the characteristics F1 to F5, which are also referred to as profiles pr, are calculated according to $\text{pr}={\displaystyle \sum {}_{i=1}^{i=5}{c}_i{F}_i}$

where c _i is the respective coefficient of the feature F _i .

To determine the profiles, the features are analyzed with regard to their discriminatory strength for the two classes. 1b) shows the result of the analysis in the feature space for the decay curves 10a for singular wavelengths and for the averaged decay curve 10b.

In the present embodiment, features that have a discrimination strength below a predefined threshold are assigned the value for the coefficient c _i = 0 in the linear combination, so that in other words they are eliminated, while the other features are assigned the coefficient value c _i = 1.

• F3:
  • - Vier Fourier-Transformation-Koeffizienten: f₁, f₂, f₃, f₄ bei 523.82 nm
  • - Drei Fourier-Transformation-Koeffizienten: f₅, f₆, f₇ bei 523.26 nm
  • - Ein Fourier-Transformation-Koeffizient: f₈ bei 524.38 nm
• F5:
  • - Entropie E1 bei 518.80 nm
  • - Entropie E2 bei 527.17 nm
  • - Entropie E3 bei 529.95 nm
  • - Entropie E4 bei 523.26 nm

This procedure is illustrated here for the profile around 524.38 nm: For this purpose, individual spectra between 518.80 nm and 529.95 nm were analyzed for the profile around 524.38 nm using machine learning methods. It turns out that the features F1, F2 and F4 do not have sufficient separation strength for this profile. Further consideration of these features would worsen the hit rate for the classification. For the features F3 and F5, the following values to be taken into account in the linear combination result:

• F3:
  • - Four Fourier transform coefficients: f ₁ , f ₂ , f ₃ , f ₄ at 523.82 nm
  • - Three Fourier transform coefficients: f ₅ , f ₆ , f ₇ at 523.26 nm
  • - A Fourier transform coefficient: f ₈ at 524.38 nm
• F5:
  • - Entropy E1 at 518.80 nm
  • - Entropy E2 at 527.17 nm
  • - Entropy E3 at 529.95 nm
  • - Entropy E4 at 523.26 nm

bei der Wellenlänge 524,38 nm berechnet sich demnach mit folgenden Koeffizienten c_i $${\text{c}}_1=\mathrm{0,}{\text{c}}_2=\mathrm{0,}{\text{c}}_3=\mathrm{1,}{\text{c}}_4=0{\text{ c}}_5=1$$

gemäß $$\begin{array}{l}p{r}_{\mathrm{524,38}nm}=c_3\left(20f_1-13f_2-6f_3-\mathrm{4,6}{f}_4+\mathrm{7,8}{f}_5-\mathrm{6,3}{f}_6+\mathrm{1,7}{f}_7+\mathrm{2,5}{f}_8\right)\\ +c_5\left(-8E_1+7E_2-\mathrm{4,5}{E}_3+\mathrm{4,8}{E}_4\right)-\mathrm{3,5}\end{array}$$

The profile $pr={\displaystyle \sum {}_{i=1}^{i=5}{c}_i{F}_i}$

at the wavelength 524.38 nm is calculated using the following coefficients c _i $${\text{c}}_1=\mathrm{0,}{\text{<figure-callout id="2" label="c" filenames="DE102023122800B3\_0007.png" state="{{state}}">c</figure-callout>}}_2=\mathrm{0,}{\text{c}}_3=\mathrm{1,}{\text{c}}_4=0{\text{ c}}_5=1$$

according to $$\begin{array}{l}p{r}_{\mathrm{524,38}nm}=c_3\left(20f_1-13{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="DE102023122800B3\_0007.png"\; state="\{\{state\}\}">f</figure-callout>}}_2-6f_3-\mathrm{4,6}{f}_4+\mathrm{7,8}{f}_5-\mathrm{6,3}{f}_6+\mathrm{1,7}{f}_7+\mathrm{2,5}{f}_8\right)\\ +c_5\left(-8E_1+7{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="DE102023122800B3\_0007.png"\; state="\{\{state\}\}">E</figure-callout>}}_2-\mathrm{4,5}{E}_3+\mathrm{4,8}{E}_4\right)-\mathrm{3,5}\end{array}$$

The value -3.5 also specifies that a classification rule is that >0 applies to one class and <0 to the other class.

After this first stage of the procedure, the classification results listed below can be achieved for the following example profiles. The hit rates were checked using two-dimensional spectroscopic data from hatching eggs that were not used to train the classifier: Profile at wavelength / nm discriminant D hit rate A / % 488.1183 0.43371 72.4567 490.9085 0.39672 72.0779 493.6985 0.53655 72.4567 496.4885 0.97459 75.7576 499.2783 0.86616 79.4371 502.0681 0.77513 75.7576 504.8577 0.68069 75.7576 507.6473 0.6117 72.4567 510.4367 0.9705 79.0584 513.2261 0.53488 72.4567 516.0153 1.1332 79.4372 518.8044 0.83231 79.4372 521.5934 0.73678 75.7576 524.3823 2.3048 90.0974 527.1710 0.89419 79.4372 529.9597 0.53765 72.4567 532.7482 0.9723 79.4372 535.5366 1.1829 79.4372 538.3249 0.56901 72.4567 541.1130 0.63482 75.3788 543.9011 1.2399 82.7381 546.6890 0.7954 75,0000 549.4768 1.0302 75.75761 552.2644 0.90166 78.6797 555.0519 0.82719 75.3788 557.8393 0.94714 79.0584 ...

D denotes the value of the discriminant function for the profiles and A denotes the accuracy of the profiles. The designation for the wavelengths corresponds either to the individual singular wavelength of the profile or to the arithmetic mean of the start and end values of the wavelength range.

In the next step of the procedure, a subset is selected from the profiles determined by analyzing the profiles with regard to their discriminatory power for the two classes. In this case, this is done using linear discriminant analysis. 2 shows schematically how the profiles represented as circles 18 are separated into two classes P ₁ and P ₂ by a discriminant function 20 found by means of linear discriminant analysis.

Taking into account this determined subset of profiles, which also includes the profile at 524.38 nm, a 100% hit rate is achieved in the second stage.

reference sign

10a

decay curve for singular wavelength

10b

averaged decay curve over wavelength range

12

y-axis

14

x-axis

16

wavelength range

18

Circle

20

discriminant function

P1, P2

classes

Claims (13)

Computer-implemented method for determining a binary classifier, wherein the classifier is set up to assign this sample to one of two possible classes (P ₁ , P ₂ ) on the basis of spectroscopic data of a sample, comprising the steps of: - receiving two-dimensional spectroscopic data of the sample, wherein the data comprise discrete values in a wavelength dimension (12) and a time dimension (14), - determining features F1 to F5 formed along the time dimension (14) of the data for several wavelengths and/or for several wavelength ranges (16), wherein the features • F1: statistical moments of the 2nd to 4th order of the data in the time dimension (14), • F2: coefficients of a best fit line of the data in the time dimension (14), • F3: real coefficients of a Fourier transform of the data in the time dimension (14), • F4: coefficients of a Best fit line through the real coefficients of the Fourier transform determined for feature F3, and • F5: entropy of the data in the time dimension (14), - determining linear combinations of the features F1 to F5 for the multiple wavelengths and/or for the multiple wavelength ranges (16) by analyzing the features with regard to their separating strength for the two classes (P ₁ , P ₂ ), and - determining a subset of the determined linear combinations by analyzing the linear combinations with regard to their separating strength for the two classes (P ₁ , P ₂ ). procedure according to claim 1 , where the sample is a fertilized bird egg and the two classes (P ₁ , P ₂ ) represent a male sex and a female sex of the fertilized bird egg. Method according to one of the preceding claims, wherein the received two-dimensional spectroscopic data are autofluorescence data of the sample and in particular autofluorescence data of the sample acquired by means of time-resolved laser-induced fluorescence spectroscopy (zLIF) and/or by means of time-correlated single photon counting (TCSPC). Method according to one of the preceding claims, wherein for determining the features F2 to F5 the data in the time dimension (14) are present as normalized data such that a mean value of the data in the time dimension (14) is zero. Method according to one of the preceding claims, wherein for determining the feature F1 the data in the time dimension (14) are present as non-normalized data. Method according to one of the preceding claims, wherein the real coefficients of the Fourier transform of the data in the time dimension (14) of the feature F3 are ordered in ascending order and/or wherein the coefficients of the best fit line are determined by the real coefficients of the Fourier transform determined for feature F3 on the basis of real coefficients ordered in ascending order. Method according to one of the preceding claims, wherein the step of determining the linear combinations of the features F1 to F5 for the plurality of wavelengths and/or for the plurality of wavelength ranges (16) by analyzing the features with regard to their separation strength for the two classes (P ₁ , P ₂ ) comprises defining a coefficient of the linear combination as zero for features whose separation strength is below a predefined threshold value. Method according to one of the preceding claims, wherein the step of determining the linear combinations of the features F1 to F5 for the plurality of wavelengths and/or for the plurality of wavelength ranges (16) by analyzing the features with regard to their separating strength for the two classes (P ₁ , P ₂ ), and/or wherein the step of determining the subset of the determined linear combinations by analyzing the linear combinations with regard to their separating strength for the two classes (P ₁ , P ₂ ) comprises analyzing by means of linear discriminant analysis. Method according to the preceding claim, wherein a discriminant function (20) and preferably the Fisher discriminant function and/or a hit rate of the determined classifier are used as a metric for the separation strength during the analysis. Computer-implemented method for assigning a sample to one of two possible classes (P ₁ , P ₂ ) on the basis of spectroscopic data of the sample, and in particular for assigning a fertilized bird egg to one of two possible sexes, comprising the steps of - receiving two-dimensional spectroscopic data of the sample, wherein the data comprise discrete values in a wavelength dimension (12) and a time dimension (14), and - applying a classifier to the received data, wherein the classifier is implemented using the method according to one of the Claims 1 until 8 was determined. Device for data processing comprising means for carrying out the method according to one of the preceding method claims. Computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method according to one of the preceding method claims. Computer-readable medium on which the computer program product according to the previous claim is stored.

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