CN106570325A - Partial-least-squares-based abnormal detection method of mammary gland cell - Google Patents

Abstract

The invention relates to a breast cell abnormality detection method based on the partial least squares method, which includes: (1) importing a data set for building a model, setting corresponding dependent variables and independent variables, standardizing the data, extracting Principal components, fitting and establishing a partial least squares linear model; (2) Observe the T ² ellipse, identify abnormal points, remove the abnormal points from the data set, obtain a new data set, and fit again until there are no abnormal points, Obtain the parameter set, obtain the expression equation of y; (3) input the data set to be tested, use the equation to calculate, obtain the predicted value y, and then judge whether the predicted value is benign or malignant according to the determined threshold. The present invention establishes a regression model for breast cell abnormality detection through the method of partial least squares regression, and generates a better detection method for benign and malignant breast cells through the training of the regression model, which has rapid detection ability and high detection accuracy .

Description

A Method for Abnormal Detection of Breast Cells Based on Partial Least Squares

technical field

The invention belongs to the technical field of human medicine, and in particular relates to a breast cell abnormality detection method based on a partial least square method.

Background technique

In computer-aided diagnosis technology, various machine learning and artificial intelligence algorithms are used in the research of auxiliary diagnosis of breast cancer, which have certain defects, such as long training time, easy to fall into local convergence, more dependent on samples, etc. These factors will affect the accuracy of auxiliary diagnosis. Breast cancer is one of the malignant tumors with a high incidence in women. Since the 20th century, the incidence of breast cancer has been on the rise all over the world. However, its etiology has not yet been fully clarified, so the detection of breast cells is particularly important. Breast cancer is a malignant tumor that occurs in the glandular epithelial tissue of the breast. The female breast is composed of skin, fibrous tissue, breast glands and fat. The breast is not an important organ to maintain human life. Breast cancer in situ is not fatal; but due to Breast cancer cells have lost the characteristics of normal cells, and the connections between cells are loose and easy to fall off. Once the cancer cells fall off, the free cancer cells can spread throughout the body with the blood or lymph fluid, forming metastasis, which is life-threatening. At present, breast cancer has become a common tumor that threatens women's physical and mental health. Early breast cancer often does not have typical symptoms and signs, and it is not easy to attract attention. Most breast cancers are usually painless masses, and only a few are accompanied by varying degrees of dull pain or tingling pain. At present, there are many methods for breast cancer detection, such as mammography, ultrasound examination, CT examination and so on. However, many methods need to be further explored, and some methods are not even suitable as the main method for detecting breast cancer. For patients, early detection of breast cancer is the key to reducing the incidence of breast cancer. Early breast cancer is mostly symptoms such as changes in breast shape or lumps, and 80% of breast cancer patients are often found to have breast lumps through physical examination or breast cancer screening. Therefore, it is possible to judge whether there is a breast mass by detecting the condition of breast cells. Therefore, the examination of breast cells is an important means to discover the existence of breast cancer cells and prevent the spread of breast cancer cells.

Contents of the invention

In order to overcome the above-mentioned factors, the present invention proposes an auxiliary diagnosis for breast cancer. A regression model for breast cell abnormality detection is established through the method of partial least squares regression, and a better regression model is generated by training the regression model. A breast cell abnormality detection method based on partial least squares with rapid detection ability and high detection accuracy for benign and malignant breast cells.

Technical scheme of the present invention is as follows:

The above-mentioned breast cell abnormality detection method based on the partial least squares method specifically includes: (1) dividing the data obtained in the data set used to establish the model into two parts, one part is used for the establishment of the model, and the other part is used for the establishment of the model. Detection, setting the corresponding dependent variable and independent variable, standardizing the data, extracting the principal components of the independent variable and dependent variable respectively, fitting and establishing the model; (2) T ² is the cumulative contribution rate of the sample point to the component, Use the software to draw and observe the T ² ellipse, identify abnormal points, remove the abnormal points from the data set, obtain a new data set and model, fit and observe the T ² ellipse again until there are no abnormal points, obtain the parameter set, and calculate Obtain the expression equation of the dependent variable y whether it is a cancer cell; (3) Input another part of the data set to be tested, use the obtained equation to bring the value into the calculation, obtain the predicted value y', determine the threshold value, and specify the prediction value greater than the threshold value The value is a malignant cell, and the predicted value is a benign cell that is less than the threshold value. Compare y' with the original value, record the correct prediction result, and calculate the correct rate of the prediction model.

Described breast cell abnormality detection method based on partial least squares method, wherein: described step (1) is to import the data set that is used for building a model by software SIMCA-P 13.0, and described independent variable mainly comprises radius, texture, girth , area, smoothness, compactness, concavity, pit, symmetry and fractal dimension; the dependent variable is whether it is a cancerous cell.

The breast cell abnormality detection method based on the partial least squares method, wherein: in the step (2), when the sample points all fall within the ellipse, the sample is considered to be uniform; if any sample point falls outside the ellipse, then it can be These points are considered to be singular points whose values are far from the average level of the sample points.

The breast cell abnormality detection method based on partial least squares method, wherein: the threshold determined in the step (3) is 0.5, and the predicted value greater than 0.5 is defined as a malignant cell, and the predicted value less than 0.5 is defined as a benign cell.

The breast cell abnormality detection method based on the partial least squares method, wherein, the step (1) specifically includes the following steps:

(1.1) Standardize the independent variable and dependent variable

The normalized data matrix of X is denoted as E ₀ =(E ₀₁ ,E ₀₂ ,...,E _0p ) _n×p , and the normalized data matrix of Y is denoted as F ₀ =(F ₀₁ ,F ₀₂ ,...,F _0q ) _n×q ;

(1.2) Extracting principal components and stepwise regression

Note that t ₁ is the first component of F ₀ , t ₁ =E ₀ w ₁ , w ₁ is the first axis of E ₀ and is a unit vector, ie ||w ₁ ||=1; note u ₁ is The first component of F ₀ , u ₁ =F ₀ c ₁ , c ₁ is the first axis of F ₀ and is a unit vector, ie ||c ₁ ||=1; the correlation between t ₁ and u ₁ When the degree reaches the maximum, that is,

Var(t ₁ )→max

Var(u ₁ )→max

According to canonical correlation analysis, the degree _of correlation between _t1 and u1 should reach the maximum value, namely:

r(t ₁ ，u ₁ )→max

When the covariance _{of t1} and u1 reaches its maximum value, that is:

max < E ₀ w ₁ , F ₀ c ₁ >

Under the condition of ||w ₁ ||＝1 and ||c ₁ ||＝1, find the maximum value;

_w1 is the matrix The eigenvector of is, and the corresponding eigenvalue is θ ₁ is the objective function, its maximum value, that is, to find the matrix The eigenvector w ₁ corresponding to the largest eigenvalue of , find the component t ₁ and the residual matrix E ₁ :

t ₁ =E ₀ w ₁

in, Find the matrix in the same way The eigenvector w ₂ corresponding to the largest eigenvalue, t ₂ and the residual matrix E ₂

t ₂ =E ₁ w ₂

in,

Calculating in this way, if the rank of X is A, we finally get:

(1.3) Fitting

Remove a certain sample point i from the sample y, use this part of the sample to extract h components to fit a regression equation, and then bring the excluded sample i into the regression equation to obtain the fitted value Then define the sum of squared prediction errors of y _i as S _{PRESS, hj} , that is

Define the error sum of squares of y _i as S _{SS, hj} , namely

The breast cell abnormality detection method based on the partial least squares method, wherein, the specific steps of the step (2) are:

Define the contribution rate of the i-th sample point to the h-th component t _h to find the singular point in the sample, and define the contribution rate for:

In the formula is the variance of component t _h , and measures the cumulative contribution rate of sample point i to components t ₁ , t ₂ ,…, t _m :

The T ² ellipse was drawn in the SIMCA-P 13.0 software, and the sample points falling outside the ellipse were the singular points, and the singular points were removed for re-fitting until there were no singular points in the sample.

Beneficial effect:

The present invention establishes a regression model for breast cell abnormality detection through the method of partial least squares regression, and generates a better prediction method for benign and malignant breast cells through the training of the regression model. Prediction, the result reached 93.67% correct rate, can effectively analyze and predict whether breast cancer cells are cancerous, and plays an important role in the diagnosis and prevention of breast cancer.

The invention uses the partial least square method to carry out regression modeling on mammary gland cells with 10 characteristic variables, and can better predict whether the cells are cancerous, with an accuracy rate of 93.67%. It can be seen from the experimental data that the radius, texture, pit, perimeter and area of the cell are positively correlated with whether the cell cancer is mutated, while the fractal dimension is negatively correlated; it can be seen from the VIP _j number that the pit, perimeter The length, radius, area, and concavity have the largest contribution to the predicted value, while the symmetry, smoothness, and fractal dimension of the cell have relatively small contributions to the predicted value. When selecting a regression variable, the contribution can sometimes be discarded independent variable with a small degree. However, the conclusions about VIP _j index analysis are basically qualitative. It can only be said that these independent variables play a greater role, and the VIP method still has some limitations. When the contribution of independent variables is very large, it cannot be said that these independent variables Variables are the best choice of variables, and sometimes we have to consider the correlation between variables to choose. Therefore, it can be seen that the present invention has appropriate detection indexes conforming to the characterization of mammary gland cells, and has a relatively high accuracy rate.

The partial least squares method can be used in many fields, and the established prediction model has good accuracy and strong usability. As breast cancer is a disease with a high incidence and good early diagnosis effect, the observation of breast cells has become an important means of preventing breast cancer. Partial least squares regression (Partial Least-Squares Regression, PLS regression) is an advanced multivariate analysis method, which consists of multiple linear regression analysis, canonical correlation analysis and principal component analysis. With such a wide range of applications, it has achieved good results in multivariate modeling and prediction, and the established prediction model has high stability, accuracy and anti-noise ability, so it is very useful for solving breast cancer. It is a better method for the problem of influencing factors. The invention selects the medical detection results of benign and malignant breast cancer cells, uses the partial least squares method to establish a regression model, and predicts the test data by selecting an appropriate judgment threshold as the discrimination standard of the detection results. It was found that the prediction model based on the method of partial least squares has fast detection ability and high detection accuracy.

Description of drawings

Fig. 1 is the flow chart of the breast cell abnormality detection method based on partial least square method of the present invention;

Fig. ² is the first fitting T2 ellipse diagram of the breast cell abnormality detection method based on partial least square method of the present invention;

Fig. ³ is the T2 ellipse diagram of multiple fittings of the breast cell abnormal detection method based on the partial least squares method of the present invention;

Fig. 4 is the histogram of the coefficients of each dependent variable of the breast cell abnormality detection method based on the partial least squares method of the present invention;

Fig. 5 is the regression coefficient table figure of the breast cell abnormal detection method based on the partial least squares method of the present invention;

Fig. 6 is the histogram of the variable projection importance of the breast cell abnormality detection method based on the partial least squares method of the present invention;

Fig. 7 is a chart of prediction results after data processing of the breast cell abnormality detection method based on the partial least squares method of the present invention.

detailed description

As shown in Figure 1, the breast cell abnormal detection method based on the partial least square method of the present invention specifically comprises the following steps:

(1) Import the data set used to build the model in the software SIMCA-P 13.0, and divide the obtained data into two parts, one part is used for model building, and the other part is used for model testing; the indicators of the data set mainly include The 10 characteristic values of radius, texture, perimeter, area, smoothness, compactness, concavity, pit, symmetry and fractal dimension and whether it is a cancerous cell; set the corresponding dependent variable (whether it is a cancerous cell) and independent variables (10 eigenvalues), use the function of the software to select the partial least squares PLS model to standardize the data, extract the principal components of the independent variable and the dependent variable, and increase or decrease the principal components as needed, and fit and build a model;

(2) T ² is the cumulative contribution rate of the sample points to the components. Use the software to draw and observe the T ² ellipse. When the sample points fall within the ellipse, the sample is considered uniform; if any sample point falls outside the ellipse, Then it can be considered that these points are singular points and the value of these singular points is far from the average level of the sample points; identify the abnormal points, use the corresponding function in the software toolbar to remove the abnormal points from the data set, and obtain a new data set and model , fit again and observe the T ² ellipse until there are no abnormal points, then the model at this time is better, so you can check the obtained parameter set in the software, and obtain the expression equation of the dependent variable y whether it is a cancer cell;

(3) Input another part of the data set to be tested, and use the obtained equation to bring the value into the calculation to obtain the predicted value y', and then determine the threshold value as 0.5, and stipulate that the predicted value greater than 0.5 is malignant cells, and the predicted value less than 0.5 For benign cells, compare y' with the original value, record how many results are correctly predicted, and calculate the correct rate of the prediction model.

The specific steps for establishing the partial least squares linear model in the above step (1) are as follows:

(1.1) Standardize the independent variable and dependent variable

The standardized data matrix of X is recorded as E ₀ =(E ₀₁ ,E ₀₂ ,…,E _0p ) _n×p , and the standardized data matrix of Y is recorded as F ₀ =(F ₀₁ ,F ₀₂ ,… , F _0q ) _n×q .

(1.2) Extracting principal components and stepwise regression

Note that t ₁ is the first component of E ₀ , t ₁ =E ₀ w ₁ , w ₁ is the first axis of E ₀ , it is a unit vector, that is ||w ₁ ||=1; record u ₁ is the first component of F ₀ , u ₁ =F ₀ c ₁ , c ₁ is the first axis of F ₀ , it is a unit vector, namely ||c ₁ ||=1; to make t ₁ and u ₁ reaches the maximum, then according to the principal component analysis, there should be:

Var(t ₁ )→max

Var(u ₁ )→max

On the other hand, due to the requirement of regression modeling, _t1 is required to have the greatest explanatory power to u1. According to the canonical correlation analysis, the degree _of correlation between _t1 and _u1 should reach the maximum value, namely:

r(t ₁ ，u ₁ )→max

To sum up, it is required that the covariance of t ₁ and u ₁ reach the maximum value, so as to solve the following optimization problems, namely:

max < E ₀ w ₁ , F ₀ c ₁ >

Therefore, under the conditions of ||w ₁ ||＝1 and ||c ₁ ||＝1, find the maximum value.

According to the book "Linear and Nonlinear Methods for Partial Least Squares Regression" written by Wang Huiwen et al., we can get Then, _w1 is the matrix The eigenvector of is, and the corresponding eigenvalue is θ ₁ is the objective function, find the maximum value, that is, find the matrix The eigenvector w ₁ corresponding to the largest eigenvalue of , and then calculate the component t ₁ and the residual matrix E ₁ :

t ₁ =E ₀ w ₁

in, Matrix can be found in the same way The eigenvector w ₂ corresponding to the largest eigenvalue, t ₂ and the residual matrix E ₂

t ₂ =E ₁ w ₂

in,

Calculating in this way, if the rank of X is A, we finally get:

(1.3) Fitting

Remove a certain sample point i from the sample y, use this part of the sample to extract h components to fit a regression equation, and then bring the excluded sample i into the regression equation of y obtained in the previous step to obtain the fitting value Then define the prediction error sum of squares of y _i as S _{PRESS, hj} , we have

Define the error sum of squares of y _i as S _{SS, hj} , have

For the sample, if the disturbance-containing error of the h component regression equation can be smaller than the fitting error of the h-1 component regression equation to a certain extent, it is considered that adding a component t _h will improve the prediction accuracy; therefore S _{PRESS, h} /S _{SS, the smaller the ratio of h-1} , the better; define the cross validity of component t _h as:

when , the component t _h has a significant contribution.

The concrete steps of above-mentioned step (2) are:

Define the contribution rate of the i-th sample point to the h-th component t _h to find the singular point in the sample, and define the contribution rate for:

In the formula: is the variance of component t _h ; thus, the cumulative contribution rate of sample point i to components t ₁ , t ₂ ,..., t _m can be measured:

In SIMCA-P 13.0, the T ² ellipse can be drawn. If the sample points fall outside the ellipse, these sample points are considered to be singular points, and these singular points can be removed for re-fitting, and this process is repeated until the sample points There are no singularities.

The importance of x _i in explaining Y can be measured by variable projection importance index VIP _j , the larger the value, the more important the independent variable is in explaining Y. The definition of VIP _j is as follows:

Wherein, Rd(Y; t _h )=r ² (y, t _h ); r(y, t _h ) is the correlation coefficient between y and t _h , and w _hj is the jth component of w _h .

Experimental verification:

Dataset introduction

The data set of this experiment comes from Wisconsin Diagnostic Breast Cancer (WDBC), which was published in November 1995 by Dr.William H.Wolberg(General Surgery Dept.University of Wisconsin), W.Nick Street(Computer Sciences Dept.University of Wisconsin ), created by OlviL.Mangasarian(Computer Sciences Dept.University of Wisconsin), donated by NickStreet ^[11] . The data has 569 cell biopsy cases, each case has 32 attributes, which contain the patient's number and cancer diagnosis result, and the other 30 attributes are real measurement values. Among the cancer diagnosis attributes, "B" stands for benign, "M" stands for malignant, and the other 30 attributes are composed of the mean, standard deviation, and maximum value of 10 features of the nucleus. The 10 features are: radius, texture, perimeter, area, smoothness, compactness, concavity, pits, symmetry, and fractal dimension.

data processing

In this experiment, "B" is defined as benign with a value of 0, "M" is defined as malignant with a value of 1 as the dependent variable, ten characteristic attributes are used as independent variables, and half of the data (284 samples) are selected as the establishment of the model, and the remaining average (285 samples) are used for verification, and the data is divided into two groups, respectively benign group: number 1, malignant group: number 2, import the processed data into SIMCA-P 13.0, and set the data to Class ID, with benign and malignant values as dependent variables. After setting, click Finish to complete the data import. Here, the benign group and the malignant group are grouped, and the class of the benign group is set as 1, and the class of the malignant group is set as 2.

Principal component analysis was performed on the data to obtain three principal components. R2X represents the cumulative explanatory ability of the principal components extracted from the X variable to X, R2Y represents the cumulative explanatory ability of the principal components extracted from the Y variable to Y, and Q2 represents the cross validity. After extracting the principal components, they The values of are 0.877, 0.616, 0.603 respectively. Using these three principal components to draw its T ² ellipse diagram, it can be seen that the model built can better distinguish the benign group from the malignant group (as shown in Figure 2). In addition, there are many abnormal points in the sample, which need to be removed, and the model fitting is performed again. After removing outliers many times, the obtained T2 ellipse is as follows (Fig. ³ ).

At this time, R2X=0.744, R2Y=0.757, and Q2=0.75. Click the Coefficient Plot button to view the regression coefficient (Figure 4, Figure 5).

The standardized regression equation is obtained as:

y＝0.941699+radius*0.154609+texture*0.16134+perimeter*0.154876+area*0.147183

+smoothness*0.0290967+compactness*0.0961712+concavity*0.121727

+concave points*0.15144+symmetry*0.0355873-fractal dimension*0.0424221

In the VIP diagram (Fig. 6), it can be seen that the cell pit, perimeter, radius, area and concavity play an important role in explaining whether it is cancerous or not.

After the data processing is completed, the prediction results can be viewed (Figure 7). For the convenience of viewing, the data were organized into Excel (Table 1).

Here, 0.5 is used as the threshold, if the predicted value is greater than 0.5, it is a malignant cell, and if the predicted value is less than 0.5, it is a benign cell. Therefore, it is calculated that among the 357 benign cells, 339 are predicted to be benign; among the 212 malignant cells, 194 malignant cells are predicted, and the correct rate of prediction reaches 93.67%, which can better predict whether the cells are cancerous.

The present invention has rapid detection capability and high detection accuracy, and is used for auxiliary diagnosis of breast cancer. A regression model for breast cell abnormality detection is established through the method of partial least squares regression, and a comparative Good benign and malignant breast cells can better predict whether the cells are cancerous.

Claims (6)

1. a breast cell abnormality detection method based on partial least squares method, is characterized in that, specifically comprises: (1) Divide the data obtained in the data set used to build the model into two parts, one part is used for the establishment of the model, and the other part is used for the detection of the model, and the corresponding dependent variables and independent variables are set to standardize the data , respectively extract the principal components of the independent variable and the dependent variable, fit and build the model; (2) T ² is the cumulative contribution rate of the sample points to the components. Use the software to draw and observe the T ² ellipse diagram, identify abnormal points, remove the abnormal points from the data set, obtain a new data set and model, and fit and observe again T ² ellipse until there are no abnormal points, obtain the parameter set, and obtain the expression equation of the dependent variable y whether it is a cancer cell; (3) Input another part of the data set to be tested, use the obtained equation to bring the value into the calculation, obtain the predicted value y', determine the threshold, stipulate that the predicted value greater than the threshold value is malignant cells, and the predicted value smaller than the threshold value is benign cells , compare y' with the original value, record the correct prediction result, and calculate the correct rate of the prediction model. 2. the breast cell abnormal detection method based on partial least squares method as claimed in claim 1, is characterized in that: described step (1) is to import the data set that is used for building a model by software SIMCA-P 13.0, and described self The variables mainly include radius, texture, perimeter, area, smoothness, compactness, concavity, pit, symmetry and fractal dimension; the dependent variable is whether it is a cancerous cell or not. 3. the breast cell abnormal detection method based on partial least squares method as claimed in claim 1, is characterized in that: in described step (2), when sample points all fall in ellipse, think that sample is even; If have If the sample points fall outside the ellipse, these points can be considered as singular points, and their values are far from the average level of the sample points. 4. the breast cell abnormality detection method based on partial least square method as claimed in claim 1, is characterized in that: the threshold value determined in the described step (3) is 0.5, stipulates that the predicted value greater than 0.5 is a malignant cell, less than 0.5 The predicted value for benign cells. 5. the breast cell abnormal detection method based on partial least squares method as claimed in claim 1, is characterized in that, described step (1) specifically comprises the following steps: (1.1) Standardize the independent variable and dependent variable $\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; ,</span>& \left(\begin{array}{cc}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}\end{array}\right)\end{array}$ $\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}<span\; class="notranslate">\; ,</span>& \left(\begin{array}{cc}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ;</span>& \mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}\end{array}\right)\end{array}$ The normalized data matrix of X is denoted as E ₀ =(E ₀₁ ,E ₀₂ ,...,E _0p ) _n×p , and the normalized data matrix of Y is denoted as F ₀ =(F ₀₁ ,F ₀₂ ,...,F _0q ) _n×q ; (1.2) Extracting principal components and stepwise regression Note that t ₁ is the first component of E ₀ , t ₁ =E ₀ w ₁ , w ₁ is the first axis of E ₀ and is a unit vector, ie ||w ₁ ||=1; note u ₁ is The first component of F ₀ , u ₁ =F ₀ c ₁ , c ₁ is the first axis of F ₀ and is a unit vector, ie ||c ₁ ||=1; the correlation between t ₁ and u ₁ When the degree reaches the maximum, that is, Var(t ₁ )→max Var(u ₁ )→max According to canonical correlation analysis, the degree _of correlation between _t1 and u1 should reach the maximum value, namely: r(t ₁ ，u ₁ )→max When the covariance _{of t1} and u1 reaches its maximum value, that is: max < E ₀ w ₁ , F ₀ c ₁ > $\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}\\ {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right.$ Under the condition of ||w ₁ ||＝1 and ||c ₁ ||＝1, find the maximum value; _w1 is the matrix The eigenvector of is, and the corresponding eigenvalue is θ ₁ is the objective function, its maximum value, that is, to find the matrix The eigenvector w ₁ corresponding to the largest eigenvalue of , find the component t ₁ and the residual matrix E ₁ : t ₁ =E ₀ w ₁ ${\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}$ in, Find the matrix in the same way The eigenvector w ₂ corresponding to the largest eigenvalue, t ₂ and the residual matrix E ₂ t ₂ =E ₁ w ₂ ${\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}$ in, Calculating in this way, if the rank of X is A, we finally get: $\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; A</span>}\mathrm{<span\; class="notranslate">\; k</span>}}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; )</span>\end{array}<span\; class="notranslate">\; ;</span>$ (1.3) Fitting Remove a certain sample point i from the sample y, use this part of the sample to extract h components to fit a regression equation, and then bring the excluded sample i into the regression equation to obtain the fitted value Then define the sum of squared prediction errors of y _i as S _{PRESS, hj} , that is ${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; P</span>}\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; E.</span>}\mathrm{<span\; class="notranslate">\; E.</span>}\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$ Define the error sum of squares of y _i as S _{SS, hj} , namely ${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; .</span>$ 6. the breast cell abnormal detection method based on partial least squares method as claimed in claim 1, is characterized in that, described step (2) concrete steps are: Define the contribution rate of the i-th sample point to the h-th component t _h to find the singular point in the sample, and define the contribution rate for: ${\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span>$ In the formula is the variance of component t _h , and measures the cumulative contribution rate of sample point i to components t ₁ , t ₂ ,…, t _m : ${\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\underset{\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ;</span>$ The T ² ellipse was drawn in the SIMCA-P 13.0 software, and the sample points falling outside the ellipse were the singular points, and the singular points were removed for re-fitting until there were no singular points in the sample.