Foam flotation working condition recognition method based on multi-target hybrid feature selection

Abstract

The embodiment of the present disclosure provides a froth flotation working condition recognition method based on multi-target hybrid feature selection, which belongs to the technical field of data recognition, and specifically comprises: extracting the data set to be processed in the froth flotation working condition for data preprocessing; sorting all features according to marginal contribution values; obtaining a preliminary screening feature subset; calculating the initial weight of each feature in the preliminary screening feature subset; setting the maximum number of iterations and the related parameters of the binary state transition algorithm, generating a plurality of candidate feature subsets according to the initial weight and the preliminary screening feature subset, selecting all non-dominated solutions in the candidate feature subset to form an initial Pareto optimal solution set; forming a target function matrix; processing the target function matrix through a two-dimensional sorting strategy, updating the initial Pareto optimal solution set; repeating steps 6 to 7 until the number of iterations is equal to the maximum number of iterations, and outputting X best as the final Pareto optimal solution set. Through the scheme of the present disclosure, the recognition efficiency and accuracy are improved.

Description

TECHNICAL FIELD

[0001] The embodiment of the present disclosure relates to the technical field of data recognition, in particular to a froth flotation working condition recognition method based on multi-objective hybrid feature selection. BACKGROUND

[0002] At present, ore dressing is an important link in mineral resource processing, and its purpose is to separate useful minerals from raw ore. Froth flotation is one of the most widely used ore dressing methods, and fine control of the flotation process is directly related to the quality of the final concentrate product. The visual features of the froth flotation bubble surface are direct indicators of the flotation process and process indicators, and are the main basis for adjusting the flotation production of the ore dressing plant. However, due to the long flotation process, unclear internal mechanism, too many influencing factors, too many and nonlinear variables involved, and the inability to monitor the process indicators online, for a long time, the flotation process has relied on manual observation of the surface froth bubble state of the flotation tank to determine the flotation condition to complete the on-site operation. However, the manual method has the problems of great subjectivity and randomness, cannot quantify the operation basis, the control precision is highly dependent on manual experience, and the operation process is difficult to form a corresponding specification, etc., which easily causes frequent fluctuations in the flotation production indicators, serious loss of raw materials, large consumption of reagents, low resource recovery rate, etc.

[0003] In recent years, using a machine vision method instead of manual recognition of the surface froth bubble state is a trend to realize the automation of the flotation process. In order to improve the recognition effect based on the machine vision method, researchers have extracted more and more features from the froth image. However, due to the lack of prior knowledge, it cannot be guaranteed that all the extracted features are beneficial to the working condition recognition task, that is, there are a considerable number of irrelevant and redundant features, which not only increase the computational complexity of the recognition method, but sometimes even lead to a decrease in the recognition effect. Therefore, it is necessary to perform feature selection on the original features to select the features most relevant to the working condition recognition, so as to improve the accuracy and real-time performance of the working condition recognition.

[0004] The purpose of feature selection is to obtain a subset by selecting relevant features of the classification task, so as to improve the recognition accuracy and reduce the training time. Generally speaking, an optimal feature subset should have the least number of features, but can produce the best recognition performance. However, these two goals are in conflict with each other, the more features used to build a classifier, the more expensive the cost of obtaining and computing the features, and the smaller the classification error rate is usually. The current feature selection method assumes that the feature acquisition is free, and does not consider the feature quantity target. It is easy to cause the problem that the final solution cannot be implemented due to the excessively high cost or difficulty of covering most scenarios of a certain feature.

[0005] Therefore, there is an urgent need for a froth flotation working condition recognition method based on multi-objective hybrid feature selection with high recognition efficiency and accuracy. SUMMARY

[0006] Therefore, the method for identifying the froth flotation working condition based on multi-target hybrid feature selection is provided, and at least part of the problems of poor recognition efficiency and accuracy in the prior art are solved.

[0007] The method for identifying the froth flotation working condition based on multi-target hybrid feature selection provided by the embodiments of the present disclosure comprises:

[0008] Step 1, extracting a data set to be processed in the froth flotation working condition for data preprocessing;

[0009] Step 2, calculating the marginal contribution value of each feature in the preprocessed data set according to the marginal contribution criterion, and sorting all features according to the marginal contribution value;

[0010] Step 3, calculating the cumulative contribution according to the sorting of the features, retaining the features with cumulative contribution greater than the threshold, and eliminating the remaining low-contribution features to obtain a preliminary screening feature subset;

[0011] Step 4, calculating the initial weight of each feature in the preliminary screening feature subset;

[0012] Step 5, setting the maximum number of iterations and the related parameters of the binary state transition algorithm, generating a plurality of candidate feature subsets according to the initial weight and the preliminary screening feature subset, and selecting all non-dominated solutions in the candidate feature subsets to form an initial Pareto optimal solution set X best ;

[0013] Step 6, generating a plurality of candidate solutions according to the initial Pareto optimal solution set X best by using the state transition operator, and calculating the classification error rate of each candidate solution by using the preset classifier, then calculating the number of features of each candidate solution to form a target function matrix F;

[0014] Step 7, processing the target function matrix by a two-dimensional sorting strategy, and updating the initial Pareto optimal solution set X best ;

[0015] Step 8, increasing the number of iterations by 1, repeating steps 6 to 7 until the number of iterations is equal to the maximum number of iterations, and outputting X best as the final Pareto optimal solution set.

[0016] According to a specific implementation mode of the embodiments of the present disclosure, the step 1 specifically comprises:

[0017] The original data set containing features and labels is obtained from historical data as the data set to be processed, and the data set to be processed is preprocessed, including removing abnormal values, missing value samples and samples without labels caused by error operation in the sampling process, and normalizing all features, and the normalization formula is as follows:

[0018]

[0019] where X represents the original data set, X min represents the minimum value of the original data set on each feature, and similarly, X max represents the maximum value of the original data set on each feature, and X' is the normalized data set.

[0020] According to a specific implementation manner of the embodiment of the present disclosure, the calculation formula of the marginal contribution value is:

[0021]

[0022]

[0023] diff(S, xj) = (val(S U {xj}) - val(S))

[0024] where φ(x j ) is the marginal contribution value of the jth feature x j , M is the total number of features, S is a certain feature combination, and val(S) represents the model output value under the feature combination S.

[0025] According to a specific implementation manner of the embodiment of the present disclosure, the step 4 specifically includes:

[0026] The marginal contribution value of each feature in the preliminary screening feature subset is normalized as the initial weight corresponding to the feature, and the normalization formula is as follows:

[0027]

[0028] where W is a weight vector composed of the marginal contribution values of the preliminary screening feature subset, w j is the weight of the jth feature, which is also the marginal contribution value of the feature, w i ' represents the normalized weight, max(W) is the maximum value of the weight vector, and min(W) represents the minimum value of the weight vector.

[0029] According to a specific implementation manner of the embodiment of the present disclosure, the step 5 specifically includes:

[0030] Step 5.1, binary coding is performed on the solution of feature selection;

[0031] Step 5.2, the feature selection problem in the froth flotation process is modeled as the following multi-objective optimization problem:

[0032] min Err(X)

[0033] min‖X‖0

[0034] s.t. X={x1,x2,…,x n}

[0035] 1≤‖X‖0≤m

[0036] where ||X||0 is the 0-norm of X, representing the number of 1 in X, i.e., the number of selected features, m is the number of features in the initial feature subset, and Err(X) is the classification error rate corresponding to the solution X;

[0037] Step 5.3, initialize a plurality of feature subsets according to the initial weights of the features in the initial feature subset, and obtain an initial non-dominated solution set by evaluation and selection. The method for initializing a solution is as follows:

[0038]

[0039]

[0040] where x i represents the selected state of the i-th feature, rand() is a random number belonging to [0, 1] and obeying a uniform distribution, p is the selection probability of a feature with a high initial weight, q is the selection probability of a feature with a low initial weight, X h is a set of P d high initial weight features, P d is a set of the remaining low initial weight features, and P l is a proportion coefficient of the high initial weight features set by a user.

[0041] Step 5.4, calculate the two objective functions of all initial solutions, i.e., Err(X) and ||X||0, by using an evaluation function, and then obtain all non-dominated solutions by using a two-dimensional sorting strategy, to obtain an initial Pareto optimal solution set X best .

[0042] According to a specific implementation manner of the embodiment of the present disclosure, the step 6 specifically includes:

[0043] Step 6.1, generate SE candidate solutions for each solution in X best by using a state transition operator, and the formula of the state transition operator is as follows:

[0044]

[0045]

[0046] where x i represents the selected state of the i-th feature, r i represents the probability of the i-th feature, and w′ ia normalized weight representing the ith feature, a negation symbol, w' min a minimum value in the normalized weights, w' max a maximum value in the normalized weights;

[0047] Step 6.2, training the classification error rate of each candidate solution by using the preset classifier, and then calculating the number of features of each candidate solution;

[0048] Step 6.3, obtaining the objective function matrix F of each candidate solution according to the objective function corresponding to the classification error rate and the number of features of each candidate solution.

[0049] According to a specific implementation manner of the embodiment of the present disclosure, the step 7 specifically comprises:

[0050] Step 7.1, sorting the objective function matrix F in descending order according to the number of features as the first key and the classification error rate as the second key to obtain F';

[0051] Step 7.2, initializing the Pareto optimal solution set X best to be empty, and adding F'0to X best , setting the global minimum value of the classification error rate

[0052] Step 7.3, sequentially traversing each candidate solution, if the number of features of the current solution F' i is same as that of the previous solution F' i-1 or the classification error rate of F' i is greater than or equal to the global error rate gErr, the current solution is skipped, otherwise, the current solution is added to X best , and gErr is updated as f i 2 ;

[0053] Step 7.4, until all candidate solutions are traversed, X best is the initial Pareto optimal solution set updated in this iteration process.

[0054] The froth flotation working condition recognition scheme based on multi-target hybrid feature selection in the embodiments of the present disclosure includes: step 1, extracting a data set to be processed in the froth flotation working condition for data preprocessing; step 2, calculating the marginal contribution value of each feature in the preprocessed data set according to the marginal contribution criterion, and sorting all features according to the marginal contribution value; step 3, calculating the cumulative contribution according to the sorting of the features, retaining the features with cumulative contribution greater than the threshold, and eliminating the remaining low-contribution features to obtain a preliminary screening feature subset; step 4, calculating the initial weight of each feature in the preliminary screening feature subset; step 5, setting the maximum number of iterations and the related parameters of the binary state transition algorithm, generating a plurality of candidate feature subsets according to the initial weight and the preliminary screening feature subset, and selecting all non-dominated solutions in the candidate feature subsets to form an initial Pareto optimal solution set X best ; step 6, generating a plurality of candidate solutions by using a state transition operator according to the initial Pareto optimal solution set X best , and then calculating the feature quantity of each candidate solution by training and calculating the classification error rate of each candidate solution by using a preset classifier, to form a target function matrix F; step 7, processing the target function matrix by a two-dimensional sorting strategy to update the initial Pareto optimal solution set X best ; step 8, increasing the number of iterations by 1, repeating steps 6 to 7 until the number of iterations is equal to the maximum number of iterations, and outputting X best as the final Pareto optimal solution set.

[0055] The beneficial effects of this disclosure are as follows: Firstly, the concept of marginal contribution from game theory, known as the Shapley value, is introduced and combined with the Filter method in feature selection to perform a relatively coarse screening of the original features of the dataset. The main purpose is to quickly eliminate a large number of irrelevant and redundant features by using the marginal contribution of features as the evaluation criterion, retaining features that constitute the initial screening feature subset, and calculating the initial weights of each feature in the initial screening subset. Then, the feature selection problem is modeled as a multi-objective optimization problem, considering both the number of features and classification accuracy as objective functions. In this process, the Wrapper method is used, employing an intelligent optimization algorithm as a search strategy to accelerate the solution process. A binary state transition algorithm is used to iteratively generate multiple candidate feature subsets of the initial screening feature subset, calculating the number of features and classification accuracy of each candidate feature subset, and continuously updating the Pareto optimal solution set through a fast two-dimensional sorting strategy. After the algorithm iterations, it outputs a Pareto optimal solution set consisting of multiple non-dominated solutions, where each Pareto non-dominated solution represents a different selection scheme. Furthermore, when generating candidate solutions, the binary state transition algorithm utilizes the normalized weights of the initial screening feature subset to design a heuristic operator, which generates potentially promising candidate solutions, ensuring the reliability of the selected feature subset. Simultaneously, considering the characteristics of multi-objective feature selection problems, a two-dimensional sorting strategy is proposed to replace the fast non-dominated sorting in traditional multi-objective optimization algorithms, significantly reducing time complexity, accelerating the algorithm's running speed, and improving recognition efficiency and accuracy. Attached Figure Description

[0056] To more clearly illustrate the technical solutions of the embodiments of this disclosure, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0057] Figure 1 A flowchart illustrating a method for identifying foam flotation conditions based on multi-objective hybrid feature selection, provided in an embodiment of this disclosure;

[0058] Figure 2 A schematic diagram of the Pareto front formed by the objective function values ​​corresponding to multiple feature subsets provided in the embodiments of this disclosure;

[0059] Figure 3 This is a visualization result diagram in two-dimensional space of various feature subset schemes provided in the embodiments of this disclosure. Detailed Implementation

[0060] The embodiments of this disclosure will now be described in detail with reference to the accompanying drawings.

[0061] Following, the embodiments of the present disclosure are described through specific examples, and other advantages and effects of the present disclosure can be easily understood by those skilled in the art from the disclosure. Obviously, the described embodiments are only a part of the embodiments of the present disclosure, rather than all the embodiments. The present disclosure can also be implemented or applied by other different specific embodiments, and various modifications or changes can be made to the details in the specification without departing from the spirit of the present disclosure. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict. Based on the embodiments in the present disclosure, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present disclosure.

[0062] It should be noted that various aspects of the embodiments described below are within the scope of the appended claims. It should be apparent that the aspects described herein can be embodied in a wide variety of forms and that any specific structure and / or function described herein is merely illustrative. Based on the teachings provided herein one skilled in the art should appreciate that an aspect described herein can be implemented independently of any other aspects and that an aspect can be implemented both as any number of software, firmware, and / or hardware structures.

[0063] It should also be noted that the figures provided in the following embodiments are only schematically illustrating the basic concepts of the present disclosure, and only the components related to the present disclosure are shown in the figures, not the number, shape and size of the components when actually implemented, and the shapes, numbers and proportions of the components when actually implemented can be arbitrarily changed, and the layout of the components can also be more complex.

[0064] In addition, in the following description, specific details are provided in order to facilitate a thorough understanding of the examples. However, one skilled in the art will understand that the aspects described can be practiced without these specific details.

[0065] The embodiments of the present disclosure provide a froth flotation working condition recognition method based on multi-target hybrid feature selection, which can be applied to the froth flotation working condition recognition process of the mineral resource processing scene.

[0066] Referring to Figure 1 A flowchart of a froth flotation working condition recognition method based on multi-target hybrid feature selection provided by the embodiments of the present disclosure is shown. As Figure 1 shown, the method mainly includes the following steps:

[0067] Step 1, extract the data set to be processed in the froth flotation process for data preprocessing;

[0068] Further, the step 1 specifically comprises:

[0069] The original data set containing features and labels is obtained from historical data as the data set to be processed, and the data set to be processed is preprocessed, including removing abnormal values, missing value samples and unlabeled samples caused by error operation in the sampling process, and normalizing all features, and the normalization formula is as follows:

[0070]

[0071] Where X represents the original data set, X min represents the minimum value of the original data set on each feature, and similarly, X max represents the maximum value of the original data set on each feature, and X' is the normalized data set.

[0072] In specific implementation, the original sample data set containing features and labels can be obtained from historical data, and the original data set is preprocessed, including removing abnormal values, missing value samples and unlabeled samples caused by error operation in the sampling process. And all features are normalized to prevent inconsistent dimensions from causing additional model preference relationships.

[0073] For example, the extracted D N×M is a set of data collected from the gold antimony froth flotation process, wherein the sample N = 672, the feature M = 38, containing 8 different categories, the data preprocessing includes removing missing values and abnormal values, and the entire data set is normalized to eliminate dimension difference. The division of training set and test set, 480 samples are selected as the training set, and the remaining 192 samples are selected as the test set; the classifier selects support vector machine (SVM), and the multi-classification mode is one-to-one.

[0074] Step 2, according to the marginal contribution criterion, the marginal contribution value of each feature in the preprocessed data set is calculated, and all features are sorted according to the marginal contribution value;

[0075] Optionally, the calculation formula of the marginal contribution value is:

[0076]

[0077]

[0078] diff(S,xj)=(val(S∪{xj})-val(S))

[0079] Where φ(x j ) is the jth feature xj the marginal contribution value, M is the total number of features, S is a certain feature combination, and val(S) represents the model output value under the feature combination S.

[0080] In implementation, the Shapley values of each feature in the data set can be calculated according to the marginal contribution in game theory as an evaluation standard, and the features are sorted according to the marginal contribution values (Shapley values). In this embodiment, only the absolute value of the Shapley value is considered, and whether it is a positive or negative influence is not considered, and then a sorted feature subset is obtained. Then the marginal contribution of the features is accumulated from large to small until the accumulated contribution value exceeds the threshold value, and the remaining features are discarded, and all the accumulated features constitute the preliminary screening feature subset. The marginal contribution represents the contribution of the feature value to the prediction, and the calculation formula is as follows:

[0081]

[0082]

[0083] diff(S,x j )=(val(S∪{x j})-val(S))

[0084] where φ(x j ) is the Shapley value of the jth feature x j , M is the total number of features, S is a certain feature combination, and val(S) represents the model output value under the feature combination S. For a certain feature x j , the contribution value needs to be calculated for all possible feature combinations (including different orders), and then the weighted sum is obtained.

[0085] Step 3, according to the sorting of the features, the cumulative contribution is calculated, the features with cumulative contribution greater than the threshold value are retained, and the remaining low-contribution features are removed to obtain a preliminary screening feature subset;

[0086] In implementation, the marginal contribution of the Shapely value can be accumulated from large to small until the cumulative contribution reaches the threshold value. In this embodiment, the threshold value is 90% of the total contribution. Then the remaining low-contribution features are removed to obtain a preliminary screening feature subset.

[0087] Starting from an empty set, the feature ranked 1 is added to the empty set to form the first feature subset. Then, according to the ranking, the feature ranked i is selected from the ranked feature set to join the i-1th feature subset to form the ith feature subset, and the marginal contribution of the ith feature is accumulated. Until the cumulative shared contribution reaches the threshold value, the current feature set is retained, and the remaining low-contribution features are removed to obtain a preliminary screening feature set.

[0088] Step 4, calculate the initial weight of each feature in the initial screening feature subset;

[0089] On the basis of the above embodiment, the step 4 specifically comprises:

[0090] The marginal contribution value of each feature in the initial screening feature subset is normalized as the corresponding initial weight, and the normalization formula is as follows:

[0091]

[0092] Wherein, W is a weight vector composed of the marginal contribution values of the initial screening feature subset, w j is the weight of the jth feature, which is also the marginal contribution value of the feature, w i ' represents the normalized weight, max(W) is the maximum value of the weight vector, and min(W) represents the minimum value of the weight vector.

[0093] In specific implementation, after obtaining the initial screening feature subset, the feature weight of each feature needs to be calculated, which plays a crucial role in the subsequent initialization and candidate solution generation. In the present application, the Shapley value of the feature is considered as the embodiment of its importance, so the normalized Shapley value is taken as the feature weight of the feature. The normalization formula is as follows:

[0094]

[0095] Wherein W is a weight vector composed of the Shapley values of the initial screening feature subset, w j is the weight of the jth feature, which is also the Shapley value of the feature, w i ' represents the normalized weight, max(W) is the maximum value of the weight vector, and min(W) represents the minimum value of the weight vector.

[0096] Step 5, set the maximum number of iterations and the related parameters of the binary state transition algorithm, generate a plurality of candidate feature subsets according to the initial weight and the initial screening feature subset, and select all non-dominated solutions in the candidate feature subset to form an initial Pareto optimal solution set X best .

[0097] Further, the step 5 specifically comprises:

[0098] Step 5.1, binary coding of the solution of feature selection;

[0099] Step 5.2, modeling the feature selection problem in the froth flotation process into the following multi-objective optimization problem:

[0100] min Err(X)

[0101] min‖X‖0

[0102] s.t. X = {x1, x2,..., xm}, ||X||0 = m n}

[0103] 1 ≤ ||X||0 ≤ m

[0104] where ||X||0 is the 0-norm of X, representing the number of 1 in X, i.e. the number of selected features, m is the number of features in the pre-screened feature subset, and Err(X) is the classification error rate corresponding to the solution X;

[0105] Step 5.3, initialize a plurality of feature subsets according to the pre-screened feature subset and the initial weights of the features thereof, and obtain an initial non-dominated solution set by evaluation and selection. The method of initializing a solution is as follows:

[0106]

[0107]

[0108] wherein, x i represents the selected state of the i-th feature, rand() is a random number belonging to [0, 1] obeying a uniform distribution, p is the selection probability of a high initial weight feature, q is the selection probability of a low initial weight feature, X h is a set of P d m features with high initial weights, P d is a proportion coefficient of high initial weight features set by a user, and X l is a set of remaining low initial weight features.

[0109] Step 5.4, calculate the two objective functions of all initial solutions, i.e. Err(X) and ||X||0, by using the evaluation function, and then obtain all non-dominated solutions by using a two-dimensional sorting strategy, to obtain an initial Pareto optimal solution set X best .

[0110] In specific implementation, the pre-screened feature subset can be further subjected to more refined feature selection. First, for the convenience of subsequent discussion and solution, the solution of feature selection is binary coded, with 0 representing that the feature is not selected and 1 representing that the feature is selected. The general form is as follows:

[0111] X = {x1,..., xm}, xi e {0, 1}, i = 1,..., M M . i

[0112] wherein x i = 0 represents that the i-th feature is not selected, and x i = 1 represents that the i-th feature is not selected. X is the state set of all features, and is also the form of the solution of the feature selection problem. ​

[0113] Then, the feature selection problem in the froth flotation process is modeled as a multi-objective optimization problem as follows:

[0114] minErr(X)

[0115] min‖X‖0

[0116] s.t.X={x1,x2,…,x n}

[0117] 1≤‖X‖0≤m

[0118] where X0is the 0-norm of X, representing the number of 1s in X, i.e., the number of selected features; m is the number of features in the pre-screened feature subset; Err(X) is the classification error rate corresponding to the solution X.

[0119] Next, the multi-objective problem is solved by using a binary state transition algorithm, including the following steps: initialization of the non-dominated solution set, generation of candidate solutions, evaluation of candidate solutions, and updating of the non-dominated solution set.

[0120] First, a plurality of feature subsets are initialized according to the pre-screened feature subset and the initial weights of the features, and an initial non-dominated solution set is obtained by evaluation and selection. The method of initializing a solution is as follows:

[0121]

[0122]

[0123] where x i i represents the selected state of the i-th feature, rand() is a random number belonging to [0,1] that follows a uniform distribution; p is the selection probability of high initial weight features, and q is the selection probability of low initial weight features; X h is a set of P d m features with high initial weights, P d is a proportion coefficient of high initial weight features set by the user; and X l is a set of remaining low initial weight features.

[0124] Then, the two objective functions of all initial solutions, i.e., Err(X) and X0, are calculated by the evaluation function, and all non-dominated solutions are obtained by using a two-dimensional sorting strategy to obtain the initial Pareto non-dominated solution set X best . The algorithm is set to retain n Pareto non-dominated solutions in each iteration process. If the number of Pareto non-dominated solutions obtained in a certain iteration is less than n, then n is selected from all non-dominated solutions on the premise of selecting the non-dominated solutions, and n is randomly selected from the dominated solutions to meet the requirement. If it is greater than n, then n is randomly selected from the non-dominated solutions as the initial solution for the next iteration.

[0125] For example, as shown in the following steps:

[0126] S51: Set the binary state transition algorithm sampling intensity SE = 20, the maximum number of iterations T = 300, the current number of iterations t = 1, the number of retained Pareto non-dominated solutions in each round n = 5, and the number of candidate solution operators L = 5. Set the completion strategy when the number of Pareto non-dominated solutions is less than n to random sampling filling.

[0127] S52: Generate multiple candidate feature subsets according to the normalized initial weights and the preliminary screening feature subset. The initialization method for generating a candidate solution is as follows:

[0128]

[0129]

[0130] In the formula, x i represents the selected situation corresponding to the i-th feature, rand() is a random number belonging to [0, 1] obeying uniform distribution; p is the selection probability of high initial weight features, and q is the selection probability of low initial weight features; X h is a set of P d high initial weight features, m is the number of features in the preliminary screening feature subset, P d is the proportion coefficient of high initial weight features set by the user; X l is a set of remaining low initial weight features.

[0131] In this embodiment, the proportion coefficient P d = 0.4, that is, 40% of the features in the preliminary screening feature subset with higher weight size are considered to be high weight features, denoted as X h , and the remaining 60% are considered to be low weight features, denoted as X l ; p = 0.75, that is, high weight features have a 75% probability of being selected. q = 0.4 represents that low weight features have only a 40% probability of being selected.

[0132] S53: Calculate the classification error rate and the number of features of all candidate solutions to form a target function matrix F, obtain a Pareto non-dominated solution set by using a two-dimensional sorting strategy, and then retain n solutions to obtain an initial Pareto optimal solution set X best . If the number of Pareto non-dominated solutions is less than n, randomly sample the remaining dominated solutions to complete to n.

[0133] Step 6: Use the state transition operator to generate multiple candidate solutions according to the initial Pareto optimal solution set X best , and use the preset classifier to train and calculate the classification error rate of each candidate solution, and then calculate the number of features of each candidate solution to form a target function matrix F.

[0134] On the basis of the above-mentioned embodiments, the step 6 specifically comprises:

[0135] Step 6.1, generating SE candidate solutions for each solution in X via a state transition operator, the formula of the state transition operator being as follows: best

[0136]

[0137]

[0138] wherein x i represents a selected case corresponding to the i-th feature, r i represents a probability of the i-th feature, w′ i represents a normalized weight of the i-th feature, represents a negation symbol, w′ min is a minimum value in the normalized weights, and w′ max is a maximum value in the normalized weights.

[0139] Step 6.2, training and calculating a classification error rate for each candidate solution by using a preset classifier, and then calculating a feature quantity of each candidate solution;

[0140] Step 6.3, obtaining a target function matrix F of each candidate solution according to a target function corresponding to the classification error rate and the feature quantity of each candidate solution.

[0141] In specific implementation, the process of generating candidate solutions can generate a larger number of candidate solutions according to the current Pareto non-dominated solution set by different operators, and the advantages and disadvantages of the candidate solutions directly affect the solving efficiency of the algorithm. The algorithm is configured to generate SE candidate solutions for each non-dominated solution by a certain specific operator in each iteration. The present application proposes a transformation operator based on feature weights to generate more potential candidate solutions, and the process is as follows:

[0142]

[0143]

[0144] wherein x i represents a selected case corresponding to the i-th feature, r i represents a probability of the i-th feature, w′ i represents a normalized weight of the i-th feature, represents a negation symbol, w′ min is a minimum value in the normalized weights, and w′ max is a maximum value in the normalized weights.

[0145] ​Finally, candidate solution matrix is obtained, a total of SE*n*L candidate solutions, n is the number of Pareto non-dominated solutions at the beginning of this round of iteration, SE is the search intensity, and L is the number of operators.

[0146] The evaluation of the solution is to calculate the two objective functions of the solution, including the classification error rate and the feature number, and the feature number is given by the 0-norm of the solution, which can be calculated according to the following formula:

[0147]

[0148] The classification error rate can be calculated according to the following formula:

[0149]

[0150] Where N represents the number of samples, y i represents the true label of the i-th sample, represents the predicted label of the i-th sample. In the algorithm, the classification error rate of the test set by the classification model is taken as the classification error rate of the solution X.

[0151] Through the evaluation of the solution, the objective function matrix F of all solutions is obtained, where F i =[f i 1 ,f i 2 ], that is, the objective function value vector corresponding to the i-th solution is F i , including two objective function values, which are the classification error rate f i 1 , and the feature number f i 2 . In this step, the objective function values corresponding to the Pareto non-dominated solution set at the beginning of this round of iteration are also added to the objective function matrix F, so as to facilitate the update of the solution.

[0152] For example, the specific steps are as follows:

[0153] S61: Each solution in X best generates SE candidate solutions via each operator, in this embodiment, X best is n, SE=20, and L=5. That is, n*SE*L=5*20*5=500 candidate solutions will be generated in each round of iteration, and the descriptions of the five operators are as follows:

[0154] Probability replacement operator:

[0155]

[0156] r i =cos(w′′*π)

[0157] where xi r represents the selected case of the i-th feature, r i w' represents the probability of the i-th feature, w' i w represents the normalized weight of the i-th feature, The operator has a high weight feature with a lower probability of taking the opposite state, which can produce more potential candidate solutions. It can change multiple position states at a time, suitable for global search.

[0158] Exchange transformation operator:

[0159] x i = x j

[0160] x j = x i

[0161] where i and j are random indices generated, representing the exchange of the i-th feature state and the j-th feature state. The operator has the ability to exchange two random position elements in the current optimal solution

[0162] Translation transformation operator:

[0163] x i = x i+1

[0164]

[0165] x j = x i

[0166] where 0≤i

[0167] Replacement transformation:

[0168]

[0169] where i is a random index, the operator has the function of reversing the state of a random position in the current optimal solution. Compared with the probability replacement, this operator can only reverse the state of one bit at a time, which is more suitable for local search.

[0170] Symmetric transformation:

[0171] x i = x j

[0172] x i+1 = x j-1

[0173]

[0174] x j-1 =x i+1

[0175] x j =x i

[0176] where 0≤i

[0177] S62: calculate candidate solution objective function matrix F 500×2 , a total of 500 candidate solutions, each candidate solution has two objective function function values. Finally, X best corresponding objective function is also added to the candidate solution objective function matrix, and finally the total objective function matrix F_last 505×2 is obtained.

[0178] where F i = [f i 1 ,f i 2 ], that is, the objective function value vector corresponding to the ith solution is F i , including two objective function values, respectively, the classification error rate f i 1 , and the feature number f i 2 .

[0179] where the feature number is given by the 0-norm of the solution, which can be calculated according to the following formula:

[0180]

[0181] The classification error rate objective function value can be calculated according to the following formula:

[0182]

[0183] In the above formula, N represents the number of samples, y i represents the true label of the ith sample, and y represents the predicted label of the ith sample. In this embodiment, the classification error rate of the classification model on the test set is taken as the classification error rate of the solution X.

[0184] Step 7, process the objective function matrix by a two-dimensional sorting strategy, and update the initial Pareto optimal solution set X best ;

[0185] Further, the step 7 specifically includes:

[0186] Step 7.1, sort the objective function matrix F in descending order according to the number of features as the first key and the classification error rate as the second key to obtain F';

[0187] Step 7.2, initialize the Pareto optimal solution set X best to be empty, and then add F'0 to X best , and set the global minimum value of the classification error rate

[0188] Step 7.3, sequentially traverse each candidate solution, if the number of features of the current solution F' i is the same as that of the previous solution F' i-1 , or the classification error rate of F' i is greater than or equal to the global error rate gErr, then skip the current solution, otherwise, add the current solution to X best , and update gErr = f i 2 ;

[0189] Step 7.4, until all candidate solutions are traversed, X best is the initial Pareto optimal solution set updated in this iteration process.

[0190] In specific implementation, considering that each solution has two objective function values, the number of features and the classification error rate, it is impossible to directly compare the sizes for solution updating. The traditional multi-objective uses the fast non-dominated sorting method to assign the front level to all solutions, which is time-consuming and has large calculation amount. Since the algorithm only needs the information of the final Pareto optimal solution set and does not care about the front level of other dominated solutions. Therefore, the application adopts a two-dimensional sorting strategy to directly obtain the Pareto non-dominated solution set, reduces the time complexity and speeds up the algorithm efficiency. The steps of the two-dimensional sorting strategy are as follows:

[0191] Sort the objective function matrix F in descending order according to the number of features as the first key and the classification error rate as the second key to obtain F'.

[0192] Initialize the Pareto optimal solution set X best to be empty, and then add F'0 to X best , and set the global minimum value of the classification error rate

[0193] Sequentially traverse each candidate solution, if the number of features of the current solution F' i is the same as that of the previous solution F' i-1 , or the classification error rate of F' i is greater than or equal to the global error rate gErr, then skip the current solution; otherwise, add the current solution to X best , and update gErr = f i 2.

[0194] until all candidate solutions are traversed, X best is the Pareto optimal solution set obtained in this iteration process, X best is also the initial Pareto optimal solution set of the next iteration.

[0195] Step 8, increase the iteration number by 1, repeat steps 6 to 7 until the iteration number is equal to the maximum iteration number, and output X best as the final Pareto optimal solution set.

[0196] In specific implementation, if the current iteration number is greater than or equal to the maximum iteration number, the next iteration process is entered, and if the current iteration process is equal to or greater than the maximum iteration number, X best is output as the Pareto optimal solution set.

[0197] The Pareto front surface obtained in the experiment in the embodiment of the present disclosure is as shown in Figure 2 The horizontal coordinate in the figure represents the number of features, and the vertical coordinate represents the classification error rate. As can be seen from the figure, the present embodiment provides 7 different solutions (i.e. 7 different feature combinations) for the decision maker. For the decision maker who considers cost more, the A, B, C three schemes may be more suitable, and for the decision maker who considers higher classification accuracy, the F, G and other schemes are good choices. For the decision maker without obvious preference, D, E is more moderate. That is, the present embodiment can provide multiple different schemes to meet the different needs of different decision makers. At the same time Figure 3 (a) to (g) in the figure show the visualization of each Pareto non-dominated solution in two-dimensional space, which can help the decision maker understand the distinguishability of the working conditions under different schemes more intuitively, and is used to assist the decision maker to make better decisions.

[0198] At the same time, the present embodiment compares the time for the single-objective method to obtain the same number of schemes and whether the schemes are contained or dominated by the non-dominated solutions in the multi-objective method by running the single-objective method 7 times, and the results are shown in Table 1.

[0199] Table 1

[0200]

[0201] As can be seen, under the same number of features, the method in the present embodiment completely contains the optimal solution of the single-objective method, and to a certain extent, the solution can achieve a lower classification error rate than the single-objective method. At the same time, the single-objective method takes about 16.32s to obtain the same number of solutions, while the method in the present embodiment only needs 9.63s, and the computing efficiency is improved by about 40%, and the computing speed is about 1.5-2 times that of the existing method.

[0202] The method for identifying froth flotation working conditions based on multi-target feature selection provided by the embodiment introduces the concept of marginal contribution in game theory, which is called Shapley value, and combines it with the Filter method in feature selection to make a rough screening of the original features of the data set. The main purpose is to quickly eliminate a large number of irrelevant and redundant features by taking the marginal contribution of features as the evaluation standard of features, and the retained features constitute the initial screening feature subset, and the initial weights of the features in the initial screening subset are calculated. Then, the feature selection problem is modeled as a multi-objective optimization problem, considering two objective functions of feature quantity and classification accuracy. In this process, the Wrapper method is used, and intelligent optimization algorithms are used as search strategies to speed up the solution process. A binary state transfer algorithm is used to iteratively generate multiple candidate feature subsets of the initial screening feature subset, calculate the feature quantity and classification accuracy of each candidate feature subset, and constantly update the Pareto optimal solution set through a fast two-dimensional sorting strategy. After the iteration of the algorithm, the Pareto optimal solution set composed of multiple non-dominated solutions is output, and each Pareto non-dominated solution represents a different selection scheme. Secondly, the binary state transfer algorithm uses the normalized weights of the initial screening feature subset to design a heuristic operator for generating potential candidate solutions, ensuring the reliability of the selected feature subset. At the same time, according to the characteristics of the multi-objective feature selection problem, a two-dimensional sorting strategy is proposed to replace the fast non-dominated sorting in the traditional multi-objective optimization algorithm, which greatly reduces the time complexity, speeds up the algorithm running speed, and improves the recognition efficiency and accuracy.

[0203] It should be understood that parts of the present disclosure can be implemented in hardware, software, firmware, or a combination thereof.

[0204] The above is only a specific embodiment of the present disclosure, but the protection scope of the present disclosure is not limited thereto. Any changes or replacements within the technical scope disclosed by the present disclosure can be easily thought of by those skilled in the art, and should be covered within the protection scope of the present disclosure. Therefore, the protection scope of the present disclosure should be subject to the protection scope of the claims.

Claims

1. A froth flotation operating condition identification method based on multi-objective hybrid feature selection, characterized in that, The method comprises the following steps: Step 1, extracting a data set to be processed in a froth flotation working condition for data preprocessing; Step 2, calculating the marginal contribution value of each feature in the preprocessed data set according to the marginal contribution criterion, and sorting all features according to the marginal contribution value; Step 3, calculating the cumulative contribution according to the sorting of the features, retaining the features with cumulative contribution greater than a threshold value, and eliminating the remaining low-contribution features to obtain a preliminary screening feature subset; Step 4, calculating the initial weight of each feature in the preliminary screening feature subset; Step 5, setting the maximum number of iterations and the related parameters of the binary state transition algorithm, generating a plurality of candidate feature subsets according to the initial weight and the preliminary screening feature subset, and selecting all non-dominated solutions in the candidate feature subset to form an initial Pareto optimal solution set ; Step 6, using state transition operator according to initial pareto optimal solution set A plurality of candidate solutions are generated, and a preset classifier is used to train each candidate solution to calculate a classification error rate, and then the number of features of each candidate solution is calculated to form a target function matrix ; The step 6 specifically comprises: Step 6.1, for each solution in is generated via a state transition operator candidate solutions, the formula of which is as follows: ； ； wherein represents a selected case corresponding to the i-th feature, represents a probability of the i-th feature, represents a normalized weight of the i-th feature, represents a negation symbol, is a minimum value in the normalized weights, is a maximum value in the normalized weights; Step 6.2, calculating the classification error rate of each candidate solution by using a preset classifier, and then calculating the number of features of each candidate solution; Step 6.

3. Obtain the objective function matrix of each candidate solution according to the classification error rate of each candidate solution and the objective function corresponding to the number of features ; Step 7, the objective function matrix is processed by a two-dimensional sorting strategy, and the initial Pareto optimal solution set is updated ; Step 8, increase the iteration number by 1, repeat steps 6 to 7 until the iteration number is equal to the maximum iteration number, output as the final pareto optimal solution set.

2. The method of claim 1, wherein The step 1 specifically comprises: An original data set containing features and labels is obtained from historical data as a data set to be processed, and the data set to be processed is preprocessed, including removing abnormal values, missing value samples and unlabeled samples caused by error operation in the sampling process, and normalizing all features, the normalization formula being as follows: ； wherein denotes the original data set, denotes the minimum value of the original data set on each feature, and denotes the maximum value of the original data set on each feature, is the normalized data set.

3. The method of claim 2, wherein The calculation formula of the marginal contribution value is as follows: ； wherein, is the marginal contribution value of the jth feature M is the total number of features, and S is a certain feature combination, represents the model output value under the feature combination S.

4. The method of claim 3, wherein The step 4 specifically comprises: The marginal contribution value of each feature in the preliminary screening feature subset is normalized as the initial weight corresponding to the feature, and the normalization formula is as follows: ； wherein W is a weight vector of marginal contribution values of the subset of screening features, is the weight of the jth feature, which is also the marginal contribution value of the feature, represents the normalized weight, is the maximum value of the weight vector, represents the minimum value of the weight vector.

5. The method of claim 4, wherein The step 5 specifically comprises: Step 5.1, binary encoding the solution of feature selection; Step 5.2, modeling the feature selection problem in the froth flotation process into the following multi-objective optimization problem: ； wherein is the 0-norm of X, representing the number of 1's in X, i.e. the number of selected features, m is the number of features of the subset of pre-screening features, is the classification error rate corresponding to the solution X. Step 5.3, initializing a plurality of feature subsets according to the preliminary screening feature subset and the initial weight of the features thereof, obtaining an initial non-dominated solution set through evaluation and selection, and the method of initializing a solution being as follows: ； In the formula, represents the selected state corresponding to the i-th feature, is a random number belonging to a uniform distribution, is the selection probability of a high initial weight feature, is the selection probability of a low initial weight feature, is a set of i features with high initial weight, is a set of i features with high initial weight, is a proportion coefficient of a high initial weight feature set by the user, is a set of remaining low initial weight features;​ Step 5.4, compute the two objective functions of all initial solutions by evaluating the functions, i.e. and Then, get all non-dominated solutions by using the two-dimensional ranking strategy, and get the initial Pareto optimal solution set .

6. The method of claim 5, wherein The step 7 specifically comprises: Step 7.1, sort the objective function matrix F in descending order according to the number of features as the first key and the classification error rate as the second key to obtain ; Step 7.2, initialize the Pareto optimal solution set If empty, then add to Set the classification error rate global minimum ; Step 7.3, iterate through each candidate solution in turn, if the number of features of the current solution is the same as the previous solution or the classification error rate of the current solution is greater than or equal to the global error rate , then skip the current solution, otherwise, add the current solution to and update ; Step 7.4, until all candidate solutions are traversed, is the initial Pareto optimal solution set updated in this iteration process.

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