Non-destructive identification of wool and cashmere fibers based on improved LDA using NIR spectroscopy

2.1 Sample source and instrumentation

In the collection of samples, samples of different varieties of wool and cashmere fibers from different regions domestically and internationally are collected, such as domestic Xinjiang fine wool, Shaanxi native fine wool, Ordos Albas white cashmere goat, Tibetan black goat cashmere, and foreign varieties such as Australian Merino wool, Mongolian purple cashmere, and Afghan purple cashmere, totaling 330 samples. Among them, different fineness are also selected for the same variety, such as 18.5, 19.5, and 20.5 nm on Shaanxi native fine wool. Different age fibers are also selected for the same variety, such as silk wool and silk lamb wool.

The spectral device used in this study is the RZNIR7900 NIR spectrometer (Shanghai Ranzi Industrial Co., Ltd.); the experimental equipment is shown in Figure 2. The sample measurement is performed by diffuse reflectance from above, and the spectral data are collected in the wavelength range from 1,000 to 2,500 nm with a resolution of 1 nm. Data analysis is carried out using the built-in spectral analysis software CloudNIR in the NIR spectrometer.

Figure 2

RZNIR7900 NIR spectrometer.

2.2 Spectral preprocessing and selection

For the analysis of NIR spectral data, the preprocessing step is vital to the performance evaluation. Spectral data preprocessing has two main objectives: first, to reduce the adverse effects of elements and environmental conditions other than the analyte of interest, which can improve the robustness of subsequent analysis models and the accuracy of prediction results; second, to compress the data and improve modeling speed [19]. Accordingly, to disperse the influence of scattering on the spectrum, spectral preprocessing methods such as S-G, SNV, and their combination are used. S-G is a moving window weighted averaging algorithm based on the least squares method, which can effectively improve the smoothness of the spectrum and reduce noise in the spectrum [20]. SNV and multiplicative scatter correction (MSC) are used to correct spectral errors caused by particle scattering in the samples. In ideal conditions, MSC is mainly used to eliminate the influence of linear scattering, and SNV is generally considered to have a stronger correction ability than MSC [21]. So, the SNV method is chosen here. Due to the complexity of cashmere and wool samples, the above single spectral preprocessing methods may not provide ideal prediction results. As a result, the combination of S-G and SNV, i.e., S-G combined with SNV followed (referred to as S-G + SNV), is used for spectral preprocessing.

To select the optimal preprocessing algorithm, a K-NN model is established using the original spectrum and the preprocessed spectral data, and the discriminant accuracy of the model is used to determine the optimal preprocessing algorithm.

2.3 Feature dimensionality reduction

NIR spectroscopy data usually have a high number of dimensions. When modeling with full spectra, the intensive computational load reduces the efficiency of the model. Additionally, the overlap of absorption peaks in the spectra generates redundant information that affects the performance of the model. Hence, before modeling the spectroscopy data, feature extraction methods are often used to reduce the dimensionality of the spectra. Feature extraction constructs a new feature matrix based on the relationships between features in the original spectral matrix [22]. The new variables can maximize the retention of the data characteristics of the original variables without any loss of information [23]. In this study, PCA, LDA, and ILDA algorithms are all used to reduce the dimensionality of NIR spectral data.

2.3.1 ILDA

LDA, also known as Fisher linear discriminant, is a technique based on linear discriminant functions that maximize the between-group variance and minimize the within-group variance [24]. It can be used for dimensionality reduction and classification tasks in data preprocessing. However, the LDA algorithm reduces the dimensions to at most K-1 for K categories, and reducing binary samples to one-dimensional features may result in high overlap in the data. Thus, it is commonly used in practical applications for classification tasks [17]. In order to address the issue of acquiring two-dimensional characteristics, other similar NIR spectra fabrics are introduced as references, allowing the algorithm to reduce the dimensionality to two. With respect to the selection of other fabrics, seven common fabrics are chosen, including acetate, polyamide, acrylic, polyester, viscose, cotton, and mulberry silk. Among them, the two classes with the most similar and largest spectral differences are selected to observe whether there are significant differences in the NIR spectra of other fabrics in terms of dimensionality reduction. Three categories are used as input to reduce the dimensions to two. Perfect binary dimensionality reduction is achieved by outputting only the dimensions of wool and cashmere categories for the reduced-dimensional features. PCA is the most widely used unsupervised dimensionality reduction method, while LDA is the most widely used supervised dimensionality reduction method. Comparing ILDA with these two methods can better demonstrate the dimensionality reduction effect of ILDA. In comparison to PCA and LDA, ILDA has specific advantages. Unlike PCA, which selects the direction of sample point projection with the largest variance, ILDA selects the projection direction with the best classification performance. Compared to LDA, it can reduce to a greater number of dimensions and provide better classification results. The basic principles of the ILDA algorithm are as follows, and the algorithm flow chart is shown in Figure 3, input dataset D:

(1) D = { ( x 1 , y 1 ) , ( x 2 , y 2 ) , … , ( x m , y m ) } .

Figure 3

Flow chart of ILDA algorithm.

Any sample x i in the set is an n-dimensional vector, y i ∈ { C 1 , C 2 , … , C k } . Let N j ( j = 1 , 2 , … , k ) be the number of samples in the jth class, X j ( j = 1 , 2 , … , k ) be the set of samples in the jth class, and μ j ( j = 1 , 2 , … , k ) be the mean vector of the jth class samples, which is shown in the following equation:

(2) μ j = 1 N j ∑ x ∈ X j x ( j = 1 , 2 … k ) .

This yields the interclass scatter matrix S b (equation (3)), the intraclass scatter matrix S w (equation (4))

(3) S b = ∑ j = 1 k N j ( μ j − μ ) ( μ j − μ ) T ,

(4) S w = ∑ j = 1 k ∑ x ∈ X j ( x − μ j ) ( x − μ j ) T ,

where μ is the vector of all sample means.

Calculate the largest d eigenvalues of the matrix S w − 1 S b and the corresponding d eigenvectors ( w 1 , w 2 , ⋯ , w d ) to get the projection matrix W. For each sample feature x i in the sample set, transform into a new sample by equation (5)

(5) z i = W T x i .

Get the dataset after output dimensionality reduction like shown in equation (6)

(6) D ' = { ( z 1 , y 1 ) , ( z 2 , y 2 ) , … , ( z m , y m ) } .

2.4 Classification

In this study, a widely used qualitative identification model is employed, specifically, the K-NN model based on preprocessed spectra, to identify cashmere and wool samples. K-NN is a method that classifies objects based on the closest training samples in the feature space [25]. This method consists of two parts: first, determining the K nearest neighbors, and second, using these neighbors to determine the class type. The training data space D, which includes n samples, is described by the equation (7)

Suppose each sample X i contains d dimensional features (see equation (8))

The entire dataset consists of C different classes. To determine the class of X ′ , it is necessary to calculate the distance between each X i in space D and X ′ , in order to determine the K data points in the nearest neighborhood of X ′ . Therefore, X ′ belongs to the class with the closest neighbors among all K data points. Here, we use the most common Euclidean distance criterion to find the nearest K neighbors [26], and equation (9) defines the Euclidean distance between X ′ and X i as well as the feature size

2.5 Sample division and model evaluation criteria

Reasonable division of the sample set helps improve the accuracy of the model. KennardStone (K-S) is a widely used sample allocation method in qualitative analysis. The purpose of K-S is to evenly distribute the samples by sequentially selecting samples with the maximum Euclidean distance between each other [27]. In the analysis process using the K-S algorithm, the data are randomly divided into a calibration set and a validation set in a ratio of 3:2. Specifically, 108 spectral data are used as the calibration set for model analysis and model establishment, 72 spectral data are used as a validation set to verify the model, which was not involved in its establishment.

The confusion matrix method is used to comprehensively evaluate the performance of the established classification discriminant model. Each column represents the predicted values, and each row represents the true values. Sensitivity, specificity, and accuracy are used as three indicators to evaluate the model performance [28]. The sensitivity is defined as the true positive rate, measuring the classifier’s ability to identify positive instances, while specificity is the true negative rate, measuring the classifier’s ability to identify negative instances. The model accuracy is its ability to differentiate between true positive and true negative among all samples, with a maximum value of 1 and a minimum value of 0, a higher value indicates a better model. The calculation formulas for these three indicators are shown in equations (10)–(12)

where TP is the number of positive cases correctly predicted by the model from the sample data; TN is the number of negative cases correctly predicted from the sample data; FP is the number of positive cases incorrectly predicted from the sample data; and FN is the number of negative cases incorrectly predicted from the sample data.

3.1 Data set preparation

Among all the collected 330 samples, 180 samples (100 wool, 80 cashmere) are randomly selected; the sample picture is shown in Figure 4(a). Before the experiment, the RZNIR7900 NIR spectrometer is warmed up for 30 min to ensure its smooth detection performance, and the self-test is carried out, which includes an energy test, X-axis frequency correction, and Y-axis repeatability test. After the self-test is completed, the wool or cashmere samples are placed on a sample rack, and NIR spectral graphs are collected using a reflection mode. Different areas are selected on each sample for merging. The merged wool or cashmere samples are then placed in a large sample pool for spectral data collection after the spectral scanning is stabilized. The scanning is performed 32 times, with five measurements on the front and five on the back of each sample. The average value of these ten measurements is taken. To avoid a low signal-to-noise ratio, the first 200 nm and the last 200 nm are removed from the spectral data, and the wavelength range of 1,200–2,300 nm is used for calculations; the spectral data are shown in Figure 4(b). All the algorithms are executed using PyCharm2020, Python 3.8 under the Windows 10 system.

Figure 4

Cashmere wool sample and spectral data: (a) partial cashmere and wool samples and (b) NIR spectrum data.

3.2 Spectral characteristics and spectral preprocessing

The main components of cashmere and wool fibers are proteins and lipids, which exhibit absorption in the NIR spectral range. As can be seen from Figure 4(b), the overall shape of NIR spectra of all wool and cashmere samples is very similar, and the spectral bands are both wide and heavily overlapping. Because their chemical structures are also very similar. Therefore, it is difficult to differentiate between cashmere and wool based solely on visual inspection of the raw NIR spectra. Despite this, there are still some differences in the NIR spectra of wool and cashmere. The absorbance of wool’s NIR spectrum overall is higher than that of cashmere, indicating that NIR spectra have a certain potential to distinguish between the two.

Due to the complexity of the spectrum, preprocessing can reduce noise and other effects. To enhance the apparent resolution of the spectra, three different methods, including SG, SNV, and S-G + SNV, are employed for data preprocessing. In S-G, the width of the smoothing window has a certain impact on the smoothing effect. A window width that is too small to achieve effective smoothing, while a window width that is too large increases computational complexity. Taking into account the influence on model performance, a polynomial fitting order of 3 and a smoothing window width of 5 are selected for S-G. The different pretreatment effects of spectral data are shown in Figure 5. As can be seen in Figure 5(a), S-G reduces noise in the spectral line, making it smoother and enlarging the value of absorbance to enhance the difference between the data, thus improving the signal-to-noise ratio. In Figure 5(b), after SNV pretreatment, it can be seen that the spectral lines are more compact, diffuse reflection is eliminated, and the absorbance of the signal changes slightly less than that of SG pretreatment. Figure 5(c) shows the preprocessing diagram of SG-SNV. The shape of the spectral line is closer, but the difference is enlarged, which not only eliminates the diffuse reflection and significantly reduces the baseline deviation but also enlarges the value of the absorbance and increases the difference of the data, thereby the resolution of the signal is significantly improved.

Figure 5

The spectra of 180 samples preprocessed using the different spectral preprocessing techniques. (a) S-G, (b) SNV, and (c) S-G + SNV.

So as to select the optimal preprocessing algorithm, a K-NN model is built using the original spectra and preprocessed spectra data. The number of nearest neighbors, K, in K-NN, is varied from 1 to 40 to find the best model parameters. The final results showed that K is 15 without any preprocessing, 6 after S-G preprocessing, 3 after SNV preprocessing, and 1 after S-G + SNV preprocessing. The results are shown in Table 1. For wool and cashmere samples, the sensitivity, specificity, and accuracy values obtained from the original spectral prediction model range from 0.9 to 0.91. It is worth noting that the model performs the worst after SNV preprocessing, with a sensitivity of only 0.82 and an overall accuracy of 0.88. However, the specificity is relatively high at 0.92, indicating a slightly higher recall for wool after SNV processing. The model preprocessed with S-G performs slightly better than the unprocessed model, indicating a positive effect of S-G preprocessing on the classification of wool and cashmere spectra. Using S-G + SNV preprocessing followed by K-NN input yields the best results, with a sensitivity of 0.94, a specificity of 0.92, and an accuracy value of 0.93. This preprocessing method demonstrates good recall rates for both wool and cashmere, indicating its effectiveness in handling complex spectra. Therefore, S-G + SNV is the best preprocessing method.

3.3 Feature variable selection

To reduce redundant wavelengths and computational load and enhance discrimination accuracy, feature variables for distinguishing between wool and cashmere are extracted. After establishing the K-NN model mentioned above, S-G + SNV is selected as the optimal preprocessing method. The original spectral data are then subjected to optimal preprocessing, followed by data dimensionality reduction using PCA, LDA, and ILDA methods, making the characteristic wavelength vectors in the 1,200–2,300 nm range significantly reduced to one- or two-dimensional characteristic variables.

In the original LDA algorithm, the number of dimensions for k categories is reduced to K−1 dimensions at most. The improved LDA algorithm is introduced to the NIR spectral data of other fabrics for comparison, allowing the algorithm to obtain two feature dimensions. In comparison to involving other fabrics, seven common fabrics are introduced: acetate, nylon, acrylic, polyester, viscose, cotton, and silk. This is to investigate whether the addition of fibers from different categories has a significant impact on the dimensionality reduction of cashmere and wool using ILDA. The spectral comparison is shown in Figure 6, which reveals that the spectral characteristics of wool and cashmere are relatively similar to cotton while significantly different from acrylic. Therefore, cotton with relatively small differences and acrylic with relatively large differences are selected.

Figure 6

Spectral difference comparison.

Figure 7 shows the dimensionality reduction results of different algorithms on the spectral data of wool and cashmere samples. After S-G + SNV-PCA processing, the two-dimensional feature variables have a large overlap, but the distance between centroids is also large. When applying S-G + SNV-LDA to the wool and cashmere datasets, only one-dimensional feature variables can be obtained. It can be seen that the features are closely arranged in a straight line with a lot of overlap. The data processed by S-G + SNV-ILDA (cotton) show a basic separation of features, but there is still some compactness at the intersection. The features obtained through S-G + SNV-ILDA (acrylic) processing also achieve basic separation, and the compactness of features at the intersection of the two categories is slightly better than ILDA (cotton).

Figure 7

Results of different algorithms for downscaling the spectra of wool cashmere samples. (a) S-G + SNV-PCA, (b) S-G + SNV-LDA, (c) S-G + SNV-ILDA (cotton), and (d) S-G + SNV-ILDA (acrylic).

3.4 Comparisons of K-NN modeling with different dimensionality reduction methods

Table 2 is a confusion matrix, accuracy, sensitivity, and specificity corresponding to the K-NN model obtained using the S-G + SNV preprocessing method and different dimensionality reduction methods on the wool and cashmere test set. The dimensionality reduction methods include PCA, LDA, and ILDA, and each model runs 20 times.

From Table 2, it can be seen that for the PCA dimensionality reduction method, the sensitivity, specificity, and accuracy of the spectral data after S-G + SNV preprocessing are the lowest. The performance is significantly lower than the sensitivity, specificity, and accuracy in Table 1 without PCA dimensionality reduction. The reason for this is that although the data reduce most of the feature dimensions in the PCA transformation, making the classification model more lightweight, it also loses some important information, leading to a decrease in accuracy. The LDA method for sensitivity, specificity, and accuracy of wool and cashmere datasets has increased by 0.17, 0.03, and 0.1, respectively, compared to the PCA-processed data, showing an overall improvement. The differences in sensitivity, specificity, and accuracy of ILDA (cotton) and ILDA (acrylic acid) are small, with both being basically equal. However, the performance is significantly better than that of PCA and LDA processing. For the ILDA (cotton) dimensionality reduction method, the sensitivity can reach 1, the specificity is 0.92, and the accuracy is 0.96, indicating that this method has excellent recall for cashmere and slightly less for wool. For the ILDA (acrylic) dimensionality reduction method, the sensitivity and specificity are both 0.97, and the accuracy is also 0.97, indicating that this method has a good recall for both wool and cashmere. However, the accuracy is 1% higher than that of ILDA (cotton), indicating a significant spectral difference between wool and cashmere, resulting in a slight improvement in accuracy. The results show that the ILDA algorithm can achieve the prediction of wool and cashmere classification.

By introducing NIR spectra of similar fabrics as references, the LDA algorithm can achieve dimensionality reduction to obtain two-dimensional features, solving the problem of high overlap and low classification prediction accuracy when reducing two class samples to one-dimensional features. These findings indicate that ILDA is a highly effective method in a series of applications involving NIR spectra.