Systems and methods for predicting sample characteristics based on spectral measurements

Abstract

A system, method, and computer program product for predicting a characteristic value of a sample based on a NIR / MIR spectrum obtained from the sample of a particular sample type are disclosed. A wavelet transform is applied to the obtained spectrum to compute a sample set of wavelet coefficients in a plurality of wavelet bands. The system accesses a library of a plurality of calibration sets of wavelet coefficients that define a calibration coefficient space. The calibration sets are computed by a wavelet transform of respective NIR / MIR spectra obtained from calibration samples of at least the particular sample type. Each calibration set is associated with one or more reference characteristic values of the respective calibration samples. The system creates a local PLS model of the characteristic value to be determined for the sample by selecting a predetermined number k of nearest neighbors of the sample set in the calibration coefficient space and computes the local PLS model based on the selected k nearest neighbors and their associated reference characteristic values. The characteristic value of the sample is predicted by applying the local PLS model to the sample set.

Description

Technical Field

[0001] The present invention relates generally to spectroscopic measurement of samples, and more particularly to predicting sample properties using measured spectra obtained by near infrared (NIR) or mid infrared (MIR) spectroscopy. Background Art

[0002] The problem in spectroscopy is the creation and evaluation of multivariate calibrations for near-infrared (NIR) or mid-infrared (MIR) spectra or other spectroscopic measurement data obtained from a sample. An example of a common NIR application is in the field of chemical analysis and addresses the quantitative analysis of chemical or physical properties of a sample, i.e., fat, protein, and water content in milk powder or animal feed, benzene content in gasoline, etc. For spectroscopic methods such as NIR, MIR, XRF, etc., calibration is required for the secondary analytical method in order to establish a relationship between one or more measured values ​​(spectra) and sample properties (concentration, density, viscosity, etc.). For this purpose, there are univariate or multivariate calibration procedures, which are mainly based on correlation and regression.

[0003] Prior art methods for solving multivariate calibration are typically based on any of the following algorithms:

[0004] PLS (Partial Least Squares or Projection to Latent Structure): Commonly used in NIR spectroscopy. PLS models always work linearly, i.e., the relationship between the characteristic to be calibrated and the latent variable (PLS score) is linearly established by regression calculation. Typically, the components of the sample are also its characteristics.

[0005] -SVR (Support Vector Regression): Based on the kernel-based SVM (Support Vector Machine) algorithm. Depending on the kernel, the model can be created linearly or nonlinearly. In many cases, SVR allows the creation of more accurate models than PLS in the case of larger and more heterogeneous datasets.

[0006] - Local regression, LOCAL and LWR (local weighted regression): ultimately based on PLS, but uses a library of spectra (spectral data) to first find spectra that match the spectrum to be analyzed. Using these, a local model is calculated and the spectra are evaluated. PLS works linearly, but by locally selecting calibration spectra that match the analysis spectrum, nonlinear effects are avoided. Another method using local regression is based on latent variables (scores) derived by principal component analysis or PLS.

[0007] ANN (Artificial Neural Network): Based on potentially several layers of internal neurons (mimicking the function of the human brain). Such models can be trained for spectral evaluation. This also allows for nonlinear modeling, i.e., the model is never strictly linear.

[0008] ANNs use random internal starting values for training and are therefore not deterministic like PLS or local regression, which can be a disadvantage.

[0009] All existing methods directly use the spectra to produce the calibrants, which is standard in the case of PLS with reasonable computation time. With SVR, local regression and ANN, the computation time becomes significantly longer than with PLS. Depending on the settings, the increase in computation time can be by a factor or even by an order of magnitude. Further, the spectra have to be pre-processed as well. That is, a spectral range selection has to be made and in any case data pre-processing (derivation, normalization) is required.

[0010] In the case of the local regression implementation (e.g. LOCAL), the model has to contain all original spectra, which makes very large files that have to be distributed in the network of NIR instruments in a lengthy process.

[0011] The effort required to establish a library containing a database of samples by measuring NIR or MIR spectra and storing such spectra together with the corresponding sample properties determined by a preliminary analysis method is very large. To prevent unauthorized access to the library, strong data protection mechanisms are required, which slow down the implementation of any new evaluation (e.g. analysis or prediction of a newly measured sample). SUMMARY

[0012] Therefore, there is a need to provide a system and method for determining sample properties from NIR / MIR spectra obtained from samples, which overcomes the above-mentioned disadvantages of the existing art multivariate calibration methods for spectral measurement data. The method disclosed herein suggests a multivariate calibration and evaluation of wavelet-transformed NIR spectra and potentially other spectral measurement data, instead of directly using the obtained spectra as in the existing art. That is, instead of evaluating the spectra, the wavelet-transformed spectra are evaluated, which has advantages like various filter and signal selection procedures not possible with the existing art methods. In particular, in embodiments where a filter function is used to filter out certain wavelet bands and / or wavelet coefficients of less information value with respect to the original signal (spectrum), it can be advantageous that it is not possible to derive the original calibration spectra from the wavelet-transformed calibration set stored in the respective library. That is, such embodiments prevent unauthorized access to the original spectra without the need for additional data protection mechanisms.

[0013] In one embodiment, a computer-implemented method is provided for predicting (estimating) a characteristic value of a sample of a specific sample type. The prediction is based on NIR / MIR spectra obtained from the sample. Sample characteristics that can be analyzed using NIR / MIR spectroscopy include, but are not limited to, the concentrations of the following (in the sample): measuring the concentration of specific compounds in the sample, iodine value, pH value, water, protein, fat, fiber, ash, fatty acids, and free fatty acids; or another concentration-independent characteristic (measurable by NIR / MIR spectroscopy) including density, viscosity, octane number, and cetane number. The method can be performed by a computer system that implements functional modules to perform the functions described below.

[0014] The method begins with applying a wavelet transform to the spectrum obtained. For example, the wavelet transform can be a discrete wavelet transform (DWT), but other wavelet transform types (e.g., continuous or multiscale wavelet transform (CWT), wavelet packet transform) can also be used. As a result, a sample set of wavelet coefficients in multiple wavelet bands is calculated. Generally, wavelet transform allows the analysis of signals at frequencies contained, but in contrast to Fourier transform (Fourier Transformation), the position of the known frequencies in the signal is (see U. Depczynski, K. Jetter, K. Molt and A. Niemoeller, Quantitative analysis of near infrared spectra by wavelet coefficient regression using a genetic algorithm, Chemometrics and Intelligent Laboratory Systems 47, 179-187, 1999). The wavelet itself has a compact support set, which means that the wavelet is not periodic. The wavelet transform of the spectrum produces a low-pass representation band and a so-called detailed band. The wavelet coefficients of the low-pass representation band (j=0) are so-called approximation or scaling coefficients. These approximation or scaling coefficients represent a low-pass representation of the signal. Such approximation coefficients do not provide valuable information for the subsequent modeling and prediction steps and are not further used in the method described herein. Valuable information about the details of the signal is found in the wavelet coefficients in the detailed band starting with band j=1. In the following description, band j=1 is always referred to as the lowest band.

[0015] There are several families with many possible wavelet types and shapes. For example, for wavelet transforms, the simplest Haar wavelet and other common Daubechies types can be used to decompose the spectrum and use the coefficients directly, and any other wavelet type containing more complex wavelets can be used. However, in the context of the method disclosed herein, the wavelet type is not very relevant, but may still have an impact on the results and complexity of the described process. The wavelet transform is very fast and applicable to each individual single spectrum. That is, any spectrum can be individually transformed into a corresponding wavelet transformed spectrum to be used in the library, and can further be used in subsequent prediction steps for new sample spectra. In other words, the library does not depend on the data set, while classical PLS or other multivariate methods that rely on factor analysis (analysis of variance), such as PCA (principal component analysis), depend on the data set. In the multivariate method, changing the library by adding or deleting samples requires completely recalculating the library (e.g., recalculating scores and loadings). That is, in wavelet space, each calibration set can be added to or deleted from the library without affecting other calibration sets in the library. For the wavelet transform, no pre-processing of the spectrum is required at all, which simplifies the calibration and optimization process.

[0016] The system then accesses a library of multiple wavelet coefficient calibration sets that define a calibration coefficient space. The library can be a built-in part of the system, or it can be provided by a remote storage device with an appropriate access interface. The calibration sets are calculated using wavelet local regression (WLR) by wavelet transforming the corresponding NIR / MIR spectra obtained from the calibration samples. In addition to calibration sets for calibration samples of the same sample type as the sample, the library can also contain calibration sets for other sample types. Each calibration set is associated with one or more reference characteristic values ​​for the corresponding calibration sample. The reference characteristic value is the value measured (or analyzed) using a reference method (primary analytical method). Each calibration set represents a point in a multidimensional wavelet coefficient space, where the coefficients of a particular calibration set represent the coordinates of this point in the multidimensional wavelet coefficients. Of course, the sample set also represents a point in this multidimensional space. For application areas such as feed and feed ingredients, grains and other agricultural products or foods, and soil, there are thousands of spectra available, and many materials and finished product formulations need to be considered. The method disclosed herein allows many sample types to be covered in one library and avoids the creation of a large number of individual PLS models as proposed in the above-mentioned prior art methods.

[0017] The construction of a WLR library does not require any type of modeling or other chemometric steps. Spectra obtained from calibration samples can be interpolated and then transformed into a calibration set using a wavelet transform. The calibration set of a library should cover one or more identical spectral ranges. The library covers the entire spectral range of the measured spectrum, but a larger sub-range or multiple sub-ranges may be sufficient as input. A typical spectral range for measured NIR spectra is 10,000 cm -1 Up to 4000cm -1 , and the typical spectral range of the measured MIR spectrum is 4000 cm -1 Up to 400cm -1 The spectra can be interpolated to obtain 2 n data points, which may be advantageous for the wavelet transform, but is not mandatory. This also allows spectra with slightly different resolutions to be used in the library when the spectral differences due to unequal resolutions are not too large. Each calibration set (wavelet transformed calibration spectrum) is represented in the library by a vector of wavelet coefficients sorted in a wavelet band. These wavelet coefficients span the multidimensional wavelet coefficient space, where new spectra (obtained from the sample) can be localized, which allows the creation of local PLS models based on the nearest neighbors described below.

[0018] Based on the calibration set of the library, the system now creates a local PLS model of the characteristic to be determined of the sample. Local regression methods are known, such as LWR (local weighted regression) or the LOCAL method of Shenk and Westerhaus (see Shenk JS, Westerhaus MO and Berzaghi P. "Investigation of a LOCAL calibration procedure for NIR instruments" Journal of Near Infrared Spectroscopy, 5, 223-232, 1997; Berzaghi P, Shenk JS and Westerhaus MO. "LOCAL prediction with nearinfrared multi-product databases" Journal of Near Infrared Spectroscopy; 8, 1-9, 2000). The method disclosed herein is based on PLS, but uses the library to first identify a suitable calibration set (k nearest neighbors (kNN) of the sample set) of the obtained spectrum to be analyzed in multidimensional wavelet space. Using such identified spectra, the local PLS model is calculated and the (obtained) spectrum to be analyzed is evaluated.

[0019] In more detail, in order to create a local PLS model, the system first identifies a predefined number of nearest neighbors of the sample set in the calibration coefficient space. For example, the nearest neighbors can be identified based on the mathematical distance between their calibration set and the sample set. This mathematical distance is a measure of the distance between objects in a multidimensional space that forms the basis of many multivariate data analysis methods. Typically, the distance between any two points in n-dimensional space can be calculated by the Minkowski equation. There are three special cases of the Minkowski distance: city block distance (Manhattan distance), Hamming distance, and Euclidean distance.

[0020] In actual experiments, the predefined number k of nearest neighbors is selected from the range of 25 to 1000. Advantageously, the predefined number k is selected from the range of 100 to 300. When creating a model using 200 nearest neighbors, very good results can be achieved. The local PLS model is then calculated based on the selected k nearest neighbors (kNN) and their associated reference characteristic values.

[0021] The local selection of the k nearest neighbor calibration set allows minimizing or even avoiding nonlinear effects in advance, since the created local PLS model needs to cover a lower spectral variance relative to the spectral variance of the selected kNN, assuming that the k nearest neighbors are similar to the sample. This approach can be advantageous in the following ways:

[0022] - Many spectra of different products (samples) and sample types can be easily combined if the library contains a sufficient number of calibration samples (wavelet transforms) for each sample type.

[0023] - On average, the local PLS model approach shows lower method error (eg, RMSEP) and is therefore more precise (accurate) than the approach using a global PLS model based on the same global dataset (of the calibration samples).

[0024] - Updating the library with additional calibration sets can be easily done by users of the system disclosed herein and does not require any activity of the central library provider (such as recalculating the library).

[0025] Finally, the system predicts the value of the property to be determined for a sample by applying the local PLS model to the sample set. Typically, the local PLS model contains weighting or regression coefficients. These coefficients form a so-called b-vector, which represents the PLS model as a result of the PLS modeling, the size of the b-vector corresponds to the number of basis wavelet coefficients (e.g. 60 wavelet coefficients) in case of using a wavelet coefficient space. It should be noted that in prior art methods working in the spectral dimension, the b-vector easily reaches a size of 500 or more (corresponding to the basis data points of the respective spectrum). By the multivariate local PLS model, each data point (i.e. each wavelet coefficient) receives a weighting. This weighting is then applied to the wavelet transform of the obtained sample spectrum. That is, the b-vector is multiplied with the wavelet transform of the obtained sample spectrum. The prediction result is obtained by adding the now weighted coefficients and adding a so-called bO coefficient.

[0026] Spectral range selection or data pre-processing is not required but can be performed. Since PLS works adaptively by the weighting of individual coefficients, it is not necessary to select any coefficients in the selected band, however filtering or thresholding can be used. Normalization of the wavelet coefficients also helps to build the library and analyze the obtained sample spectra. Some optional embodiments implement such additional filtering functions which allow filtering of the wavelet coefficients for various purposes as described below.

[0027] In one embodiment, the wavelet coefficients of the sample set can be normalized by using vector normalization.

[0028] In one embodiment, for each wavelet coefficient of the calibration set, the respective variance of the selected k nearest neighbors can be determined. Then, when creating the local PLS model for property value prediction, the wavelet coefficients whose variance is lower than the maximum variance of 5% are not used. This function allows to filter out wavelet coefficients which do not show variance over the whole data set, e.g. wavelet coefficients representing a baseline or total absorbance region in the calibration set. Since this filtering criterion is independent of the sample properties, it can typically be used to reduce the number of wavelet coefficients used for the local PLS model.

[0029] In one embodiment, the correlation of the selected k nearest neighbors with the actual property of interest of the respective calibration sample is determined. When creating the local PLS model, the wavelet coefficients whose correlation is lower than a predefined correlation threshold are not used. A suitable correlation threshold is about 85%. In other words, using the correlation r 2The selection performed allows to consider only coefficients with a correlation higher than a correlation threshold. Filtering out wavelet coefficients with too low correlation improves the prediction accuracy of the local PLS model, since wavelet coefficients that are not relevant and are affected by noise are not used. Since this filtering criterion depends on the sample characteristics, it can be used to reduce the number of wavelet coefficients for a dedicated local PLS model for a specific characteristic.

[0030] In one embodiment, applying the wavelet transform comprises computing a universal threshold for the wavelet coefficients of the highest wavelet band of the sample set for the selected k nearest neighbors. Donoho and Johnstone proposed a universal threshold as a threshold parameter (see Ideal spatial adaptation by wavelet shrinkage, Biometrika, Vol. 81, No. 3, September 1994, pp. 425-455). The universal threshold acts as a filtering function that allows to ignore all wavelet coefficients with a value lower than the computed universal threshold when creating the local PLS model. This thresholding filtering function allows to truncate wavelet coefficients with too small values that are comparable to noise. Again, this filtering criterion is independent of the sample characteristics and can also be used to reduce the number of wavelet coefficients for a local PLS model.

[0031] In one embodiment, the rank of the local PLS model for the corresponding characteristic can be set. One option is to manually set the characteristic and the rank of the whole library to a global rank. However, this option is based on trial and error and is very time consuming. A more advantageous option is an automated and novel approach, where each calibration set in the library has a rank that is determined by a cross-validation of the whole library for all respective calibration sets with respect to the respective characteristic. The rank of the created local PLS model for determining the characteristic value of the sample can then be computed based on the ranks of the identified nearest neighbors. In one implementation, the rank of the created local PLS model can be computed as the rank associated with the majority of the nearest neighbors. In an alternative implementation, the system can compute the rank as a rounded average of the ranks of the nearest neighbors of the sample set in the multi-dimensional wavelet coefficient space. The computed rank of the local PLS model is typically in the range of 1 to 35, advantageously, the rank is in the range of 2 to 15. When creating the library, a so-called cross-validation is performed. That is, each calibration set is analyzed by itself with the WLR and the appropriate rank is determined by comparing the rank dependent result with the known reference value of the calibration set and finding the lowest absolute difference. This best rank is saved in the library for each calibration set. When creating a new local PLS model for analyzing a new spectrum (of the sample), the rank determined by the majority principle or the rounded average rank of the local PLS models can be used for the spectral analysis. When extending the library, only a new cross-validation for the new calibration set or new characteristic reference value is required.

[0032] In one embodiment, when creating a local PLS model and predicting sample characteristic values, at least the lowest and highest wavelet bands of the calculated sample set are ignored. This selection of wavelet bands typically ignores at least the lowest and highest bands because the lowest and highest bands do not contain relevant information because NIR / MIR signals are almost always reflected in wavelet bands between such extreme bands. Based on user input, the system can receive one or more additional higher bands to be ignored. By selecting the wavelet bands for characteristic value prediction analysis (parameters of WLR), coefficients are selected band by band and then used. For example, the system can use only the coefficients of one wavelet band to perform the nearest neighbor search in the library to keep the calculation time low. The nearest neighbor search on kNN decreases exponentially with the increase in dimensionality. Medium wavelet bands can already represent the most important spectral information (with sufficient variance) to identify the appropriate region in the library using an appropriate kNN. However, multiple wavelet bands can be used for local PLS modeling because this provides more information and the increase in the number of variables does not burden the PLS calculation of the local modeling.

[0033] Wavelet transformation of the spectra and truncation of complete wavelet bands, along with optional initial filtering, allows data compression when storing the library without losing important NIR / MIR related information. This is advantageous when providing such libraries across a network of instruments where file size is still a concern in areas with poor internet connectivity.

[0034] In general, a wavelet transform to any wavelet type can be used. This includes, but is not limited to, the following wavelet types: Haar wavelet; Daubechies wavelets db2, db4, db6, and db8; Morlets wavelet; Symlets wavelet; Coiflets wavelet; and biorthogonal wavelet. Other wavelet types may also be used.

[0035] In one embodiment, a computer program product for predicting a characteristic value of a sample of a specific sample type based on NIR / MIR spectra obtained from the sample is provided. The computer program product has computer-readable instructions that, when loaded into a memory of a computing device and processed by one or more processors of the computing device, cause the computing device to perform the method steps of the computer-implemented method disclosed herein.

[0036] In one embodiment, a computing system for predicting characteristic values ​​of a sample of a specific sample type based on NIR / MIR spectra obtained from the sample is provided. The system includes functional modules adapted to perform the method steps of the computer-implemented method disclosed herein. For example, the computer system includes a memory for loading the computer program product and one or more processors for executing the program to implement the functional modules.

[0037] Other aspects of the invention will be realized and attained by the elements and combinations particularly described in the appended claims.It should be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention described. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A block diagram of an exemplary embodiment of a computer system for predicting a property value of a sample based on an NIR / MIR spectrum obtained from the sample is included;

[0039] Figure 2 is a simplified flow chart of a computer-implemented method for predicting a property value of a sample based on an NIR / MIR spectrum obtained from the sample;

[0040] Figure 3 Shows examples of wavelet types from the common Daubechies wavelet family;

[0041] Figure 4 The expansion and translation of Daubechies 4 wavelet on three low-frequency wavelet bands are shown;

[0042] Figure 5A 、 5B The wavelet transformation of a spectrum combining two absorption bands, baseline and noise into several bands (levels) with wavelet coefficients is demonstrated;

[0043] Figures 6A to 6J Wavelet transformation of multiple NIR spectra obtained from different sugar product samples into several bands (levels) with wavelet coefficients is demonstrated;

[0044] Figure 7 is a schematic overview of the structure of a library having a plurality of calibration sets of wavelet coefficients defining a calibration coefficient space according to an embodiment; Figure 8 A scheme for determining the optimal rank of a calibration set with respect to a specific characteristic of a corresponding calibration sample is presented; and

[0045] Figure 9 is a diagram illustrating examples of general-purpose computer devices and general-purpose mobile computer devices that can be used with the techniques described herein. DETAILED DESCRIPTION

[0046] Figure 1 A block diagram of an exemplary embodiment of a computer system 100 for predicting a characteristic value of a sample 201 based on an NIR / MIR spectrum 211 obtained from the sample 201 using an appropriate NIR / MIR spectrometer 200 is shown. The sample 201 can have a variety of characteristics. In the examples described herein, the characteristic of interest is characteristic P1 for which the corresponding characteristic value is to be predicted. Examples of characteristics that can be based on NIR / MIR spectra include, but are not limited to, the concentration of a specific compound in the measured sample, iodine value, pH value, the content of water, protein, fat, fiber, ash, fatty acids, and free fatty acids; or another characteristic that is independent of concentration, including density, viscosity, octane number, and cetane number. The sample 201 in the example has a sample type ST1.

[0047] Figure 2 is a simplified flow chart of a computer-implemented method 1000 for predicting a characteristic value of a sample based on an NIR / MIR spectrum obtained from the sample. The method 1000 may be performed by Figure 1 The system 100 is now described in the context of a simplified flowchart of the method 1000. Figure 1 Therefore, the following description refers to the system 100. Figure 1 and Figure 2 Thus, the system 100 is configured to perform the method 1000 when a corresponding computer program is loaded into a memory of the system and executed with a processing device of the system.

[0048] The wavelet transform module applies the wavelet transform 110 to the obtained spectrum 211 and thereby calculates a sample set 111 of wavelet coefficients in a plurality of wavelet bands B0, B1, B2. The sample set 111 is shown as having three wavelet bands. However, typically the number of wavelet bands is higher. Briefly go to Figure 3, three different example wavelet types DT1, DT2 and DT4 of the common Daubechies wavelet family are shown. DT1 demonstrates Daubechies type 1 (commonly known as Haar). DT2 and DT4 demonstrate Daubechies type 2 and type 4, respectively. Such simple wavelet transform types can be used to operate the wavelet transform 110 because they are used to decompose the spectrum 211 using the calculated wavelet coefficients of the sample set directly. Specifically, when using a discrete wavelet transform, the coefficients of the wavelet transform and the sample set 111 are orthogonal. For other types of wavelet transforms, it is still possible to select orthogonal coefficients. This characteristic of the wavelet transform is advantageous because it allows wavelet transforms to be selected or combined as needed in the modeling step of a later PLS or multivariate method. Optionally, the wavelet coefficients of the sample set can be normalized by using vector normalization.

[0049] Briefly go to Figure 4 , shows the expansion variation and translation of the Daubechies 4 wavelet over three low-frequency wavelet bands j=0, j=1 and j=2. The wavelet band j=0 can be adapted in width to cover different frequency components in the signal in higher bands. For example, the width of the wavelet is reduced in band j=1 and reduced again in band j=2. Narrow-scale wavelets can also analyze higher frequencies. By translating the wavelet over the signal, this frequency can be analyzed at different locations of the spectrum. Similarly, an even narrower wavelet in band j=2 can be used to analyze the spectrum at four different spectral positions (k=0 to k=3).

[0050] Briefly go to Figure 5A 、 5B , the wavelet transform 110 is further explained by using an example with a spectrum f comprising two absorption bands 501, 502, a baseline (a curved bow curve 503 extending from 0 to 1024 data points) and some noise superimposed on the baseline. For ease of explanation, the example spectrum f has been obtained by simulation.

[0051] The wavelet coefficients of the wavelet transform are sorted in wavelet bands (or levels) starting from the low-frequency band (j=1), where only one or two coefficients cover the entire spectral range of the signal (analog spectrum f). As mentioned before, the coefficients of band j=0 are so-called approximation or scaling coefficients that are irrelevant to the method and system disclosed herein and are therefore ignored by the further processing steps. In the example described, band j=1 has coefficients 3, 4, band j=2 has coefficients 5 to 8, band j=3 has coefficients 9 to 16, and so on. The number of coefficients is always doubled in the next higher band, and the corresponding analysis frequency increases. Figure 5BThe highest bands in the example (j=8, j=7) mainly show noise. However, in the case of a smoothed spectrum, such highest frequency bands may also contain some valuable information. Valuable coefficients are coefficients whose values ​​are higher than the values ​​that only represent noise. In the simulated spectrum f, it is easy to see which coefficients are important or valuable, because the coefficients contain information about the two absorption bands. The wavelet bands below band j=3 mainly represent baseline information or less important low-frequency information. On the other hand, the higher bands j=7 and j=8 mainly represent noise. That is, the valuable information about the two absorption peaks in spectrum f is in bands j=3 to j=6.

[0052] exist Figures 6B to 6J In the example shown, the Figure 6A Nine wavelet bands (bands 1 to 9) obtained in the real NIR spectrum are shown. Figure 6A Four NIR spectra 601 to 604 are shown, wherein each NIR spectrum is represented by a different line type. Figures 6B to 6J The wavelet transform in [ 60 ] uses the corresponding line shape for the corresponding wavelet transform. Similarly, for the wavelet transform of the real NIR spectra 601 to 604, the results are similar, as the results show that the valuable information is distributed in different bands, but always in the expected position. The shape of the wavelet coefficient pattern changes with the frequency analyzed, and allows the selection of such wavelet coefficients that are favorable for the given characteristic to be calibrated. It should be noted that when the absorbance of the sample increases, the wavelet coefficients increase. In other words, Beer's law still holds.

[0053] Briefly go to Figure 1 and 2 System 100 accesses 1200 a library 300 containing a plurality of calibration sets 311-1 through 311-n, 311c that define a calibration coefficient space 311. The library may also be a built-in component of system 100, or it may be stored on a remote storage device accessible to system 100 via an appropriate interface. For example, library 300 may be stored on a public or private cloud server, and system 100 may access the library via the Internet or an intranet, respectively. Calibration sets 311-1 through 311-n, 311c have been calculated using wavelet transforms of corresponding NIR / MIR spectra 300-1 through 300-n obtained from calibration samples. The library contains at least one calibration set associated with a specific sample type ST1 of measurement sample 201. Each calibration set is associated with at least one reference property value PV-1 through PV-n for a specific property of the corresponding calibration sample. However, multiple reference property values ​​for multiple properties may have been measured for the calibration sample and stored in the library along with the corresponding calibration set.

[0054] Briefly go to Figure 7 , shows a scheme of library 300 together with sample set ss1 derived from the acquired NIR / MIR spectra by wavelet transform. Sample set ss1 contains the wavelet coefficients in bands B0 to Bm. Calibration sets cs1 to csn in library 300 have the same structure as sample set ss1. Each calibration set contains the wavelet coefficients calculated from the corresponding calibration spectrum in bands B0 to Bm. In addition, for each calibration set, one or more reference values ​​for one or more properties P1, P2 of the corresponding calibration sample are stored. As mentioned above, the reference values ​​are measured by using a suitable reference (calibration) method.

[0055] Briefly go to Figure 1 and 2 , the PLS modeler module 120 of the computer system 100 now creates 1300 a local PLS model 121 of the characteristic value to be determined for the sample 201 based on the information retrieved from the library 300. In a first step, the PLS modeler 121 selects 1310 a predefined number k of nearest neighbors 311k (kNN) of the sample set in the calibration coefficient space 311. Figure 1 In FIG, a simplified two-dimensional coefficient space 311 is shown. In practice, the coefficient space 311 is multi-dimensional, with the number of dimensions corresponding to the number of wavelet coefficients in the bands B0 to Bm (see Figure 7 ).exist Figure 1 , the points in the coefficient space 311 that correspond to the coefficients of the wavelet transformed sample spectrum are shown by black dots 311s. All other white filled circles 311c and dot filled circles 311k are points representing the calibration set in the coefficient space 311. Therefore, the k nearest neighbors selected are represented by dot filled circles 311k. As mentioned above, very good results have been achieved with k in the range of 100 to 300, with 200 showing the most favorable results. The selection of kNN is based on the mathematical distance between the sample point 311s and any calibration set in the multidimensional space 311. For example, such mathematical distance can be calculated by the equation given by Minkowski:

[0056]

[0057] Where k in Equation 1 is the index of the coordinate, and p determines the type of distance.

[0058] The variant of the Minkowski distance with p=2 corresponds to the well-known Euclidean distance, which can be used, for example, to determine the distance between a calibration set and a sample set. More details on the calculation of the Minkowski distance can be found in: "Fundamentals of Statistics - Distance and Similarity Measures", which is available at http: / / www.statistics4u.com / fundstat_eng / cc_distance_meas.html.

[0059] The PLS modeler 120 ultimately selects the k calibration sets with the shortest distances to the point 311s as kNNs in the multidimensional coefficient space 311. In one embodiment, the selection 1310 of the kNNs may use only the wavelet coefficients of a single wavelet band, while the following calculation 1320 of the local PLS model 121 may use the wavelet coefficients of multiple wavelet bands.

[0060] In the next step, the PLS modeler finally calculates 1320 a local PLS model 121 based on the selected k nearest neighbors 311k and their associated reference characteristic values. Typically, the PLS modeler can use all wavelet coefficients of all bands of the calibration set for this calculation. It is advantageous to use multiple wavelet bands for local PLS modeling because more information is provided thereby. It should be noted that those skilled in the art generally know how to calculate local PLS models based on multiple vectors in a multidimensional space. Typically, for large data sets with many calibration sets (typically hundreds or thousands), or when combining many calibration sets of different samples or sample types, the local PLS model approach shows a lower method error (e.g., a lower root mean square error of prediction RMSEP) and is therefore more accurate than a global PLS model based approach using the same calibration set.

[0061] When computing the local PLS model, the PLS modeler may further apply an optional filter function 122 to the kNN calibration set. Figure 7Two optional filter embodiments are briefly described in the context of the above. In one embodiment, for each wavelet coefficient of the calibration set csn, a respective correlation cor-csn-P1 with the property P1 of the respective calibration sample is calculated. This correlation is calculated for all selected k nearest neighbors. Wavelet coefficients with a correlation below a predefined correlation threshold are then not used by the PLS modeler for creating the local PLS model. In other words, only calibration wavelet coefficients that are at or above the predefined threshold are used for calculating the local PLS model. The PLS modeler can use wavelet coefficients with a correlation above the correlation threshold. A suitable correlation threshold is 0.85, but other thresholds can also be used. By way of example, the correlation coefficient r 2 Filtering by the correlation of the wavelet coefficients (e.g. with the concentration values or other property values of the respective NIR samples) can be used to eliminate non- or low-correlated coefficients, and to reduce the computation time and improve the results. Indirectly, this embodiment is also a filter for filtering out coefficients that do not have a certain variance in the dataset.

[0062] In a further embodiment, for each wavelet coefficient of the calibration set csn, a respective variance var-csn is determined for the selected k nearest neighbors. For example, when creating the local PLS model for the selected k nearest neighbors, wavelet coefficients with a variance below 5% of the maximum variance can not be used (i.e. filtered out) of the wavelet coefficients. Filtering out wavelet coefficients that show low or no variance on the kNN calibration set allows to eliminate such coefficients that represent baseline or total absorption regions in the underlying spectra, and further reduces the computation time.

[0063] A further filter embodiment can use Hard-Thresholding or shrinkage (see Ideal Spatial Adaptation for Wavelet Shrinkage, Biometrics, Vol. 81, No. 3, September 1994, pages 425-455) to deal with too small wavelet coefficients. For example, wavelet coefficients of the calibration set that are smaller than the average of the wavelet coefficients in the highest band can represent noise, and can be filtered out without losing relevant information when creating the local PLS model. That is, this filtering allows to eliminate parts of the underlying signal that do not contribute to relevant information, and further saves computation time.

[0064] In still a further filter embodiment, the PLS modeler can completely ignore at least the lowest and the highest wavelet band of the respective calibration set when creating the local PLS model. As mentioned before, the lowest and highest bands usually do not provide valuable information. The system 100 can also provide a user interface to a user of the system for receiving user input indicating further bands to be ignored when creating the local PLS model. For example, the analysis Figures 6G to 6JA user of bands 6 to 9 in may recognize that these bands show significant redundancy and therefore provide user input: in addition to the highest band 9, the PLS modeler will also ignore bands 7 and 8 when creating the local PLS model.

[0065] When creating the library 300, a cross-validation module 320 (CV) can be associated with the library so that a so-called cross-validation can be performed. In such a cross-validation, each calibration set is analyzed using WLR, and the appropriate rank is determined by comparing the rank-dependency results of the corresponding calibration set with the corresponding known reference value. In this embodiment, the best rank can be saved with each calibration set in the library. Figure 7 The library 300 is further illustrated as being expanded, wherein, in addition to reference values ​​for properties P1, P2, corresponding ranks R1, R2 of the corresponding calibration sets are stored. In other words, in this embodiment, each calibration set cs1 to csn in the library 300 has a rank R1 associated with the corresponding property, which is determined by cross-validation of the corresponding local regression model for the corresponding calibration set with respect to the corresponding properties P1, P2. When the library is expanded in this embodiment with new calibration sets based on corresponding calibration NIR / MIR spectra, new cross-validation becomes necessary, but only for those new sets.

[0066] Figure 8 A scheme 800 is shown for determining the optimal rank 801 of a calibration set for a particular characteristic of a corresponding calibration sample. The rank of a PLS model is defined as the number of factors used in the PLS model. Selecting the optimal number of factors (or loadings) in a multivariate calibration can avoid underfitting or overfitting of the local PLS model. If too few factors are used, an underfitting model is obtained, which means that the model does not adequately cover the important and analyte-related variability in the data. If too many variables or factors are used, an overfitting model may be obtained, in which noise and small or irrelevant changes are included in the model. Both of these situations will lead to poor predictions for the measured NIR / MIR samples. The rank of a PLS model can be determined by plotting the absolute difference between the reference value of the characteristic to be modeled (of the corresponding calibration set) and the predicted value (the value predicted by the local PLS model with the corresponding number of factors) and the results are shown in Figure 8. Figure 8 The optimal number of factors (i.e., the optimal rank) is determined by the relationship between the number of PLS ​​factors shown in the example. The optimal rank is the number of factors for which the plotted curve has the minimum value. In the example, the best result is obtained by a local PLS model with a rank of 10.

[0067] When the PLS modeler creates a local PLS model, the rank of the created local PLS model for determining the value of the characteristic to be determined for the sample can be determined by using the rank associated with the majority of the selected k nearest neighbors or by calculating the rank as the rounded average of the ranks of the selected k nearest neighbors.

[0068] Compared to the spectral-based methods of the prior art, the calibration library disclosed herein with a calibration set (wavelet transform of the original calibration spectrum) achieves significant data reduction. When using the various optional wavelet coefficient filtering mechanisms disclosed above, data compression rates of up to 90% are achieved. On the one hand, this allows significantly accelerating the calculations for creating local PLS models when analyzing new NIR / MIR spectra obtained from the corresponding samples. On the other hand, the filtering mechanism allows the library to be distributed on the corresponding NIR / MIR devices in the network. Such networked NIR / MIR devices are becoming increasingly important, and the data load is not only related to storage capacity, but more importantly to the global distribution of the library. This is specifically limited by the time required to transmit the device settings with calibration. Building a library based solely on a wavelet-transformed calibration set is a model-free approach that allows the library to be easily expanded by simply adding new calibration sets to the library without having to perform any additional operations on the entire library (this is the case for local regression methods based on latent variables (scores) derived from principal component analysis or PLS). In this context, advantageously, the methods disclosed herein also allow users of the system to extend the library with their own calibration data while using a global rank setting, without requiring any centralized vendor-side update process.

[0069] Back to Figure 1 , the predictor module 130 of the system 100 finally predicts 1400 the value of the characteristic to be determined PV1 of the sample 201 by applying the local PLS model 121 to the sample set 111. A person skilled in the art understands "applying the local PLS model to the sample set" as performing partial least squares regression, for example, as described in the following link in Wikipedia: https: / / en.wikipedia.org / wiki / Partial_least_squares_regression:

[0070] Partial least squares regression (PLS regression) is a statistical method somewhat related to principal components regression; instead of finding the hyperplane that maximizes the variance between the response and the independent variables, a linear regression model is found by projecting the predicted and observed variables into a new space. Because both the X and Y data are projected into a new space, the PLS family of methods is called a bilinear factor model. PLS is used to find the underlying relationship between two matrices (X and Y), i.e., a latent variable approach to modeling the covariance structure in these two spaces. The PLS model attempts to find the multidimensional directions in the X space that explain the maximum multidimensional variance in the Y space. PLS regression is particularly well suited when the predictor matrix has more variables than observations and when there is multicollinearity between the X values. In contrast, standard regression fails in these situations (unless it is regularized)."

[0071] There are many PLS variants for estimating factors and loading matrices T, U, P, and Q. Most PLS variants construct the linear regression estimate between X and Y as

[0072] In embodiments where the library 300 also stores the best rank of the calibration set, the rank of the created local PLS model used to determine the characteristic value of the sample is calculated based on the ranks R1 of the k nearest neighbors. Thus, the rank associated with the majority of the selected k nearest neighbors is used as the rank of the local PLS model for making predictions, or the rank of the local PLS model is calculated as the rounded average of the ranks of the selected k nearest neighbors.

[0073] Figure 9 is a diagram illustrating an example of a general purpose computer device 900 and a general purpose mobile computer device 950 that can be used with the techniques described herein. In some embodiments, the computing device 900 can be related to the system 100 (see Figure 1 ). Computing device 950 is intended to represent various forms of mobile devices, such as personal digital assistants, cellular phones, smartphones, and other similar computing devices. In the context of the present disclosure, computing device 950 may provide I / O devices for a user to interact with computing device 950 (e.g., for receiving a selection of a wavelet band). The components shown here, their connections and relationships, and their functions are exemplary only and are not meant to limit the embodiments of the present invention described and / or claimed in this document.

[0074] The computing device 900 includes a processor 902, a memory 904, a storage device 906, a high-speed interface 908 connected to the memory 904 and a high-speed expansion port 910, and a low-speed interface 912 connected to a low-speed bus 914 and the storage device 906. Each of the components 902, 904, 906, 908, 910, and 912 is interconnected using various buses and is appropriately mounted on a common motherboard or otherwise mounted. The processor 902 can process instructions for execution within the computing device 900, including instructions stored in the memory 904 or on the storage device 906 to display graphical information of a graphical user interface (GUI) on an external input / output device (such as a display 916 coupled to the high-speed interface 908). In other embodiments, multiple processors and / or multiple buses can be used together with multiple memories and multiple types of memory as appropriate. In addition, multiple computing devices 900 can be connected together, with each device providing a portion of the necessary operations (e.g., a server group, a group of blade servers, or a multi-processor system).

[0075] Memory 904 stores information within computing device 900. In one embodiment, memory 904 is one or more volatile memory units. In another embodiment, memory 904 is one or more non-volatile memory units. Memory 904 can also be another form of computer-readable medium, such as a magnetic disk or optical disk.

[0076] Storage device 906 can provide mass storage for computing device 900. In one embodiment, storage device 906 can be or contain a computer-readable medium, such as a floppy disk drive, a hard disk drive, an optical disk drive, or a magnetic tape drive, a flash memory or other similar solid-state memory device, or a device array comprising devices in a storage area network or other configuration. A computer program product can be tangibly embodied in an information carrier. A computer program product can also include instructions that, when executed, perform one or more methods, such as those described above. The information carrier is a computer- or machine-readable medium, such as memory 904, storage device 906, or memory on processor 902.

[0077] The high-speed controller 908 manages bandwidth-intensive operations of the computing device 900, while the low-speed controller 912 manages lower bandwidth-intensive operations. This allocation of functions is exemplary only. In one embodiment, the high-speed controller 908 is coupled to the memory 904, the display 916 (e.g., via a graphics processor or accelerator), and is coupled to a high-speed expansion port 910 that can accept various expansion cards (not shown). In the described embodiment, the low-speed controller 912 is coupled to the storage device 906 and the low-speed expansion port 914. The low-speed expansion port can be coupled to one or more input / output devices, such as a keyboard, pointing device, scanner, or networking device (e.g., a switch or router), for example, via a network adapter. The low-speed expansion port can include various communication ports (e.g., Universal Serial Bus (USB), Bluetooth, Ethernet, wireless Ethernet).

[0078] Computing device 900 can be implemented in a variety of different forms, as shown. For example, it can be implemented as a standard server 920, or it can be implemented multiple times in a group of such servers. The computing device can also be implemented as part of a rack server system 924. In addition, the computing device can be implemented in a personal computer such as laptop computer 922. Alternatively, the components of computing device 900 can be combined with other components in a mobile device (not shown) such as device 950. Each of these devices can contain one or more of computing devices 900, 950, and the entire system can be composed of multiple computing devices 900, 950 communicating with each other.

[0079] The computing device 950 includes a processor 952, a memory 964, an input / output device (such as a display 954), a communication interface 966, and a transceiver 968, among other components. The device 950 may also be provided with a storage device, such as a microdrive or other device, for providing additional storage. Each of the components 950, 952, 964, 954, 966, and 968 are interconnected using various buses, and several components may be appropriately mounted on a common motherboard or otherwise.

[0080] The processor 952 can execute instructions within the mobile computing device 950, including instructions stored in the memory 964. The processor can be implemented as a chipset including a single chip or multiple chips including analog and digital processors. The processor can provide, for example, coordination of other components of the device 950, such as control of a user interface, applications executed by the device 950, and wireless communications performed by the device 950.

[0081] The processor 952 can communicate with the user through a control interface 958 and a display interface 956 coupled to the display 954. The display 954 can be, for example, a TFT LCD (thin film transistor liquid crystal display) or an OLED (organic light emitting diode) display or other suitable display technology. The display interface 956 may include appropriate circuitry for driving the display 954 to present graphics and other information to the user. The control interface 958 can receive commands from the user and convert the commands to be submitted to the processor 952. In addition, an external interface 962 can provide communication with the processor 952 to enable near-area communication between the device 950 and other devices. The external interface 962 can, for example, provide wired communication in some embodiments, or provide wireless communication in other embodiments, and multiple interfaces can also be used.

[0082] Memory 964 stores information within computing device 950. Memory 964 can be implemented as one or more computer-readable media, one or more volatile memory units, or one or more non-volatile memory units. An expansion memory 984 can also be provided and connected to device 950 via an expansion interface 982, which can include, for example, a SIMM (Single In-line Memory Module) card interface. Such expansion memory 984 can provide additional storage space for device 950 or can also store applications or other information for device 950. Specifically, expansion memory 984 can include instructions for implementing or supplementing the processes described above and can also include security information. Thus, for example, expansion memory 984 can act as a security module for device 950 and can be programmed with instructions that allow secure use of device 950. In addition, security applications can be provided along with other information via a SIMM card, such as placing identification information in an unbreakable manner on the SIMM card.

[0083] The memory can include, for example, flash memory and / or NVRAM memory, as described below. In one embodiment, the computer program product is tangibly embodied in an information carrier. The computer program product contains instructions that, when executed, perform one or more methods (such as those described above). The information carrier is a computer-readable medium or machine-readable medium, such as a memory 964, an expansion memory 984, or a memory on a processor 952 that can be received, for example, by a transceiver 968 or an external interface 962.

[0084] The device 950 can communicate wirelessly through the communication interface 966, which can include digital signal processing circuitry where necessary. The communication interface 966 can provide for communications under various modes or protocols, such as GSM voice calls, SMS, EMS, or MMS messaging, CDMA, TDMA, PDC, WCDMA, CDMA2000, or GPRS, among others. Such communication can occur, for example, through the radio-frequency transceiver 968. In addition, short-range communication can occur, such as using a Bluetooth, WiFi, or other such transceiver (not shown). In addition, a GPS (Global Positioning System) receiver module 980 can provide additional navigation- and location-related wireless data to the device 950, which can be used as appropriate by applications running on the device 950.

[0085] The device 950 can also communicate audio

[0086] The computing device 950 can be implemented in a number of different forms, as shown in the figure. For example, it can be implemented as a cellular telephone 980. It can also be implemented as part of a smart phone 982, personal digital assistant, or other similar mobile device.

[0087] Various implementations of the systems and techniques described here can be realized in digital electronic circuitry, integrated circuitry, specially designed ASICs (application specific integrated circuits), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include implementation in one or more computer programs that are executable and / or interpretable on a programmable system including at least one programmable processor, which can be special or general purpose, coupled to receive data and instructions from, and to transmit data and instructions to, a storage system, at least one input device, and at least one output device.

[0088] These computer programs (also referred to as programs, software, software applications, or code) include machine instructions for a programmable processor and may be implemented in high-level procedural and / or object-oriented programming languages ​​and / or in assembly / machine language. As used herein, the terms "machine-readable medium," "computer-readable medium," and "computer-readable medium" refer to any computer program product, apparatus, and / or device (e.g., a magnetic disk, an optical disk, a memory, a programmable logic device (PLD)) for providing machine instructions and / or data to a programmable processor, including machine-readable media that receive machine instructions as machine-readable signals. The term "machine-readable signal" refers to any signal for providing machine instructions and / or data to a programmable processor.

[0089] To provide for interaction with a user, the systems and techniques described herein can be implemented on a computer having a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user, and a keyboard and pointing device (e.g., a mouse or trackball) through which the user can provide input to the computer. Other types of devices can also be used to provide for interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and the input from the user can be received in any form, including sound input, voice input, or tactile input.

[0090] The systems and techniques described herein can be implemented in a computing device that includes a back-end component (e.g., as a data server), or includes a middleware component (e.g., an application server), or includes a front-end component (e.g., a client computer with a graphical user interface or a web browser through which a user can interact with embodiments of the systems and techniques described herein), or any combination of such back-end, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include local area networks (LANs), wide area networks (WANs), and the Internet.

[0091] The computing device may include a client and a server. The client and server are generally remote from each other and typically interact through a communication network. The client-server relationship arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.

Claims

1. A computer-implemented method (1000) for predicting a characteristic value (PV1) of a sample (201) of a specific sample type (ST1) based on an NIR / MIR spectrum (211) obtained from the sample (201), the method comprising: applying a wavelet transform (110) to the obtained spectrum (211) to calculate a sample set (111) of wavelet coefficients in a plurality of wavelet bands (B0, B1, B2); accessing a library (300) comprising a plurality of calibration sets (311-1 to 311-n, 311c) of wavelet coefficients defining a calibration coefficient space (311), the calibration sets (311-1 to 311-n, 311c) being calculated by wavelet transform of corresponding NIR / MIR spectra (300-1 to 300-n) previously obtained from at least calibration samples of the specific sample type (ST1), each calibration set being associated with one or more reference property values ​​(PV-1 to PV-n) of the corresponding calibration sample, wherein each calibration set in the library has a rank (R1) determined by cross-validation of a corresponding local regression model for the corresponding calibration set with respect to the corresponding property (P1); A local PLS model (121) of the characteristic value (PV1) of the sample (201) to be determined is created by: selecting a predefined number k nearest neighbors (311k) of the sample set (111) in the calibration coefficient space (311), and Calculating the local PLS model (121) based on the selected k nearest neighbors (311k) and their associated reference feature values; wherein the rank of the created local PLS model for determining the characteristic value (PV1) of the sample (201) is calculated based on the ranks of the selected k nearest neighbors; The characteristic value (PV1) of the sample (201) is predicted by applying the local PLS model (121) to the sample set (111). 2 . The method of claim 1 , wherein the wavelet coefficients of the sample set are normalized by using vector normalization. 3 . The method of claim 1 , wherein the k nearest neighbors are selected based on the Minkowski distance between the corresponding calibration set and the sample set.

4. A method according to claim 1 or 2, wherein for each wavelet coefficient of the calibration set, a corresponding variance is determined for the selected k nearest neighbors, and wherein when creating the local PLS model for the selected k nearest neighbors, wavelet coefficients whose variance is lower than 5% of the maximum variance among the wavelet coefficients are not used.

5. Method according to claim 1 or 2, wherein for each wavelet coefficient of the calibration set (csn), a correlation (cor-csn-P1) with a property (P1) of the corresponding calibration sample is calculated for the selected k nearest neighbors, and wherein wavelet coefficients having a correlation below a predefined correlation threshold are not used for creating the local PLS model.

6. The method according to claim 1 or 2, wherein the rank of the created local PLS model used to determine the characteristic value of the sample is calculated by any one of the following: using the rank associated with the majority of the selected k nearest neighbors; or The rank is calculated as the rounded average of the ranks of the selected k nearest neighbors.

7. A method according to claim 1 or 2, wherein applying the wavelet transform includes calculating a common threshold of the wavelet coefficients of the highest wavelet band of the sample set for the selected k nearest neighbors, and ignoring all wavelet coefficients whose values ​​are lower than the calculated threshold when creating the local PLS model.

8. The method according to claim 1 or 2, wherein when creating the local PLS model, at least the lowest wavelet band and the highest wavelet band of the calculated sample set are ignored.

9. The method according to claim 1 or 2, wherein the wavelet transform transforms the obtained spectrum into any one of the following wavelet types: Haar wavelet; Daubechies wavelet db2, db4, db6 and db8; Morlets wavelet; Symlets wavelet; Coiflets wavelet; and biorthogonal wavelet.

10. The method according to claim 1 or 2, wherein the characteristic value of the sample corresponds to any one of the following: The concentration of specific compounds, iodine value, pH value, water, protein, fat, fiber, ash, fatty acids and free fatty acids in the sample are measured; or Other properties that can be measured by NIR / MIR spectroscopy include density, viscosity, octane number, and cetane number.

11. The method according to claim 1 or 2, wherein the wavelet transform is a discrete wavelet transform.

12. The method according to claim 1 or 2, wherein selecting a predefined number k of nearest neighbors (311k) uses the wavelet coefficients of a single wavelet band, and calculating the local PLS model (121) uses wavelet coefficients of multiple wavelet bands.

13. A computer program product for predicting a characteristic value of a sample (201) of a specific sample type (ST1) based on an NIR / MIR spectrum (211) obtained from the sample (201), the computer program product comprising computer readable instructions which, when loaded into a memory of a computing device and processed by one or more processors of the computing device, cause the computing device to perform a method according to any one of the preceding claims.

14. A computer system (100) adapted to predict characteristic values ​​of a sample (201) of a specific sample type (ST1) based on an NIR / MIR spectrum (211) obtained from the sample (201), the computer system comprising functional modules adapted to perform the method according to any one of claims 1 to 12.

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