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Original article
05 2023
:16;
104690
doi:
10.1016/j.arabjc.2023.104690

Multi-wavelength HPLC fingerprint similarity metric for cold-hot nature identification of Chinese herbal medicines

Key Laboratory of Theory of TCM, Ministry of Education of China, Shandong University of Traditional Chinese Medicine, Jinan 250355, China
Affiliated Hospital of Jining Medical University, Jining 272000, China

⁎Corresponding authors. bmie530@163.com (Guohui Wei), zhenguow@126.com (Zhenguo Wang)

Disclaimer:
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.

Peer review under responsibility of King Saud University.

Abstract

Cold-hot nature theory is the core basic theory of the nature of Chinese herbal medicines (CHMs). It is found that the material basis of cold-hot nature is CHM ingredients. In view of this, our group proposed a scientific hypothesis that “CHMs with similar nature should have similar material basis”. To demonstrate this hypothesis, we developed a novel multi-wavelength high performance liquid chromatography (HPLC) fingerprint similarity metric scheme for cold-hot nature identification. We explored a multi-wavelength distance metric learning model to compute the similarity of CHM ingredients, and developed an improved k-nearest neighbor algorithm based on multi-wavelength HPLC fusion (KMHF) to predict cold-hot nature of CHMs. Firstly, multi-wavelength HPLC fingerprints were used to extract the characteristic information of CHM ingredients. Secondly, we defined the similarity of CHM ingredients as semantic relevance and fingerprint similarity. We studied a multi-wavelength distance metric to measure the similarity of CHM ingredients. The learned distance metric could discover complementary characteristics of different wavelength HPLC through an optimization algorithm. Finally, an improved multi-wavelength k-nearest neighbor algorithm KMHF was proposed to analyze the relationship between cold-hot nature and CHM ingredients. Numerous experiments were designed to test the feasibility of the proposed KMHF algorithm. Experimental results indicate that the performance of our KMHF algorithm outperforms that of the compared algorithms. Experimental results demonstrate that the hypothesis that CHMs with similar cold-hot nature have similar material basis. The KMHF model is evaluated to be feasible for nature identification.

Keywords

Cold-hot nature
Nature identification
Chinese herbal medicines
Similarity metric
HPLC
1

1 Introduction

Cold-hot nature theory is the core theory of the nature of Chinese herbal medicines (CHMs), which has attracted the attention of investigators for many years (Gao et al., 2007). “Treating the cold syndrome with hot nature medicines and treating the hot syndrome with cold nature medicines” is the theoretical basis of clinical treatment of traditional Chinese medicine (TCM). This suggests that the concept of cold-hot nature patterns has been a guiding principle in TCM for administering CHMs (Ouyang et al., 2006; Wu et al., 2007). Therefore, correct discrimination of cold-hot nature of CHMs is the key to TCM research.

Numerous specialists attempted to explain the scientific connotation of cold-hot nature of CHMs from different perspectives. From one perspective, the material basis of cold-hot nature is confirmed as CHM ingredients (Fu et al., 2017; Wei et al., 2019b). Scientists developed numerous scientific hypotheses to demonstrate that the material basis of cold-hot nature was CHM ingredients, including Zhang’s hypothesis of “Three element” (Jin et al., 2014), Wang’s hypothesis of “Tri-element of property-effect-material”(Zhang, 2012), and Fu’s hypothesis of “Nature-Structure Relationship” (Fu et al., 2017). They constructed a lot of experiments to prove that the hypothesis was true. A typical method was to extract the ingredient information with chemical fingerprints, and establish the correlation between cold-hot nature and CHM ingredients with machine learning algorithms (Wei et al., 2019b). From another perspective, energy metabolism, such as oxygen consumption and ATPase activity, was introduced to study cold-hot nature of CHMs (Huang et al., 2014). CHMs with hot nature may increase the activity of SDH enzyme and promote the decomposition of muscle glycogen. These regulated the level of energy metabolism, so as to produce more ATP. CHMs with cold nature could significantly decrease the energy metabolism in normal rats (Wu et al., 2007). From the third perspective, some research analyzed cold-hot nature of CHMs with bioinformatics methods. Network pharmacology and in silico analysis were introduced to reveal the scientific connotation of cold-hot nature (Fu et al., 2017; Liang et al., 2013). Fu et al. proposed a hypothesis of “nature-structural relationship”, and integrated bioinformatics and network pharmacology methods to explore the scientific connotation of cold-hot nature of CHMs from molecular level (Shao et al., 2020). They found that CHMs with cold nature were related with mental and behavioural disorders diseases, and CHMs with hot nature were associated with endocrine, nutritional and metabolic diseases. As mentioned above, researches from different perspectives have made numerous achievements. However, the scientific connotation of cold-hot nature of CHMs needs further study. Our group attempts to utilize machine learning methods and chemical fingerprints to build a correlation between cold-hot nature and CHM ingredients to reveal the scientific connotation of CHM nature.

A number of studies have been performed to analyze the relationship between CHM ingredients and cold-hot nature (Fu et al., 2017; Wei et al., 2019b; Shao, 2020). It is found that the material basis of cold-hot nature of CHMs is chemical ingredients. Therefore, research on the relationship between cold-hot nature and CHM ingredients mainly includes ingredient information representation and nature classification. Ingredient information is the general characteristic of the ingredients contained in CHMs. Ingredient information representation has always been a research hotspot. Current research focused on chemical fingerprints and molecular descriptors of compounds. Chemical fingerprints, including infrared spectrum, ultraviolet spectrum, gas chromatography (GC), high performance liquid chromatography (HPLC), have been usually applied to study the ingredients of CHMs (Zhang, 2012). Wang et al. used HPLC fingerprint and gas chromatography fingerprint for systematic analysis of chemical compositions in Curcumae Rhizom and introduced chemometrics including unsupervised principal component analysis, supervised linear discriminant analysis, k-nearest neighbors (KNN) for the species authentication and quality control (Wang et al., 2021). CHMs are typically mixtures of compounds. Since chemical structure is the molecular basis of compound activity, characterization of molecular structure is essential to further understand CHM nature. Molecular descriptors were widely applied to extract the feature information of CHM compounds. Fu et al. computed compound-nature pairs of CHMs to study their physicochemical domain and introduced in silico target prediction to study differences related to their modes-of-action against proteins (Fu et al., 2017).

Nature classification introduces classical intelligent algorithms or builds machine learning algorithms to study the relationship between CHM ingredients and cold-hot nature. Classical intelligent algorithms, such as support vector machine, partial least square method and random forest, were usually introduced to predict cold-hot nature of CHMs. Xue’s group analyzed the CHMs with efficacy and indications, and constructed classical intelligent algorithms for cold-hot nature prediction (Zhang, 2012). Long et al. and Wang et al. calculated molecular descriptor of CHM compounds, and applied classical classifiers to discriminate cold-hot nature (Long et al., 2011; Wang et al., 2016). Nie et al. analyzed Metabonomics information of CHMs and used a random forest algorithm to identify the cold-hot nature of CHMs (Nie et al., 2015). Our group had made some explorations in the identification of cold-hot nature of CHMs (Wei et al., 2019b, 2021a). We introduced an extreme learning machine (ELM) algorithm to analyze CHM nature with molecular descriptors. Inspired by the similarity of CHM ingredients applied to evaluate the quality of CHMs (Wei et al., 2021a), our group explored the similarity of CHM ingredients to build machine learning algorithms for cold-hot nature prediction. For example, we proposed a novel multi-solvent UV spectrum similarity measure retrieval scheme for discriminating CHMs cold or hot (Wei et al., 2019b).

As mentioned above, numerous achievements have been made in the research of cold-hot nature. However, chemical fingerprint technology for nature prediction has not been comprehensively studied. Our group used UV spectrum and GC to analyze CHM ingredients for nature identification without considering HPLC (Wei et al., 2019b, 2021b). Compared with UV spectrum and GC, HPLC can better separate the components of CHMs and extract the information of CHM components (Qi et al., 2011). It is possible to obtain high prediction accuracy of cold-hot nature by studying the identification method of CHM nature based on HPLC. Furthermore, there is a hypothesis that CHMs with similar cold-hot nature have similar material basis. Designing a special nature identification algorithm according to this hypothesis and HPLC fingerprints may achieve higher prediction accuracy rates. In this work, HPLC fingerprints were applied to extract the information of CHM ingredients. With the obtained HPLC fingerprints, the similarity of CHM ingredients was defined as a Mahalanobis distance metric. This distance metric was learned by a constructed distance metric learning model. Finally, an improved multi-wavelength k-nearest neighbor algorithm was developed for predicting cold-hot nature of CHMs.

2

2 Materials and methods

2.1

2.1 CHM dataset

In this work, representative CHMs with clear nature were selected to study the correlation between CHM ingredients and cold-hot nature (Zhang, 2012). All selected CHMs were recorded in ‘Shen Nong’s Herbal Classic’ and the classical ‘Chinese Materia Medica’. The screening criteria of representative CHMs are as follows: (1) Traditional natural plant medicine only; (2) Clear CHM nature, high clinical recognition and no academic disputes. Finally, 61 CHMs were screened for nature identification, in which 30 CHMs are cold, and others are hot. The 61 CHMs are listed in Table 1.

Table 1 The experimental 61 representative CHMs.
Chinese Herbal Medicines Nature Source Sampling area
Curculiginis Rhizoma Hot Hai Yao Ben Cao Yibin, Sichuan
Pinelliae Rhizoma Hot Shen Nong’s Herbal Classic Dazhou, Sichuan
Magnoliae Officinalis Cortex Hot Shen Nong’s Herbal Classic Guangyuan, Sichuan
Euodiae Fructus Hot Shen Nong’s Herbal Classic Tongren, Guizhou
Arisaematis Rhizoma Hot Shen Nong’s Herbal Classic Heze, Shandong
Ephedrae Herba Hot Shen Nong’s Herbal Classic Chifeng, Sichuan
Chuanxiong Rhizoma Hot Shen Nong’s Herbal Classic Pengzhou, Sichuan
Zingiberis Rhizoma Hot Shen Nong’s Herbal Classic Leshan, Sichuan
Corydalis Rhizoma Hot Paozhi Lun Jinhua, Zhejiang
Chaenomelis Fructus Hot Shen Nong’s Herbal Classic Xuancheng, Anhui
Aucklandiae Radix Hot Shen Nong’s Herbal Classic Lijiang, Yunnan
Eucommiae Cortex Hot Shen Nong’s Herbal Classic Mianyang, Sichuan
Santali Albi Lignum Hot Mingyi bielu Guangdong
Epimedii Folium Hot Shen Nong’s Herbal Classic Shanxi
Roasted Corydalis Hot Paozhi Lun Jinhua, Zhejiang
Nardostachyos Radix et Rhizoma Hot Supplement to Materia Medica Aba, Sichuan
Fructus Piperis Alba Hot Tang materia medica Wenchang, Hainan
Mustard Seeds Hot Tang materia medica Anhui
Carthami Flos Hot Tang materia medica Xinxiang, Henan
Asari Radix et Rhizoma Hot Shen Nong’s Herbal Classic Dandong, Liaoning
Notopterygii Rhizoma et Radix Hot Shen Nong’s Herbal Classic Aba, Sichuan
Cinnamomi Cortex Hot Shen Nong’s Herbal Classic Hechi, Guangxi
Atractylodis Rhizome Hot Shen Nong’s Herbal Classic Jiangsu
Alpiniae Katsumadai Semen Hot Paozhi Lun Hainan
Piperis Longi Fructus Hot Tang materia medica Wenchang, Hainan
Ligustici Rhizoma et Radix Hot Shen Nong’s Herbal Classic Aba, Sichuan
Psoraleae Fructus Hot Nature theory Sichuan
Aconiti Lateralis Radix Praeparata Hot Shen Nong’s Herbal Classic Jiangyou,Sichuan Province
Citri Reticulatae Pericarpium Hot Shen Nong’s Herbal Classic Jiangmen,Guangdong
Alpiniae Officinarum Rhizoma Hot Mingyi bielu Zhanjiang,Guangdong Province
Clematidis Radix et Rhizoma Hot Tang materia medica Jiangsu
Platycladi Cacumen Cold Mingyi bielu Linyi, Shandong
Kochiae Fructus Cold Shen Nong’s Herbal Classic Feicheng, Shandong
Ecliptae Herba Cold Tang materia medica Jinan, Shandong
Isatidis Folium Cold Mingyi bielu Tangshan, Hebei
Rhei Radix et Rhizoma Cold Shen Nong’s Herbal Classic Dingxi, Gansu
Asparagi Radix Cold Shen Nong’s Herbal Classic Huairen, Guizhou
Fritillariae Cirrhosae Bulbus Cold Shen Nong’s Herbal Classic Aba, Sichuan
Bupleuri Radix Cold Shen Nong’s Herbal Classic Nanyang, Henan
Gardeniae Fructus Cold Shen Nong’s Herbal Classic Zhangshu, Jiangxi
Rhizoma Anemarrhenae with Peet Cold Shen Nong’s Herbal Classic Baoding, Hebei
Sargassum
Cold Shen Nong’s Herbal Classic Weihai, Shandong
Lophatheri Herba Cold Shen Nong’s Herbal Classic Yuyao, Zhejiang
Trichosanthis Fructus Cold Shen Nong’s Herbal Classic Feicheng, Shandong
Kansui Radix Cold Shen Nong’s Herbal Classic Shanxi
Dried Rehmannia Root Cold Shen Nong’s Herbal Classic Jiaozuo, Henan
Dianthi Herba Cold Shen Nong’s Herbal Classic Laiwu, Shandong
Fraxini Cortex Cold Shen Nong’s Herbal Classic Lingning
Arnebiae Radix Cold Shen Nong’s Herbal Classic Urumqi, Xinjiang
Trachelospermi Caulis et Folium Cold Shen Nong’s Herbal Classic Suzhou, Jiangsu
Aloe Cold Nature theory Yunnan
Puerariae Lobatae Radix Cold Shen Nong’s Herbal Classic Zibo, Shandong
Taraxaci_Herba Cold Tang materia medica Linyi, Shandong
Menthae Haplocalycis Herba Cold Tang materia medica Haimen, Jiangsu
Alizaris Radix Cold Tang materia medica Zhenjiang, Jiangsu
Plantaginis Semen Cold Shen Nong’s Herbal Classic Jiujiang, Jiangxi
Lonicerae Japonicae Flos Cold Tang materia medica Linyi, Shandong
Stephaniae Tetrandrae Radix Cold Shen Nong’s Herbal Classic Quzhou, Zhejiang
Phellodendri Chinensis Cortex Cold Shen Nong’s Herbal Classic Bazhong, Sichuan
Coptidis Rhizome Cold Shen Nong’s Herbal Classic Shizhu, Chongqing
Gentianae Radix et Rhizoma Cold Shen Nong’s Herbal Classic Fushun, Liaoning

2.2

2.2 Hplc

In this work, we analyzed the ingredient information of CHMs with HPLC technology. The experimental methods of HPLC, including preparation of the test solution and chromatographic conditions, were configured in detail in Rf. Zhang, et al. 2012. We give a brief introduction as follows.

The preparation of the test solution is as follows: Firstly, we precisely measured about 0.5 g of the test medicinal powder, and put it in a tapered bottle with a stopper. Secondly, we precisely poured 50 ml of 50 % methanol into the bottle. We weighed and put it in 60℃ water bath for ultrasonic extraction for 30 min. After the extraction was completed, we cooled and weighed again, and supplemented the lost mass with 50 % methanol. Finally, we take the continuous filtrate to obtain a 50 % methanol extract. The chromatographic conditions are as follows: (1) Chromatographic column: Agilent XDB-C18 column (4.6 mm* 250 mm, 5 μm). (2) Mobile phase: acetonitrile–water (3:97) → acetonitrile–water (100:0), linear gradient elution for 90 min. (3) Flow rate: 1.0 ml/min. (4) Injection volume: 20 ml. (5) Column temperature: 35℃.

The test solution was obtained based on the given chromatographic conditions, and the DAD (diode array detector) was introduced for full wavelength scanning of 190–400 nm. Finally, each CHM was collected at 211 wavelengths of 190–400 nm, and the data were obtained for 6524 retention time points. Since the data are too large to allow further modeling and analysis, and the chromatographic data of the same CHM at adjacent wavelengths are highly correlated, the chromatographic data at representative wavelengths of each CHM were selected according to the characteristics of UV wavelength. In this study, the chromatographic data at three representative wavelengths of 210 nm, 227 nm, 236 nm were analyzed to build the nature classification model. We processed the representative fingerprints, and extracted the spectral interval with a prediction accuracy of more than 75 % based on a step length of 5 absorption values and an interval length of 95 absorption values. Finally, the absorption value of the fingerprint interval was adjusted in steps of 5.

2.3

2.3 HPLC fingerprint similarity

To analyze the relationship between CHM ingredients and cold-hot nature, our group developed a hypothesis that CHMs with similar cold-hot nature should have the similar material basis (Wei et al., 2021b). In our previous work, we had tested this hypothesis by characterizing the ingredient information with UV spectrum (Wei et al., 2019b, 2021a). In this work, our group attempted to reveal the relationship between CHM ingredients and cold-hot nature by testing this hypothesis with HPLC fingerprints. Therefore, CHMs with similar cold-hot nature should have similar HPLC fingerprints of CHMs. It means that if the HPLC fingerprints of two CHMs are similar, they are considered to be similar cold-hot nature.

The similarity of HPLC fingerprints had been widely investigated in studying CHM ingredients for quality evaluation of CHMs (Mao, 2020). In this work, the similarity of HPLC fingerprints was modeled for cold-hot nature prediction. Analyzing the definition of similarity, our group defined the similarity of HPLC fingerprints as semantic relevance and fingerprint similarity. Semantic relevance means the consistency of CHM cold-hot nature, which represents that if the cold-hot nature of two CHMs is similar, they are semantic similarity (Wei et al., 2018). Fingerprint similarity means the similarity of CHM HPLC fingerprints, which represents that two CHMs have similar ingredients related to cold-hot nature. We explored to learn a Mahalanobis distance to measure the similarity of HPLC fingerprints, which were both semantic relevance and fingerprint similarity. Smaller distance metric means more similar fingerprints.

2.3.1

2.3.1 Distance metric learning

Define X = x 1 , , x n R d n to represent the CHM fingerprint dataset in the input space, in which n being the total number of CHMs and x i R d being the ith sample. Denote superscript T as the transpose of a vector or a matrix, the Mahalanobis distance between xi and xj can be defined as (Weinberger et al., 2009):

(1)
d M ( x i , x j ) = ( x i - x j ) T M ( x i - x j ) where M is a positive semi-definite matrix, which can be decomposed into M = AAT. Therefore, Eq. (1) can be rewritten as:
(2)
d A ( x i , x j ) = ( x i - x j ) T A A T ( x i - x j ) = | | A T ( x i - x j ) | |

Eq. (2) illustrates that calculating Mahalanobis distance between x i and x j is equivalent to learning a transformation of Euclidean distance in the input space. In this work, the transformation matrix A is learned based on the HPLC similarity of CHMs. After learning matrix A , Mahalanobis distance d ( x i , x j ) between x i and x j in Eq. (2) can be obtained.

2.3.2

2.3.2 Similarity metric

In this work, a Mahalanobis distance was learned to quantify the similarity of HPLC fingerprints (Liu et al., 2010). However, previous distance metric learning studies mainly focused on the analysis of semantic relevance, ignoring the study of fingerprint similarity. We defined the similarity of CHM HPLC fingerprints as semantic relevance and fingerprint similarity. Therefore, the transformation matrix A in Eq. (2) contained two sources: the transformation matrix A 1 of semantic relevance and the transformation matrix A 2 of fingerprint similarity.

The conception of semantic relevance describes the separability of cold and hot categories. This requires that the class separability increases when the inter class divergence matrix increases or the intra class divergence matrix decreases. We modeled the semantic relevance with differential scatter discriminant criterion (DSDC) algorithm (Wei et al., 2016), the formula is as follows:

(3)
A 1 = arg max ( t r ( A T S B A ) - λ t r ( A T S W A ) )

Our model uses the variation of DSDC:

(4)
A 1 = arg max ( t r ( A T S B A ) - λ t r ( A T S W A ) ) = arg min ( t r ( A T ( S W - λ S B ) A ) )

In Eq. (4), is the inter class divergence matrix, is the intra class divergence matrix. is a nonnegative balance parameter, which tunes the relative merits of maximizing the inter class divergence to the minimization of the intra class divergence. The obtained matrix. A 1 is the transformation matrix from semantic relevance.

According to the definition of fingerprint similarity, it describes the similarity of HPLC fingerprints. This represents the similarity of CHM ingredients. In previous studies, feature similarity of pulmonary nodule images had been modeled as patch alignment frameworks. Inspired by the definition of feature similarity, we explored the patch alignment framework to study the similarity of CHM HPLC fingerprints.

Define a HPLC fingerprint dataset in input space X = x 1 , , x n T R n d , for each x i X , its local patch is X i = [ x i , x i 1 , x i 2 , . . . , x i k ] T R ( k + 1 ) d . x i k is the k - nearest neighbor of x i based on Euclidean distance. For each patch X i , there is a transformation model h i : X i Y i , Y i is the set of sample maps in feature space Y i = [ y i , y i 1 , . . . , y i k ] T R ( k + 1 ) l . To solve such transformation model h i , one solution is to minimize the error between the linear mapping of patch X i and the feature representation Y i , and then align all the patches (Zhang et al., 2009). We minimized the local patch errors as:

(5)
min W i , b i X i T W i + 1 k + 1 b i T - Y i 2 + μ W i F 2

In Eq. (3), W i R d l is the local mapping matrix, b i R l denotes the bias, 1 k + 1 R k + 1 is the vector of all ones, μ is a regularization parameter.

There is an assumption that the fingerprint samples are centered, i.e., X i T 1 k + 1 = 0 .To calculate the optimal solution of Eq. (5), we set the derivatives of the objective function in regard to b i and W i to zeros. The solution is:

(6)
b i = 1 k + 1 Y i T 1 k + 1 W i = X i H k + 1 X i T + μ I d - 1 X i H k + 1 Y i where H k + 1 = I k + 1 - 1 k + 1 1 k + 1 1 k + 1 T is the local centering matrix. By putting W i and b i into (5) by (6), (6) is then rewritten as:
(7)
min Y i t r ( Y i T L i Y i )

In (7), L i = H k + 1 - X i T X i X i T + μ I d - 1 X i , and then, the global alignment is (Zhang et al., 2009):

(8)
min Y t r ( Y T L Y ) where the global alignment matrix L is
(9)
L = [ S 1 , . . . , S n ] L 1 . . . 0 . . . . . . . . . 0 . . . L n [ S 1 , . . . , S n ] T

In (9), { S i } i = 1 n is a selection matrix such that Y i = S i T Y .

Define Y R n l is a representation of dataset X in feature space. On the basis of the assumption of linearization that Y = X T A , the global patches errors is as follows:

(10)
A 2 = arg min ( t r ( A T X L X T A ) )

Therefore, semantic relevance produced the transformation matrix A 1 in Eq. (4), and fingerprint similarity learned the transformation matrix A 2 in Eq. (10). By integrating Eq. (4) and Eq. (10), we obtained a similarity metric model. The model is as follows:

(11)
A = arg min t r ( A T ( S W - λ S B + X L X T ) A ) = arg min t r ( A T Q A ) where Q = S W - λ S B + X L X T , the optimal transformation matrix A * learned from Eq.(11) can preserve both semantic relevance and fingerprint similarity.

2.3.3

2.3.3 Projection learning

To calculate the optimal transformation matrix A * in Eq.(11) for similarity metric, the low dimensional representation of HPLC fingerprints should avoid redundancy as much as possible. To solve this problem, an orthogonal projection learning method was studied. We learned the transformation matrix A * as follows:

(12)
A * = arg min t r ( A T Q A ) s . t . A T A = I

To solve Eq. (12), eigenvalue decomposition on matrix Q was used to obtain the optimal projections. We built the optimal solution matrix A * with u eigenvectors of Q corresponding to the u smallest eigenvalues.

2.4

2.4 Multi-wavelength HPLC fingerprint fusion

In this study, three wavelength HPLC fingerprints were used to analyze the ingredient information of CHMs. Different wavelength HPLC fingerprints mine different characteristics of CHM ingredients, which usually have different physical properties. Therefore, it is perhaps not optimal to concatenate three wavelength HPLC fingerprints straightforwardly into a long fingerprint vector (Yu et al., 2012). This would cause curse-of-dimensionality and over-fitting problems. In particular, it is difficult to learn a robust distance measure in a high-dimensional feature space if the number of CHM fingerprints is not large enough. To solve this problem, multi-wavelength HPLC fingerprint fusion scheme was explored for nature identification.

In this section, we extended single wavelength HPLC fingerprint similarity metric to multi-wavelength feature spaces. We utilized multi-wavelength HPLC fingerprints to learn multiple transformation matrices to build multi-wavelength distance metric. We linearly integrated the similarity metrics learned from multi-wavelength HPLC fingerprints with the weights β i and added a regularizer to the weights. Thus, the objective function is as follows:

(13)
ϕ ( β , A ( 1 ) , A ( 2 ) , . . . , A ( N W ) ) = i = 1 N W β i t r ( A ( i ) T Q i A ( i ) ) + ρ | | β | | 2 s . t . i = 1 N W β i = 1 where A ( i ) is the k th transformation matrix learning from the i th wavelength fingerprint set, Q = S W - λ S B + X L X T . N W is the number of wavelength, β = β 1 , β 2 , . . . , β N W T .

Therefore, the objective function (12) was constructed to learn a distance metric for each wavelength fingerprint data, while the objective function (13) was built to integrate the information of the multi-wavelength HPLC fingerprints with the combination weights. This scheme mitigates the over-fitting problem and decreases the complexity of the model.

To calculate the solution of objective function (13), firstly, the optimal transformation matrices A ( i ) | i = 1 N W were learned on the basis of Eq. (12) corresponding to different wavelengths. Secondly, the optimum solution was obtained by introducing the lagrangian multiplier method. Based on a Lagrange multiplier η , the objective function is transforms to:

(14)
L ( β , η ) = i = 1 N W β i t r ( A ( i ) T Q i A ( i ) ) + ρ | | β | | 2 - η ( i = 1 N W β i - 1 )

To solve this problem, we took the partial derivatives of L ( β , η ) with regard to β and η to be zeros. We obtained:

(15)
L β 1 = t r ( A ( 1 ) T Q 1 A ( 1 ) ) + 2 ρ β 1 - η = 0 . . . L β N W = t r ( A ( N W ) T Q N W A ( N W ) ) + 2 ρ β N W - η = 0 L η = i = 1 N W β i - 1 = 0

Integrating the equations in (15), we obtained:

(16)
i = 1 N W tr ( A ( i ) T Q i A ( i ) ) + 2 ρ i = 1 N W β i - η N W = 0

Since i = 1 N W β i = 1 , we get the solution of η as follows:

(17)
η = i = 1 N W tr ( A ( i ) T Q i A ( i ) ) + 2 ρ N W

Putting the solution of η into (15), we can obtain:

(18)
β i = η - t r ( A ( i ) T Q i A ( i ) ) 2 ρ = 2 ρ + i = 1 N W tr ( A ( i ) T Q i A ( i ) ) - N W t r ( A ( i ) T Q i A ( i ) ) 2 ρ N W

With multi-wavelength HPLC fingerprint fusion, we could get the Mahalanobis distance d ( i ) ( x a , x b ) between x a and x b and weight value β i corresponding to the i th wavelength HPLC fingerprints. Finally, we obtained a multi-wavelength Mahalanobis distance d ( x a , x b ) between fingerprints x a and x b as follows:

(19)
d ( x a , x b ) = i = 1 N W β i d ( i ) ( x a , x b )

2.5

2.5 Cold-hot nature identification scheme

As mentioned above, a multi-wavelength Mahalanobis distance d ( x a , x b ) was learned to measure the similarity of CHM HPLC fingerprints. With this similarity metric, an improved k-nearest neighbor algorithm based on multi-wavelength HPLC fusion (KMHF) was proposed for cold-hot nature identification. Fig. 1 displays the cold-hot nature identification based on similarity metric of multi-wavelength HPLC. For a query CHM with unclear nature, we firstly studied the ingredient information of this CHM with multi-wavelength HPLC fingerprints. The multi-wavelength distance metric was learned to measure the similarity of HPLC fingerprints. With the learned distance metric, we then computed the Mahalanobis distances between the query CHM and CHM dataset. The calculated Mahalanobis distances were sorted from small to large in monotonically increasing order. The most similar k CHMs corresponding to the smallest k Mahalanobis distances were chosen to analyze cold-hot nature of the query CHM. Finally, we introduced a cold nature probability ( P q ) to evaluate the cold-hot nature of this query CHM with the most similar k CHMs. The cold nature probabilities of the query CHMs represented their cold degree, which could be calculated by the ratio of the weights of cold CHMs to the total weights of CHMs retrieved. The cold nature probability was calculated as:

(20)
P q = i = 1 c W i i = 1 c W i + j = 1 h W j , c + h = k where c is the number of cold CHMs, h is the number of hot medicines, k is the number of most similar CHMs, W i is the similar weight of a CHM, which can be calculated as W i = 1 / d i , d i is the corresponding Mahalanobis distance. Given a threshold of P T , if P q < P T , we infer that the nature of the query CHM is hot, otherwise, it’s nature is cold. We consider P T as 0.5 for further study.
Cold-hot nature identification based on similarity metric of multi-wavelength HPLC.
Fig. 1
Cold-hot nature identification based on similarity metric of multi-wavelength HPLC.

2.6

2.6 The proposed KMHF scheme for nature identification

An improved k-nearest neighbor algorithm based on multi-wavelength HPLC fusion (KMHF).

Given a CHM HPLC dataset X = [ X 1 , X 2 , . . . , X N W ] , X i is the i th wavelength HPLC fingerprints, X i = [ x i 1 , x i 2 , , x in ] R d n , and the number of nature classes C = 2 .

  1. Transformation matrics A ( i ) | i = 1 N W construction. Calculate the matrix Q i | i = 1 N W , which is corresponding to the i th wavelength HPLC fingerprints. Eigenvalue decomposition on matrix Q i to get the m eigenvalues of Q corresponding to the smallest m eigenvectors. Construct the transformation matrix A ( i ) with the smallest m eigenvectors.

  2. Mahalanobis distance d ( x a , x b ) learning. Calculate d ( x a , x b ) between HPLC fingerprints x a and x b with the transformation matrices A ( i ) | i = 1 N W and the weight value β i | i = 1 N W based on Eq.(2) and (19).

  3. Similarity metric. Retrieve the k most similar CHMs, which have the smallest k Mahalanobis distances between the query CHM and the CHM dataset.

  4. Cold-hot nature identification. Compute the ratio of the weights of cold CHMs to the total weights of CHMs retrieved.

2.7

2.7 Performance evaluation

In this subsection, the feasibility and effectiveness of the KMHF scheme for cold-hot nature identification were evaluated with numerous built experiments. We compared the prediction identification performance of KMHF scheme with that of some classical algorithms, such as the classical distance metric learning algorithms (large margin nearest neighbor (LMNN) (Weinberger et al., 2009), information-theoretic metric learning (ITML)) (Davis et al., 2007), the cold-hot nature classification schemes (Pearson correlation coefficient (PCC) (Wei et al., 2021c), retrieval system (RS) (Wei et al., 2019a), and extreme learning machine (ELM)). All evaluation experiments were performed in the environment of multi-wavelength HPLC fingerprint dataset. The similar CHMs with clear nature were calculated to discriminate the cold-hot nature of CHMs with unclear nature. We firstly used multi-wavelength HPLC fingerprints to analyze the ingredient information of CHMs. Secondly, we developed a KMHF scheme to discriminate the cold-hot nature of CHMs. Finally, numerous experiments were built to evaluate the feasibility and effectiveness of the KMHF scheme.

In our experiments, we introduced stability evaluation to estimate the identification performance of our KMHF scheme. Stability evaluation describes the proportion of calculated similar CHMs that are semantic relevance with the query CHMs. Leave-one-CHM-out approach was introduced to assess the stability evaluation in the whole CHM multi-wavelength HPLC fingerprints. In each case, one CHM was left as the test query CHM, and remaining 60 CHMs were selected as the reference training CHM dataset. Because every CHM should be selected as a query-one, this process was performed 61 times. Cold probability of each test CHM was calculated to represent the extent that the nature of this CHM belongs to cold. In our scheme, we found k reference CHMs which were most similar to the query CHM, and calculated the cold probability of the query CHM. As a result, 61 cold probabilistic values were obtained. By varying the threshold of the cold probability, a Receiver Operating Characteristic (ROC) curve was drawn. The area under the ROC curve (AUC) and identification accuracy (ACC) were used to test the performance of our KMHF scheme. The formula of identification accuracy is defined as:

(20)
ACC = F ( q i k ) = j = 1 k I [ y i = = y j ] k

In (20), F ( q i k ) represents a ratio of the number of accurately identified CHMs from the i th query CHM to the number of the most similar CHMs k . Therefore, F ( q i k ) is a function of number k , and ACC value changes with the change of number k . Finally, the AUC and ACC values were calculated to analyze the performance of our KMHF scheme.

3

3 Results

3.1

3.1 Parameter configurations

In this study, several parameters in KMHF scheme should be optimized for cold-hot nature identification. The balance parameter λ in (4), parameter μ in (5), parameter ρ in (13), parameter k in (20) need to be studied for the optimal identification model. All parameters are configured in the environment of multi-wavelength HPLC fingerprints.

Our experiments introduced stability evaluation to study the parameters for the optimal KMHF scheme. AUC and ACC were used as the evaluating indicators to evaluate the performance of our KMHF scheme with varying the values of parameters ( λ , μ , ρ and k). As a result, AUC and ACC values were studied as functions of the tuning parameters ( λ , μ , ρ and k) to describe more comprehensive curves for the optimal KMHF scheme. We tuned the parameter λ in (4) in the range of [10-8, 10-6, 10-4, 10-2, 1, 102, 104, 106, 108]. Fig. 2 displays the AUC and ACC curves for nature identification of CHM HPLC fingerprints when the tuning parameter λ varies from 10-8 to 108. From Fig. 2, our KMHF scheme is not suitable for a larger parameter λ . If λ > 10 2 , the identification performance of KMHF scheme is poor. If λ 10 2 , the identification performance is relatively stable. By studying AUC and ACC curves, our KMHF scheme reaches optimal when defining the parameter λ = 1 . In the experiments, parameter μ in (5) is set as 103, parameter ρ in (13) is set as 10, the number of retrieved CHMs k in (20) is set as 7.

The curves of AUC and ACC values with different λ .
Fig. 2
The curves of AUC and ACC values with different λ .

In this work, we evaluated the performance of cold-hot nature identification with different parameter μ in Eq.(5). We tuned the parameter μ in (5) in the range of [10-3, 10-2, 10-1, 1, 101, 102, 103, 104, 105]. Fig. 3 displays the AUC and ACC value curves for nature identification with different μ . From Fig. 3, our KMHF scheme is sensitive to parameter μ . By studying AUC and ACC curves, our KMHF scheme reaches optimal when defining the parameter μ = 10 3 . In this experiment, the parameter λ is set as 1, parameter ρ in (13) is set as 10, the number of retrieved CHMs k in (20) is set as 7.

The AUC and ACC curves with different μ .
Fig. 3
The AUC and ACC curves with different μ .

In this study, we analyzed the impact of different parameter ρ on our scheme for cold-hot nature identification. We tuned the parameter ρ in (13) in the range of [10-3, 10-2, 10-1, 1, 101, 102, 103]. Fig. 4 displays the AUC and ACC value curves for nature identification with different ρ . From Fig. 4, our KMHF scheme is more suitable for a large parameter ρ . The AUC and ACC curves both have a peak when ρ = 10 . Comprehensively analyzing the AUC and ACC curves, we define ρ as 10. when ρ = 10 , our scheme is optimal. In this experiment, the parameter λ is set as 1, parameter μ in (5) is set as 103, the number of retrieved CHMs k in (20) is set as 7.

The AUC and ACC curves with different ρ .
Fig. 4
The AUC and ACC curves with different ρ .

Furthermore, we configured the number of retrieved CHMs k in (20) for evaluating the identification performance of our scheme. We tuned the parameter k in (20) in the range of [1, 3, 5, 7, 10, 12, 15, 20]. Fig. 5 shows the AUC and ACC curves with different parameter k. According to this figure, AUC and ACC curves have fluctuations when parameter k takes different values, which indicates that the performance of our KMHF scheme fluctuates slightly with the increase of k. Comprehensively analyzing the AUC and ACC curves, our KMHF scheme reaches optimal performance when k = 7. In this experiment, the tradeoff parameter λ is set as 1, the parameter μ is set as 10 3 , parameter ρ in (13) is set as 10.

The AUC and ACC curves with different k.
Fig. 5
The AUC and ACC curves with different k.

3.2

3.2 Performance evaluation

Performance evaluation was performed to verify the feasibility of our KMHF scheme with the stability evaluation. Leave-one-CHM-our method was constructed to perform the stability evaluation. Several classical identification schemes were introduced to compare the cold-hot nature classification performance with our KMHF scheme, including our nature identification schemes (RS, PCC and ELM) and distance metric learning models (i.e., LMNN, ITML). RS and PCC schemes have been used for nature classification of CHMs with UV fingerprints. ELM has been utilized to analyze the nature of CHM compounds. A long fingerprint vector from straightforwardly concatenating three wavelength HPLC fingerprints was included as a comparative reference. The similarity metric from optimal solution matrix A * in Eq. (12) was used to tackle this long fingerprint vector. We marked this scheme as LFV. Table 2 displays the performance comparison of our KMHF scheme and several classical identification schemes. From the comparison results in Table 2, we obtained the following conclusions. Firstly, our KMHF scheme outperforms the comparative LFV in nature identification. This demonstrates our inference that it is not optimal for straightforwardly concatenating three wavelength HPLC fingerprints as a long vector. Secondly, the classification performance of our KMHF scheme is better than that of the comparison classification schemes. This indicates that our scheme comprehensively analyzes the semantic relevance and fingerprint similarity of CHMs, and has better identification performance of cold-hot nature. Especially, different wavelength HPLC fingerprints can better mine the ingredient information of CHMs for cold-hot nature identification. Thirdly, the identification performance of our KMHF scheme outperforms that of RS. Compared with our scheme, RS does not consider the fingerprint similarity. Therefore, fingerprint similarity is an effective complement to semantic relevance. Fourth, the similarity metric methods (including ITML, LMNN and RS) have better classification performance than PCC and ELM. This shows that similarity metric methods are more effective for nature classification of CHMs. Furthermore, the similarity metric experiments confirm the proposed theoretical hypothesis that CHMs with similar cold-hot nature have similar material basis. Fifth, the performance of ELM algorithm is poor for cold-hot nature prediction. Finally, in summary, the constructed experiments verify the feasibility of our KMHF scheme.

Table 2 Comparison of stability evaluation.
Classifiers AUC ACC
ITML 0.739 0.672
LMNN 0.766 0.681
ELM 0.625 0.592
RS 0.789 0.650
PCC 0.604 0.581
LFV 0.808 0.734
KMHF 0.819 0.771

3.3

3.3 Nature identification examples

Leave-one-CHM-out method was introduced to give the examples of nature identification. Two representative CHMs, including Lophatheri Herba (cold) and Rhizoma Arisaematis (hot), were selected as query instances to illustrate nature identification. Table 3 reports two query CHM examples obtained from our KMHF scheme, in which query CHMs are listed in the second row and top k = 7 similar CHMs are showed in other rows. The top k = 7 similar CHMs are arranged in monotonically increasing order of Mahalanobis distance. Lophatheri Herba is chosen as a typical cold medicine to explain nature identification. The calculated similar CHMs include six cold reference CHMs and one hot reference CHM. Its cold nature probability we obtained is 92.5 %, which indicates that Lophatheri Herba is probably cold. Rhizoma Arisaematis is chosen as a typical hot medicine to analyze the nature identification. The calculated similar CHMs include five hot reference CHMs and two cold reference CHMs. Its cold nature probability we obtained is 3.1 %, which indicates that Rhizoma Arisaematis is probably hot. The nature identification instances demonstrate the relationship between CHM ingredients and cold-hot nature.

Table 3 The nature identification instances. Nature labels are marked in brackets.
Identification Instances CHMs with cold nature CHMs with hot nature
Query CHMs Lophatheri Herba (cold) Rhizoma Arisaematis (hot)
The similar reference CHMs Anemarrhena Asphodeloides Bunge (cold) Clematidis Radix et Rhizoma (hot)
Rhei Radix et Rhizoma (cold) Mustard Seeds (hot)
Dianthi Herba (cold) Corydalis Rhizoma (hot)
Notopterygii rhizoma et radix (hot) Ligustici Rhizoma et Radix (hot)
Gardeniae Fructus (cold) Aconiti Lateralis Radix Praeparata (hot)
Stephaniae Tetrandrae Radix (cold) Ecliptae Herba (cold)
Puerariae Lobatae Radix (cold) Trachelospermi Caulis et Folium (cold)

3.4

3.4 Overall identification performance

In this work, the overall identification performance of our KMHF scheme was analyzed with four evaluation indices, including confusion matrix, F-score, precision, and recall. All evaluation indices were obtained from leave-one-CHM-out method. Table 4 displays the confusion matrix from nature identification of 61 CHMs. The identification accuracy rate of hot CHMs is 64.5 % (20/31), while the prediction accuracy rate of cold CHMs is 90.0 % (27/30). Therefore, the total prediction accuracy rate of 61 CHMs is 77.0 % (49/61). According to Table 4, our scheme has higher identification accuracy for cold CHMs, but poor identification accuracy for hot CHMs. Table 5 shows the precision, recall, and F-score of nature identification of 61 CHMs. By summarizing Table 4 and Table 5, we conclude that our scheme is effective in nature identification of 61 CHMs with HPLC fingerprints. The ingredient information can be used to analyze cold-hot nature of CHMs.

Table 4 Confusion matrix of 61 CHMs.
Ground Truth Identification
Cold Hot
Cold 27 3
Hot 11 20
Table 5 The recall, precision and F-score of 61 CHMs.
Cold Hot
Recall 90.0 % 64.5 %
Precision 71.1 % 87.0 %
F-score 79.4 % 74.1 %

4

4 Discussion

HPLC has been widely used in the analysis of CHM ingredients, including nature identification and quality evaluation. Its advantage is that it can quantitatively and qualitatively test CHM ingredients. Our group has done a lot of work in the nature identification, but mainly focused on the UV spectrum. Therefore, this study explores to introduce HPLC to analyze the CHM ingredients, and build a classification model for nature evaluation. Multi-wavelength HPLC fingerprints are used to extract different characteristics of CHM ingredients. The experimental results find that HPLC can extract more feature information of CHM ingredients related to CHM nature.

Multi-wavelength HPLC fingerprints challenge the classical classifiers. These algorithms may not be able to mine the feature information of CHM components, resulting in low accuracy of cold-hot nature identification. Especially, different wavelength HPLC fingerprints represent different physical properties of CHM ingredients. The classical classifiers cannot adapt to this data feature. It perhaps leads to low identification accuracy by straightforwardly concatenating three wavelength HPLC fingerprints into a long vector. In this study, our scheme introduced a multi-wavelength distance metric learning algorithm for cold-hot nature identification. The experimental results demonstrate that our scheme can better mine characteristic information of CHM ingredients related to CHM nature.

The theoretical basis of this study comes from a hypothesis that CHMs with similar cold-hot nature have the same or similar material basis. This study introduced a multi-wavelength distance metric learning algorithm to measure the similarity of CHM ingredients and proposed an improved KNN scheme for cold-hot nature evaluation. Experimental results indicate that there is a close relationship between CHM nature and its ingredients. From the perspective of HPLC, our experiments find that CHMs with similar ingredients related to cold-hot nature have similar cold-hot nature. Our experimental results support the hypothesis.

Distance metric learning algorithms, such as LMNN, ITML and RS, mainly focus on semantic relevance of CHMs without considering fingerprint similarity of CHM HPLC. However, semantic relevance of CHMs cannot reflect the whole concept of similarity measure. Our group defines the similarity metric as semantic relevance and fingerprint similarity. Experiments indicate that fingerprint similarity is an important complement to similarity measurement, which can improve the identification accuracy of cold-hot nature.

However, there are some problems to be solved in the future. Firstly, multi-wavelength HPLC fingerprints are used to analyze CHM ingredients. Gas chromatography and spectroscopy are not taken into account. Multi-fingerprints technology can extract different characteristic information of CHM ingredients, and perhaps improve the accuracy of nature identification. As a result, nature identification scheme based on multi-fingerprints fusion is the focus of future research. Secondly, the dataset in this study is a small sample and high-dimensional dataset. This poses a challenge to most classifiers. It is the direction of future research by designing special classifiers according to the characteristics of data. Thirdly, in this study, a HPLC data of 61 CHMs was used to test the proposed KMHF scheme. However, this is a primary assessment, which needs more CHM HPLC fingerprints to verify. Consequently, an extended dataset and an independent testing dataset are needed in the future studies.

5

5 Conclusions

In this study, a KMHF scheme was developed to fuse multi-wavelength HPLC fingerprints for cold-hot nature identification. Multi-wavelength HPLC fingerprints of CHMs were used to analyze the characteristic information of CHM ingredients. An improved KNN scheme was proposed for nature identification. Numerous experiments demonstrate that cold-hot nature of CHMs is closely related to CHM ingredients. Comparative experiments indicate that the nature identification performance of our scheme is the best. Therefore, our scheme can better mine the ingredient information related to cold-hot nature. Furthermore, our experiments support the scientific hypothesis that CHMs with the same cold-hot nature have similar material basis.

Author contributions

G.W. conceived and designed the project, M. Q., analyzed the Chinese medicine data sets. Z.W. collected data and provided expert knowledge. All authors read and approved the final manuscript.

Acknowledgments

The research is supported by the national key basic research development program (973Program) (No. 2007CB512600); National Natural Science Foundation of China (No. 81473369); Qi Huang Scholars Support Projecting; Shandong Province medical and health science and technology development plan (No. 202109040649); Shandong Provincial Natural Science Foundation (No. ZR2022MH203).

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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