Biomedical image classification is an important point of any automated diagnostic system. The disadvantage of existing studies is the use of a limited number of machine learning algorithms for classification, data segmentation. The impact of image quality on classification and especially segmentation results is particularly noticeable when processing biomedical images. Since the nuclei of cells in biomedical images are characterized by the complexity of processing, the use of one or two algorithms for all types of images is insufficient. In this work, modern machine learning algorithms with and without a teacher are used to classify the quantitative characteristics of cell nuclei. In this work, the use of an ensemble approach with a combination of several algorithms and the use of the soft, hard voting principle is proposed. The proposed solution allowed to obtain an accuracy of 99.22% for the training sample and 83.12% for the test sample.
Methods for classifying biomedical images are key to modern medical diagnostics, since classification can increase the automation of processes and increase the accuracy of detecting pathological changes in cells. However, the efficiency of classification of individual models may decrease due to the influence of noise, artifacts, or significant variability of the data. To solve these problems, ensemble machine learning methods, such as Random Forest, Gradient Boosting, etc., are increasingly used.
The relevance of suction is due to the ability to combine the results of many weak models into a mixed hybrid predictor. This approach provides increased accuracy and reliability of classification. Also, the use of several algorithms provides a reduction in errors and resistance to changes in data. The use of such methods in the classification of cytological, histological, immunohistochemical images is a promising direction for improving automatic diagnostics and decision support in biomedical research and clinical practice.
Calculation of quantitative characteristics of cell nuclei on immunohistochemical, histological and cytological images is relevant, as it allows for an objective assessment of morphological changes accompanying pathological processes. The main parameters that describe cell nuclei are: area, perimeter, circumference, length of the major and minor axes. Automated quantitative analysis increases the objectivity of the assessment and contributes to the development of computer-aided decision-making systems in medical practice. Another advantage of using such an approach to diagnosis is the absence of the need to process large-sized images with a large noise component and erroneous data. The use of quantitative characteristics for classification allows you to speed up the classification process and avoid the need for large processing resources. Hard voting and soft voting algorithms play an important role in increasing the accuracy and reliability of classification in machine learning tasks. Their use allows for more efficient combination of the results of a specific set of basic models, which in turn provides more accurate forecasting.
The object of the study is the quantitative characteristics of biomedical image kernels.
The subject of the study is an ensemble method for classifying quantitative characteristics, which uses hard voting and soft voting.
The purpose of this work is to develop an ensemble method for classifying quantitative characteristics of biomedical image kernels. A feature of the proposed work is the use of the PCA algorithm to increase the accuracy of classification in combination with the ensemble method.
The following tasks were performed in this work: 1. an analysis of machine learning algorithms for classifying quantitative characteristics of objects was performed; 2. an analysis of approaches to calculating quantitative characteristics of cell nuclei in biomedical images was performed; 3. a comparative analysis of machine learning algorithms using ensemble methods to obtain the best result was performed.
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The above analysis demonstrates the relevance of the application of ensemble methods in medicine, in particular in the tasks of classifying data in the form of quantitative characteristics of cell nuclei.
To obtain information about the quantitative characteristics of cell nuclei, image processing was performed using preprocessing and segmentation. The main characteristics of cells are: 1. 2. 3.
area; perimeter; length of the main and lateral axes; 2.
After the calculations are performed, the results are stored in a csv file for further processing by the classifier.
Classification Algorithms
Ensemble learning helps improve the performance of a machine learning model by combining multiple models. This approach allows for better prediction performance compared to a single model. The main causes of training errors are noise, bias, and variance. Ensemble helps minimize these factors.
Bagging is the application of the Bootstrap procedure to a high-variance machine learning algorithm, typically a decision tree. Boosting is a sequential process where each subsequent model tries to correct the errors of the previous model. Subsequent models depend on the previous model.
Bagging and Boosting reduce the variance of a single estimate because they combine multiple estimates from different models.
Logistic Regression
The essence of regression analysis is to analytically or experimentally determine the coefficients of the features of objects in such a way as to minimize the total error between the values of the model function and the experimental data for the entire input sample.
Logistic regression is a type of multiple regression used to study the relationship between a
binary or categorical outcome and several influencing factors. The paper [
The objective function of linear regression is defined as the minimization of the mean square
error between the predicted and actual values of the observed parameter [
F = 1 n
∑ ( ^yi - yi)2 → min n i=1 where ^yi – predicted (analytical) value, linear concerning the desired coefficients; yi – the actual value; n – data sample length.
General linear regression model:
m ^y = w0 + w1 x1 + w2 + … + wm xm = ∑ wi xi = W T X ϵ RI ,
i=0 where W T =( w0 , w1 , … , wm ) - weights of object features; wi ϵ RI; X=(1,x1,x2 , … , xm) – object predictors; m – number of features of the object; Τ – transposition symbol.
Random Forest
Random forest is an ensemble machine learning method used to solve classification, regression,
and other types of prediction problems. Its working principle is to create a set of decision trees
during model training, after which a class is selected for classification based on the majority of
votes. For regression, the average value of the predictions of all trees is calculated. The algorithm is
given in [
Algorithm for building a committee:
Generating a random subsample with repetition of size n from the training sample; Randomly select m predictors (features) from M; (1) (2)
The decision tree is constructed by selecting the features based on which the partition is performed, not from all M features, but only from m randomly selected ones; Dividing the trait X into two classes X i ≥ Si and X i < Si; Measure homogeneity in two new classes using the Gini criterion; Take the following value of the "split point" Si feature Х, for which maximum class homogeneity is achieved; The tree is built until the subsample is fully used without applying the pruning procedure; Returning to step 1, generate a new sample and repeat steps 2–4 to build the next tree.
Classification of objects is carried out by voting: each tree in the ensemble assigns the object to one of the classes, and the class that received the most significant number of votes from the trees is chosen.
Gradient Boosting
Gradient Boosting is a machine learning technique used to solve classification and regression problems. The basic idea is that a collection of weak models can produce a more accurate predictor when working together. Gradient boosting combines several weak models to form a single strong model. Although algorithms with fast learning can be challenging to optimize, their accuracy is significantly improved by sequential coupling. In contrast, models with a slower learning curve adapt better to statistical patterns in the data. Weak learners are added in such a way that each subsequent learner takes into account the residuals obtained in the previous stage during the model development process. The final model combines the results of all stages, forming a strong learner. The residuals are calculated using a loss function.
Hard voting is a simple algorithm that can be used to combine predictions from multiple classifiers. The algorithm works by first predicting each classifier. The ensemble prediction is then simply the majority vote of the individual classifiers.
The simplicity of hard voting makes it a popular choice for machine learning practitioners. Hard voting is also very efficient and can often outperform other ensemble learning algorithms. Finally, hard voting can be used with any classifier, making it a versatile tool. Hard voting can also be less robust to noise in the data. This is because hard voting is based on the majority votes of the individual classifiers. If the data is noisy, it is more likely that the majority of votes will be wrong.
Predict the class label ^y by the majority vote of each classifierC j where X A is the characteristic function [C j ( x ) = i ϵ A ,]and A is the set of unique class labels Soft Voting ^y = mode {C1 ( x ) , C2 ( x ) , … , Cm ( x )} ^y = mode {0 ,0 ,1}= 0
m ^y = arg max ∑ w j X A ( C j ( x ) = i ) j =1 (3) (4) (5) For example, if two classes provided zero and one class provided 1:
In addition to simple majority voting as described above, a weighted majority vote can be calculated by relating the weight:
Soft voting is an algorithm that can be used to combine the predictions of multiple classifiers based on their probabilities. The algorithm works by first assigning a probability to each class. The ensemble prediction is then simply the class with the highest overall likelihood.
Soft voting has several advantages over hard voting. First, it is more accurate than hard voting. Second, it is more robust to noise in the data. Third, it can be used with any classifier where w j is the weight that can be assigned to the jth classifier.
Using uniform weights, we calculate the average probabilities
m ^y = arg max ∑ w p
j ij j =1 ^y = arg max [ p (i0 | X ) , p (i0 | X )] (6) (7)
A statistical description of the parameters of cytological examination of quantitative characteristics of cell nuclei is given in Figure 3.
The correlation matrix of the input data is shown in Figure 4. The results of the classifiers without PCA are given in Table 2.
The correlation between classes after PCA is shown in Figure 5. The above description allows us to evaluate the input data better and understand the range of values for each of the parameters after PCA processing.
The correlation matrix of the input data after PCA is shown in Figure 6.
The classification results after using data reduction are shown in Table 3. Voting hard Decission Tree SVM 58.31 61.91 20.85 73.4 38.03 47.35 82.94 75.32 78.12 99.75 95.3 86.38 97.81 97.02 99.86
As a result of the comparative analysis, it was found that the ensemble method based on the random_forest and bagging_classifier algorithms showed the best results compared to other classical data classification algorithms.
Based on the experimental approach, it was also found that the use of data reduction significantly increases the classification accuracy.
The classification accuracy using ensembles is 99.22% for the training sample and 83.12% for the test sample. The worst indicators were shown by approaches based on neural networks, the support vector method, and Adaboost.
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