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

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.

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 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.

2.4 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 ${\beta }_i$ and added a regularizer to the weights. Thus, the objective function is as follows:

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 $\eta$ , the objective function is transforms to:

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

Integrating the equations in (15), we obtained:

Since ${\sum }_{i=1}^{N_W}{\beta }_i\text{=}1$ , we get the solution of $\eta$ as follows:

Putting the solution of $\eta$ into (15), we can obtain:

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 ${\beta }_i$ 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:

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:

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Fig. 1

Cold-hot nature identification based on similarity metric of multi-wavelength HPLC.

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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 $i\text{th}$ wavelength HPLC fingerprints, $X_i=[x_{i1},x_{i2},\cdots ,x_{\mathit{in}}]\in R^{d\ast n}$ , and the number of nature classes $C\text{=}2$ .

1. Transformation matrics $A^{(i)}{\text{|}}_{i=1}^{N_W}$ 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 $A^{(i)}{\text{|}}_{i=1}^{N_W}$ and the weight value ${\beta }_i{\text{|}}_{i=1}^{N_W}$ 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 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:

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.

3.1 Parameter configurations

In this study, several parameters in KMHF scheme should be optimized for cold-hot nature identification. The balance parameter $\lambda$ in (4), parameter $\mu$ in (5), parameter $\rho$ 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 ( $\lambda$ , $\mu$ , $\rho$ and k). As a result, AUC and ACC values were studied as functions of the tuning parameters ( $\lambda$ , $\mu$ , $\rho$ and k) to describe more comprehensive curves for the optimal KMHF scheme. We tuned the parameter $\lambda$ 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 $\lambda$ varies from 10^-8 to 10⁸. From Fig. 2, our KMHF scheme is not suitable for a larger parameter $\lambda$ . If $\lambda >{10}^2$ , the identification performance of KMHF scheme is poor. If $\lambda ⩽{10}^2$ , the identification performance is relatively stable. By studying AUC and ACC curves, our KMHF scheme reaches optimal when defining the parameter $\lambda \text{=}1$ . In the experiments, parameter $\mu$ in (5) is set as 10³, parameter $\rho$ in (13) is set as 10, the number of retrieved CHMs k in (20) is set as 7.

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Fig. 2

The curves of AUC and ACC values with different $\lambda$ .

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In this work, we evaluated the performance of cold-hot nature identification with different parameter $\mu$ in Eq.(5). We tuned the parameter $\mu$ 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 $\mu$ . From Fig. 3, our KMHF scheme is sensitive to parameter $\mu$ . By studying AUC and ACC curves, our KMHF scheme reaches optimal when defining the parameter $\mu \text{=}{10}^3$ . In this experiment, the parameter $\lambda$ is set as 1, parameter $\rho$ in (13) is set as 10, the number of retrieved CHMs k in (20) is set as 7.

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Fig. 3

The AUC and ACC curves with different $\mu$ .

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In this study, we analyzed the impact of different parameter $\rho$ on our scheme for cold-hot nature identification. We tuned the parameter $\rho$ 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 $\rho$ . From Fig. 4, our KMHF scheme is more suitable for a large parameter $\rho$ . The AUC and ACC curves both have a peak when $\rho \text{=}10$ . Comprehensively analyzing the AUC and ACC curves, we define $\rho$ as 10. when $\rho \text{=}10$ , our scheme is optimal. In this experiment, the parameter $\lambda$ is set as 1, parameter $\mu$ in (5) is set as 10³, the number of retrieved CHMs k in (20) is set as 7.

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Fig. 4

The AUC and ACC curves with different $\rho$ .

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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 $\lambda$ is set as 1, the parameter $\mu$ is set as ${10}^3$ , parameter $\rho$ in (13) is set as 10.

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Fig. 5

The AUC and ACC curves with different k.

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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 $A\text{*}$ 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.

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.

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.