Journal of Spectroscopy

Volume 2017 (2017), Article ID 9165247, 11 pages

https://doi.org/10.1155/2017/9165247

## Application of Permutation Entropy in Feature Extraction for Near-Infrared Spectroscopy Noninvasive Blood Glucose Detection

School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China

Correspondence should be addressed to Chengwei Li

Received 28 December 2016; Revised 20 March 2017; Accepted 16 April 2017; Published 9 August 2017

Academic Editor: Feride Severcan

Copyright © 2017 Xiaoli Li and Chengwei Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Diabetes has been one of the four major diseases threatening human life. Accurate blood glucose detection became an important part in controlling the state of diabetes patients. Excellent linear correlation existed between blood glucose concentration and near-infrared spectral absorption. A new feature extraction method based on permutation entropy is proposed to solve the noise and information redundancy in near-infrared spectral noninvasive blood glucose measurement, which affects the accuracy of the calibration model. With the near-infrared spectral data of glucose solution as the research object, the concepts of approximate entropy, sample entropy, fuzzy entropy, and permutation entropy are introduced. The spectra are then segmented, and the characteristic wave bands with abundant glucose information are selected in terms of permutation entropy, fractal dimension, and mutual information. Finally, the support vector regression and partial least square regression are used to establish the mathematical model between the characteristic spectral data and glucose concentration, and the results are compared with conventional feature extraction methods. Results show that the proposed new method can extract useful information from near-infrared spectra, effectively solve the problem of characteristic wave band extraction, and improve the analytical accuracy of spectral and model stability.

#### 1. Introduction

Diabetes is one of the major diseases threatening human health, and the number of people with diabetes is growing at an alarming rate. More than one hundred million people suffer from diabetes; furthermore, the number is expected to increase to 592 million by 2035 [1]. Although proper diet and insulin injection can be used to regulate blood glucose levels, serious complications are caused in the later stage of diabetes, such as heart failure and blindness [2]. Therefore, the treatment of diabetes is very important, and the concentration of blood glucose detection is the foundation of diabetes treatment. The noninvasive blood glucose detection technology that measures the glucose concentration in the blood under the condition of no skin damage includes near-infrared spectroscopy, photo acoustic spectroscopy, polarization method, fluorescence method, and dielectric spectroscopy method [3–5]. Compared with the near-infrared spectra method, other noninvasive blood glucose detection methods are not perfectly suitable for real-time detection. The signals are hard to be detected and easy to be interfered by other components. At present, noninvasive blood glucose detection based on near-infrared spectra has become the research focus at home and abroad. Near-infrared spectroscopy (NIR), which is generated from molecular vibrations and reflects the chemical bond information, such as C-H, O-H, N-H, and S-H, can measure most kinds of compounds and their mixtures. Compared with the traditional analytical techniques, NIR has been widely applied because it is highly efficient and causes no damage and pollution [6–8]. The main structure and composition of glucose information is contained in the near-infrared spectra. The useful glucose information can be extracted form spectral data; then, the data after pretreatment are used to establish a mathematical model to calculate the glucose concentration. In the field of biomedicine, NIR combined with chemometrics is considered one of the most effective methods for noninvasive blood glucose concentration detection [3]. The common chemometrics methods include multiple linear regression (MLR), principal component regression (PCR), partial least squares regression (PLSR), and support vector regression (SVR). The MLR is limited by the noise in spectral data, and the irrelevance between some principal components and the actual content appears in the PCR. Therefore, the PLSR method and SVR method are applied in this paper. However, certain technical difficulties exist in noninvasive blood glucose measurement because near-infrared spectral samples cannot be pretreated, namely, the complex background, overlapped spectral peaks, and less effective information rate. Therefore, extracting effective information from the original spectra is critical for establishing an ideal mathematical model. The effective extraction of glucose characteristic information from nonlinear and nonstationary near-infrared spectral signals can improve the detection efficiency and detection precision.

In 1984, Shannon introduced entropy to the field of information theory and proposed the concept of information entropy to measure the uncertainty of events [9]. Subsequently, the concept of entropy was gradually generalized. In 1991, Pincus proposed the concept of approximate entropy (ApEn), which has the advantages of short required calculating data and excellent antinoise ability [10] and offsets the shortcomings of nonlinear analysis. However, the data has no relevance and the errors are produced in the computational process of ApEn. To observably improve the accuracy and efficiency of the ApEn method, Richman and Moorman proposed an improved ApEn in 2000 called sample entropy (SampleEn) [11]. Compared with the ApEn algorithm, SampleEn has short required data and robust antinoise and anti-interference abilities, well consistent in the range of large parameters such unique advantages. The definition of SampleEn must contain a template match; otherwise, it is meaningless. Therefore, Chen et al. improved SampleEn and first defined a new measure of sequence complexity, named fuzzy entropy [12]. This new measure fuzzifies the similarity measure formula with an exponential function to enable the fuzzy entropy value to transition smoothly with changing parameter. Its definition still has significance when the parameter is small, and it inherits the relative consistency and short data set-processing characteristics of SampleEn. Bandt and Pompe proposed a randomness detection method of a time series, namely, permutation entropy (PE), which can detect the randomness of time series and dynamic mutation behavior [13–18]. Permutation entropy calculates entropy based on permutation patterns by comparing the neighboring values of the time series [19]. PE between 0 and 1 has the advantages of simple concept, fast calculation speed, and robust anti-interference ability, and it is especially suitable for nonlinear data.

The key point of near-infrared spectra noninvasive blood glucose detection is to extract the characteristic information from the spectral signal. The near-infrared spectral signals of glucose solution are nonstationary and noisy, but the calculation of PE has a certain antinoise and anti-interference ability. In this study, the feature extraction of spectral information is investigated with glucose solution as the research object from the perspective of whole information from a signal. This paper is organized as follows. Section 2 describes the principles of ApEn, SampleEn, fuzzy entropy, and PE and then briefly introduces the methods of near-infrared spectral characteristic band extraction of a glucose solution, such as fractal dimension, mutual information, and the modeling methods, such as PLSR and SVR. In Section 3, the application of the proposed method is presented, and PLSR and SVR are used to establish calibration models with the extracted characteristic bands, as well as verify the validity and superiority of the proposed method. Finally, the conclusion is drawn in Section 4.

#### 2. Theory and Methods

##### 2.1. Entropy

###### 2.1.1. Approximate Entropy

In 1991, Pincus defined ApEn as a conditional probability that the similarity vector maintains its similarity when it increases from dimension to dimension. The physical meaning is the probability of generating a new pattern of time series when the dimension changes. ApEn has the following advantages: (1) short required data, (2) robust antinoise and anti-interference abilities, and (3) applicability for deterministic and stochastic signals and a mixed signal composed of deterministic and stochastic signals. The steps of the ApEn algorithm are as follows [10]:
(1)Given a time series of length , , reconstruct a *m*-dimensional vector according to the formula .(2)Compute the distance between arbitrary the vector and the vector .
The distance between the two vectors is the maximum absolute value of the difference between two corresponding elements in two vectors.(3)Specify the threshold , which is typically between 0.2 and 0.3. For each vector , find the number of ( is the standard deviation of the sequence) and calculate the ratio between this number and the total number of distances , which is denoted as .(4)Take the logarithm of , average for all , and denote .
(5)Increase by 1 and repeat steps 1 to 4 to obtain and .(6)Obtain the ApEn from .
(7)For a finite time series, ApEn can be estimated by a statistical value.

The parameters ,, and in the above steps are the length of time series, length of the comparison window, and margin of similarity, respectively. The bigger the value of is, the more dynamic the process can be reconstructed.

###### 2.1.2. Sample Entropy

The physical meaning of SampleEn is the same as that of ApEn. The larger SampleEn is, the higher the complexity of the sequence and the greater the probability of generating the new pattern will be. The specific algorithm implementation process is as follows [11]: (1)Given the time series , compose a set of dimension vectors according to the serial number order. (2)Define the distance between vector and vector as the largest difference between their corresponding elements, namely, (3)Define the threshold . For the value of each , find the number of , and calculate the ratio between and the total number of distances , which is denoted as . The average for all is as follows: (4)Increase the dimension to and repeat the above steps to obtain (5)Theoretically, the SamEn of this sequence is as follows: where . In practice, is not an infinite value. When is a finite value, SamEn is calculated as follows:

###### 2.1.3. Fuzzy Entropy

In the definition of fuzzy entropy, the concept of a fuzzy set is introduced, and the exponential function is chosen as the fuzzy function to measure the similarity of two vectors. The exponential function has the following expectation properties: (1) continuity of the exponential function ensures that its value does not have a mutation and (2) the nature of the exponential function ensures that the self-similarity value of the vector is maximum. The definition of fuzzy entropy is as follows [12]: (1)The sampling sequence with points is .(2)Compose a set of -dimensional vectors according to the serial number order. where represents the continuous values of starting from the th point. is its mean value. (3)Define the distance between vector and vector as the largest difference between their corresponding elements, namely, (4)Define the similarity between vector and vector , with a fuzzy function , namely, where the fuzzy function is an exponential function, and and are the gradient and width of the exponential function boundary, respectively.(5)Define the function as follows: (6)Similarly, repeat steps 2 to 5, reconstruct a set of -dimensional vector according to the serial number order, and define the following function: (7)Define the fuzzy entropy as follows: When is a finite value, the value obtained by the above steps is the estimated value of the fuzzy entropy of the sequence with length .

###### 2.1.4. Permutation Entropy

According to [13], the definition of PE is setting a time sequence , and reconstruct it in phase space to obtain the matrix where and are the embedding dimension and delay time, respectively, and . Each row in the matrix can be regarded as a reconstructed component, with a total of reconstruction components. The th reconstruction component of the reconstruction matrix is rearranged according to the values in ascending order. represents the index of the column in which the individual elements of the reconstructed component are as follows:

If equal values in the reconstructed component are observed, the components are arranged according to the size of the value of and , that is, when , .

Therefore, for an arbitrary time series , a set of symbol sequences can be obtained from each row in the reconstructed matrix
where and . is observed when the -dimensional phase space map has a different symbolic sequence , and the symbolic sequence is one kind of arrangement. If the probability of the occurrence of each symbol sequence is , the PE of *k* kinds of different symbol sequences of time series in terms of Shannon entropy is as follows:
When , reaches the maximum value . For convenience, is typically normalized with , namely,

The magnitude of represents the randomness degree of the time series . The smaller the value of is, the more inerratic the time series will be; otherwise, the more stochastic the time series will be. The change in reflects and amplifies the minute details of the time series.

###### 2.1.5. Application to Simulation Signal

In order to compare the ApEn, SampleEn, fuzzy entropy, and PE, define a mixed signal composed of deterministic signal and stochastic signal with a different probability, where , is the stochastic signal in , is the data length, and . Considering the four kinds of entropy of signal with and , note ApEn1, SampleEn1, FuzzyEn1, PE1, ApEn2, SampleEn2, FuzzyEn2, and PE2 for convenience, respectively. Their change relation with signal amplitude , signal length , and signal-to-noise ratio of signal are shown in Figures 1–3.