You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


1. Introduction {#sec1-sensors-17-02739}
===============

Every year, the number of cancer-caused deaths rises \[[@B1-sensors-17-02739]\]. Among all types of cancer, colorectal cancer is the third most common cause of cancer death worldwide, with an annual incidence of approximately one million cases and 600,000 deaths. The high mortality rate is partially attributed to the fact that established clinical procedures lack reliability and sensitivity for finding cancer at early stages \[[@B2-sensors-17-02739],[@B3-sensors-17-02739]\]. Thus, the importance of early diagnosis in preventing and treating cancer mandates development of an accurate, fast, convenient, and inexpensive diagnostic tool for early detection \[[@B4-sensors-17-02739]\].

Substantial modifications in cancer cells at the molecular level occur prior to morphological changes could be observed in tissues. Therefore, molecular spectroscopes are promising tools to detect cancer-related chemical changes at an early stage \[[@B1-sensors-17-02739]\]. In particular, Fourier transform infrared spectroscopy (FTIR), a popular tool in modern analytical chemistry labs, provides rich information about the bio-molecules that act as building blocks in tissues and cells \[[@B5-sensors-17-02739],[@B6-sensors-17-02739],[@B7-sensors-17-02739],[@B8-sensors-17-02739]\]. Existing clinical diagnosis requires taking biopsy via endoscope, which causes pain and requires lengthy pathological exams. In addition, surgical resection can lead to taking biopsies from non-cancerous tissues due to a number of factors, and there is always a possibility that malignant cells could go into blood stream during such invasive procedure. Therefore, being able to diagnose colorectal cancer in vivo or ex vivo could largely overcome the limitations of existing procedures, providing accurate and rapid determination of proper operative treatment. Combining an attenuated total reflectance (ATR) fiber probe-coupled FTIR spectrometer with an endoscope, a simple, rapid, and noninvasive method to detect human cancer tissues directly with minimal sample preparation may achieve results comparable to the gene expression-based method \[[@B9-sensors-17-02739],[@B10-sensors-17-02739],[@B11-sensors-17-02739],[@B12-sensors-17-02739],[@B13-sensors-17-02739]\]. The current work was carried out on ex vivo tissues using an ATR-FTIR probe.

In recent years, the use of FTIR to diagnose various cancers, such as lung, breast, gastric, liver, and colorectal cancer, has been reported \[[@B14-sensors-17-02739],[@B15-sensors-17-02739],[@B16-sensors-17-02739],[@B17-sensors-17-02739],[@B18-sensors-17-02739],[@B19-sensors-17-02739],[@B20-sensors-17-02739],[@B21-sensors-17-02739],[@B22-sensors-17-02739],[@B23-sensors-17-02739]\]. Chemometric methods, such as support vector machine (SVM) \[[@B21-sensors-17-02739]\], K-nearest neighbor classifier (KNN) \[[@B22-sensors-17-02739]\], and K-local hyperplane distance nearest neighbor (HKNN), enable efficient information extraction and classification model calibration \[[@B24-sensors-17-02739],[@B25-sensors-17-02739]\]. These afore mentioned reports indicate that FTIR spectroscopy along with an effective chemometric classifier could be a useful tool for screening a variety of human tumors. Until now, few studies have been developed for diagnosis and discrimination of colorectal cancers and colitis using FTIR spectroscopy \[[@B26-sensors-17-02739]\]. Most research efforts focus on enabling a high-accuracy and high-sensitivity algorithm for cancer diagnosis. In this study, we combine preprocessing techniques and a novel classification method for analyzing FT-IR spectral data and achieve high accuracy in diagnosing colorectal cancer tissues.

2. Materials and Methods {#sec2-sensors-17-02739}
========================

2.1. Tissue Specimens {#sec2dot1-sensors-17-02739}
---------------------

All colorectal cancer and colitis tissues were provided by the Medical Division of the First Hospital of Xi'an Jiaotong University, China. Informed consent was obtained from each patient prior to the study, and clinical diagnosis was confirmed by histopathology. A total of 88 tissue samples from 42 female and 46 male patients, were obtained. The average age was 53.7 years old with the oldest being 76 years and the youngest age being 21 years. One fresh endoscopic biopsy of 1--3 mm in diameter was obtained from each patient. According to the pathological exam results, the samples consisted of 41 cases of colitis and 47 cases of cancer.

2.2. Instrumentation and FTIR Data Collection {#sec2dot2-sensors-17-02739}
---------------------------------------------

A WQF-500 FTIR spectrometer linked with a modified attenuated total reflectance (ATR) fiber probe (Beijing No. 2 optical instrument factory, Beijing, China) was used to acquire spectra. The FTIR spectrometer was equipped with a liquid-nitrogen-cooled mercury cadmium telluride (MCT) detector. Specimens were frozen and transported to the laboratory. Before experiment, frozen specimens were thawed at room temperature for approximately 3--5 min. Then, a background spectrum was acquired first. The ATR probe was placed at a 90° angle on the tissue specimen surface for spectrum acquisition. To achieve an acceptable signal-to-noise ratio at a resolution of 4 cm^−1^, 32 scans were recorded with wavenumbers ranging from 1000 cm^−1^ to 4000 cm^−1^. The procedure took approximately 1--2 min. After sample spectra were recorded, samples were stored in liquid nitrogen and sent for the histological examination as reference for spectral analysis.

2.3. Spectra Preprocessing Method {#sec2dot3-sensors-17-02739}
---------------------------------

Two preprocessing methods, viz., smoothing and standard normal variate (SNV) \[[@B27-sensors-17-02739],[@B28-sensors-17-02739],[@B29-sensors-17-02739]\], were performed on the FTIR spectra. First, the Savitsky--Golay algorithm with a window width of 5 points was applied to each spectrum to reduce random noise in the data. Then, all available spectra were normalized by the SNV method to remove multiplication interference, slope variation, and scatter effects generated by particles of the sample.

For spectrum $x_{ij}$ of sample $i$ at wavenumber $j$, SNV standardization is defined as follows: $$x_{ij,SNV} = \frac{x_{ij} - {\overline{x}}_{i}}{\sqrt{\sum_{j = 1}^{n}\left( {x_{ij} - {\overline{x}}_{i}} \right)^{2}}}\left( {n - 1} \right)^{1/2}$$ where ${\overline{x}}_{i}$ denotes the average spectrum of sample $i$, $n$ denotes the number of wavelengths, and $\left( {n - 1} \right)$ denotes the degree of freedom.

2.4. Entropy Weight Local-Hyperplane K-Nearest Neighbor Method {#sec2dot4-sensors-17-02739}
--------------------------------------------------------------

A novel classification method called entropy weight local-hyperplane k-nearest neighbor (EWHK) is proposed for discrimination between colorectal cancer and colitis. For the EWHK method, which is an upgrade of K-local hyperplane distance nearest neighbor (HKNN) algorithm \[[@B24-sensors-17-02739],[@B25-sensors-17-02739]\], feature weights of training sets based on the information entropy are objectively considered to measure the importance of each single feature and to avoid the bias in high dimensions and the limit in small values of the nearest neighbor. On the other hand, HKNN treats every variable as an equally relevant component for classification. Therefore, the class labels of unknown samples are calculated according to the feature weights, the Euclidean distance, and the local hyperplane.

Suppose that training set $X = \left( {x_{1},\cdots,x_{m}} \right)^{T}$ consists of $m$ training instances with $L$ classes. Each training instance consists of $n$ input features $x_{i} = \left( {x_{i1},\cdots,x_{in}} \right)^{T}$ with known class label $y_{i} = c$, for $i = 1,\cdots,m$ and $c = 1,\cdots,L$. The class label of a query with input vector $q = \left( {q_{1},\cdots,q_{n}} \right)^{T}$. The three stages in the proposed method were as follows: prototype selection, local hyperplane construction, and query classification.

Firstly, the feature weight is estimated objectively based on the concept of information entropy to figure out the entropy weight according to the variance of every variable. Low information entropy resulted in high feature weight, which corresponds to a feature with better class separation capability. The entropy weight $w_{j}$ is calculated according to the following formula: $$\begin{array}{l}
{z_{ij} = \frac{x_{ij}}{\sum_{i = 1}^{m}x_{ij}},\beta = \frac{1}{\ln(m)}} \\
{H_{j} = - \beta{\sum_{i = 1}^{m}{z_{ij}\ln(z_{ij})}}} \\
{w_{j} = \frac{1 - H_{j}}{n - {\sum_{j = 1}^{n}H_{j}}},\,{\forall j = 1,\cdots,n}} \\
\end{array}$$ where $z_{ij}$ denotes the normalized $j$th component of sample $i$ in the training set; $\beta$ denotes the regularization parameter; $H_{j}$ denotes the information entropy of the $j$th feature of the sample. Hence, new weighted Euclidean distance metric $D$ between $x_{i}$ and $q$ is defined as follows: $$D(x_{i},q) = \sqrt{\sum\limits_{j = 1}^{n}{w_{j}{(x_{ij} - q_{j})}^{2}}}.$$

Then, a local hyperplane of class $c$ is constructed for the given query $q$ according to the distance metric $D$ and the number $k$ of nearest neighbors of class $c$. Formally, the formula is as follows: $$\begin{array}{l}
{LH_{c}(q) = \left\{ {s\left| {s = {\sum\limits_{i = 1}^{k}{\alpha_{i}V_{.i} + m_{c}}}} \right.} \right\}} \\
{m_{c} = \frac{1}{k}{\sum\limits_{i = 1}^{k}p_{ci}}} \\
{V_{.i} = p_{ci} - m_{c}} \\
{\alpha = {(\alpha_{1},\cdots,\alpha_{k})}^{T}} \\
\end{array}$$ where $p_{i}$ is the $i$th nearest neighbor of class $c$; $\alpha$ is solved by minimizing the distance between $q$ and $LH_{c}(q)$ using regularization. Thus, the calculated minimum distance is as follows: $$\begin{array}{l}
{J_{c}(q) = \min\limits_{\alpha}{\sum\limits_{j = 1}^{n}{w_{j}{(V_{j.}\alpha + m_{cj} - q_{j})}^{2} + \lambda\alpha^{T}\alpha}}} \\
{\text{~\quad\quad} = \min\limits_{\alpha}{(s - q)}^{T}W(s - q) + \lambda\alpha^{T}\alpha} \\
{W = diag(w_{1},\cdots,w_{n})} \\
\end{array}$$ where $\lambda$ is the regularization parameter. $J_{c}(q)$ is minimized, and the equation $(U^{T}V + \lambda I_{k})\alpha = U^{T}(q - m_{c})$, where $U^{T} = V^{T}W$ is used to calculate $\alpha$, is derived. Finally, the class of the query $q$ is assigned as follows: $class(q) = \arg\ \min_{c}\ J_{c}(q)$.

3. Results and Discussion {#sec3-sensors-17-02739}
=========================

3.1. Preprocessing of FTIR Spectra {#sec3dot1-sensors-17-02739}
----------------------------------

In the process of measurement, the obtained spectra contain not only useful information regarding the molecular structure and the components of the measured samples, but also the noises, such as the high-frequency random noise, the baseline drift, and the stray light. This additional noise needs to be eliminated; otherwise, they will affect the discrimination result.

Prior to classification analysis, data preprocessing is necessary to improve performance of the classification model. Savitzky--Golay (SG) smoothing reduces random noise, and SNV was applied to remove unwanted background variances to some extent. There is no bio-molecules absorbance peak in the 1800--2800 cm^−1^ region, the majority of peaks are in the 1000--1800 cm^−1^ region and in the 2800--3800 cm^−1^ region. Thus, the SNV method was separately used from 1000 to 1800 cm^−1^ and from 2800 to 3800 cm^−1^.The FTIR spectra of colitis and cancerous tissues before and after preprocessing are shown in [Figure 1](#sensors-17-02739-f001){ref-type="fig"}. After performing background correction and normalization, useful information of all spectra (such as at the wavenumber near 1743 cm^−1^, 2858cm^−1^, and 2924 cm^−1^) were marked as shown in [Figure 2](#sensors-17-02739-f002){ref-type="fig"}. The quality of FTIR spectra was greatly improved after data preprocessing.

3.2. Analysis of FTIR Spectra {#sec3dot2-sensors-17-02739}
-----------------------------

A total of 88 spectra were obtained by FTIR spectroscopy within the spectral region between 1000 and 4000 cm^−1^. Because there were no bio-molecule absorbance peaks in the 1800--2800 cm^−1^ region, the SNV method was separately used from 1000 to 1800 cm^−1^ and from 2800 to 3800 cm^−1^ after smoothing.

[Figure 2](#sensors-17-02739-f002){ref-type="fig"} shows the spectra of colitis and colorectal cancer biopsies after preprocessing, where the band assignments of major absorption in the FTIR spectra of colorectal tissue are marked. The major peaks are similar for the spectra of colitis and colorectal cancer. However, the differences including peak shape and relative intensity can be observed. These results are reasonable because significant changes occurred in both the structure and composition of the main bio-molecules, which constitute the cell such as DNA, water, protein, and lipids, between cancerous and colitis tissues.

As is shown in [Figure 2](#sensors-17-02739-f002){ref-type="fig"}, the spectral profile of cancerous tissues indicates the presence of fewer lipids and more proteins compared with colitis tissues. The peak intensity of the C=O band assigning to the lipids (near 1743 cm^−1^) and the peak intensity of C-H stretching vibration bands relating to the lipids (near 2958 cm^−1^, 2924 cm^−1^, and 2858 cm^−1^) decrease and even disappear in the spectra of malignant tissues, making it essential to consume fat in the malignant tissue to meet the nutritional and energy requirements in carcinoma development. The spectral profile of cancerous tissues indicates the presence of proteins at wavenumbers \~1643 cm^−1^ and \~1550cm^−1^, which belong to amide I band and amide II band of the protein, respectively. The relative intensity near $I_{1550}/I_{1643}$ decreases more for the spectra of cancerous tissues than for those in colitis biopsies because of the changes in the proportion of proteins during tumor formation. The intensity of the \~1460 cm^−1^ peak is weaker than that of the \~1400 cm^−1^ peak in the spectra of the cancerous samples, while the peak at \~1460 cm^−1^ is stronger than or equal to that of \~1400 cm^−1^ in the spectra of colitis samples. Cancerous tissue contains greater amounts of nucleic acids, collagen, and certain amino acids compared to the colitis ones. In colitis tissues, the peak at \~1240 cm^−1^ is weaker, and the band near 1310 cm^−1^ becomes weak and sometimes disappears. The absorption peak \~1080 cm^−1^ assigned to nucleic acid is obviously weaker in the spectra of colitis samples than that in the spectra of cancerous tissues. The peak at \~1160 cm^−1^ assigned to carbohydrate decreases noticeably in the spectra of the cancerous samples. Thus, the characteristics mentioned above between cancerous and colitis tissues provide the basis for spectroscopic diagnosis.

Specific assignments of individual peaks can be found in [Table 1](#sensors-17-02739-t001){ref-type="table"}.

3.3. Classification Analysis {#sec3dot3-sensors-17-02739}
----------------------------

After spectra preprocessing, 88 spectra data (41 colitis and 47 cancers) were analyzed to identify their class labels. The total 88 spectra were divided into two data sets. The 44 FTIR spectra (21 colitis and 23 cancers) after preprocessing were randomly selected as the training set. The other 44 FTIR spectra (20 colitis and 24 cancers) after preprocessing were randomly selected as the test set. Both EWHK and traditional classification models were built by the training set and validated by the test set. Traditional classification models include SVM and HKNN in this paper. These procedures were repeated five times. The five predicted results were averaged. [Table 2](#sensors-17-02739-t002){ref-type="table"} shows the classification results of colorectal tissues with entropy weight local-hyperplane k-nearest neighbor (EWHK). [Table 3](#sensors-17-02739-t003){ref-type="table"} shows the average of the five results using the three different methods.

The experiment results are summarized in [Table 2](#sensors-17-02739-t002){ref-type="table"} and [Table 3](#sensors-17-02739-t003){ref-type="table"}. The classification results of colorectal tissue samples with EWHK ([Table 2](#sensors-17-02739-t002){ref-type="table"}) showed that, among the 88 cases of colorectal tissue samples, only three colitis samples and nine cancer samples are misclassified. In [Table 3](#sensors-17-02739-t003){ref-type="table"}, EWHK achieved a high accuracy, viz., 85.91%. In addition, other statistics results of detection of colorectal biopsies by FTIR spectroscopy with EWHK and traditional classification models are shown in [Table 3](#sensors-17-02739-t003){ref-type="table"}. For colorectal cancer diagnosis with EWHK, sensitivity is 81.38%, specificity is 92.69%, predictive value of a positive test is 92.68%, and the predictive value of a negative test is 80.85%. In comparison, statistical analysis results with HKNN were worse than those with EWHK in diagnosing colorectal cancer tissues, achieving 66.46% sensitivity and 79.77% accuracy. The SVM works worse than HKNN. SVM can perform well with large-scale data. However, the choices of the parameters for the kernel are complex and unstable. The HKNN works well only for small values of the nearest-neighbor. However, the accuracy decreases as values of the nearest-neighbor increase. The FTIR spectra can be classified accurately with EWHK because it considers the influence of feature weight according to the information entropy of every variable. In conclusion, the results indicate that the EWHK has better capability in identifying colorectal cancer from colitis.

4. Conclusions {#sec4-sensors-17-02739}
==============

This study shows that it is feasible to classify colitis and cancers using FTIR spectroscopy and chemometrics. FTIR fiber-optic ATR spectroscopy is a powerful tool to detect changes at the molecular level and can rapidly capture small changes in molecular compositions and structures. Therefore, it has the potential to be further developed into noninvasive, in vivo, and real-time detection tools of cancerous tissues before a surgical operation is required. Data pre-processing such as smoothing and SNV greatly improved the signal-to-noise ratio for the FTIR spectra of colorectal tissues, and the EWHK classifier achieved a classification accuracy of 85.91%. The reason that EWHK performs well is because feature weights are calculated according to the information entropy of every variable. The proposed preprocessing and classification method using FTIR spectroscopy is effective and practical for in vivo colorectal cancer or other malignant tissue diagnosis and will be pursued in future studies.

The authors gratefully acknowledge the Medical Division of the First Hospital of Xi'an Jiaotong University for providing the tissue specimens and Beijing No. 2 Optical Instrument Factory (Beijing, China) for excellent technical assistance. This work was financially supported by the National Natural Science Foundation of China (Grant No. 61575015).

Qingbo Li proposed the algorithm, conceived and designed the experiments; Can Hao processed the spectral data, analyzed the spectral data and wrote the manuscript; Xue Kang was responsible for data preprocessing; Jialin Zhang performed the experiments; Xuejun Sun provided the samples and the pathological results; Wenbo Wang contributed to literature search and modified the English articles; Haishan Zeng completed final draft.

The authors declare no conflict of interest.

###### 

The Fourier transform infrared spectra (FTIR) of colitis and cancerous tissues. (**a**) Original spectra of colitis tissues; (**b**) original spectra of cancerous tissues; (**c**) preprocessed spectra of colitis tissues using smoothing and standard normal variate (SNV); (**d**) preprocessed spectra of cancerous tissues using smoothing and SNV.

![](sensors-17-02739-g001a)

![](sensors-17-02739-g001b)

![The typical FTIR spectra of colorectal biopsies after preprocessing.](sensors-17-02739-g002){#sensors-17-02739-f002}

sensors-17-02739-t001_Table 1

###### 

Peak positions and assignments of FTIR bands in colon tissues.

  Peak Positions (cm^−1^)   Major Assignment
  ------------------------- ---------------------------------------------------------------------
  1080                      Stretching vibration(DNA, RNA)
  1160                      Carbohydrate
  1240                      Asymmetric stretching vibration(RNA)
  1310                      C-H deformation vibration & Amide III (protein)
  1550                      amide II (protein)
  1643                      amide I (protein)
  1743                      C=O stretching vibration(lipids)
  2858, 2924, 2958          C-H stretching vibration (lipids)
  3300                      N-H stretching vibration( protein), O-H stretching vibration(water)

sensors-17-02739-t002_Table 2

###### 

The average of predict results of colorectal tissues with entropy weight local-hyperplane k-nearest neighbor (EWHK).

  Histologic Examination   The Predicted Results of Fourier Transform Infrared Spectroscopy (FTIR) Spectra   
  ------------------------ --------------------------------------------------------------------------------- ----
  Cancer                   38                                                                                9
  Colitis                  3                                                                                 38

sensors-17-02739-t003_Table 3

###### 

Comparison of the average of statistical analysis results with several classification models.

  Method   Sensitivity (%)   Specificity (%)   PPV ^1^ (%)   NPV ^2^ (%)   Accuracy (%)
  -------- ----------------- ----------------- ------------- ------------- --------------
  EWHK     81.38             92.69             92.68         80.85         85.91
  HKNN     66.46             96.19             95.25         70.43         79.77
  SVM      72.46             68.70             70.30         71.87         70.45

Note: ^1^ Positive predictive value; ^2^ Negative predictive value.