A method and system for dividing construction engineering indicators based on improved clustering algorithm

Abstract

The present invention discloses a method and system for dividing construction engineering indicators based on an improved clustering algorithm, wherein the method includes: determining the construction engineering indicators to be divided and their reference characteristics for division, obtaining survey data and summarizing them into a multidimensional characteristic matrix; performing preliminary clustering analysis on the multidimensional characteristic matrix to determine the number of interval divisions of the construction engineering indicators to be divided; based on the number of interval divisions, transforming the characteristic dimension of the multidimensional characteristic matrix to achieve improved clustering of multidimensional data with the indicator dimension to be divided as the core and the reference characteristic dimension for division as the auxiliary; determining the interval division result of the indicator to be divided according to the result obtained by the improved clustering method. The present invention realizes the objective and accurate division of construction engineering indicators through the improved clustering algorithm, and can also be extended to the division of indicators in other fields with similar structural problems, or the division of other objects with similar characteristics to indicators.

Description

Technical Field

[0001] The invention relates to a construction engineering index division method and system based on an improved clustering algorithm, belonging to the technical field of electrical digital data processing. Background Art

[0002] The division of construction project indicators is a common problem in the construction field, involving the formulation of relevant engineering specifications. Due to their abstractness or complexity, some indicators often have difficulty in dividing the indicator interval. The data form of this type of problem is generally: for a given multi-dimensional data source, the indicator dimension is divided into intervals, and the data of other dimensions are used to assist in the division of indicators. The purpose of this type of problem is to analyze the impact mechanism of an indicator that measures the characteristics of a building or a complex of buildings in a certain aspect on the characteristics measured by the indicator, so as to define the qualified threshold, excellent standards, etc. for the indicator, and finally provide it to the government for decision-making to formulate relevant regulations. It should be added that this type of problem will occur in but not limited to the above-mentioned construction engineering field, and other fields may also face such problems.

[0003] Regarding the above-mentioned problems of dividing an indicator into intervals, setting qualified thresholds, and excellent standards, the commonly used methods can be roughly divided into three categories:

[0004] The first type of method is the expert decision-making method. This method mainly relies on the experience of experts to make judgments and makes comprehensive decisions by consulting multiple experts. Since the division of most indicators is difficult to quantify, and this method is simple and easy to implement, it is widely used for indicators with lower importance. However, the expert decision-making method relies entirely on subjective experience and lacks objective guidance, which has significant disadvantages;

[0005] The second type of method is regression analysis. This type of method provides guidance for the interval division of indicators by establishing a functional relationship between the indicator dimension and the auxiliary dimension. This method introduces certain quantitative calculations, but it has many limitations. First, the regression method generally adopts linear regression, which may have large errors; second, after the regression is completed, the indicator cannot be directly divided into intervals, and certain subjective judgments are still required. Therefore, although the regression analysis method is more objective than expert decision-making, its objectivity is incomplete and limited;

[0006] The third method is the natural breakpoint method, which can divide indicators through completely objective calculations, but is limited to one-dimensional data and has low problem adaptability.

[0007] In summary, there is currently no completely targeted technical path for the problem of construction engineering index division, that is, the problem of single-dimensional interval division under multi-dimensional data sources. This study proposes to use an improved clustering algorithm to solve this problem.

[0008] Clustering in a general sense is an unsupervised machine learning technique, which aims to divide the entire set of research objects into multiple subsets with highly similar internal sample points. Mainstream clustering algorithms include but are not limited to K-Means clustering algorithm, mean shift clustering algorithm, DBSCAN clustering algorithm, hierarchical clustering method, etc. Their common feature is to use the distribution of data in multidimensional space to divide categories, and their classification results are all presented in the form of groups, which cannot meet the following special requirements: from a certain specified dimension, the intervals corresponding to each category on this dimension that just accommodate all sample points are separated from each other and do not overlap. Therefore, there is currently no precedent for using clustering algorithms to solve the problem of indicator division under multidimensional data sources. The present invention improves the basic principles of conventional clustering algorithms, so that clustering ideas can be applied to the problem of dividing construction engineering indicators, and provides a more objective and accurate method for the problem of indicator division in the construction field or other fields with similar needs. Summary of the invention

[0009] In order to solve at least one technical problem existing in the above-mentioned prior art, the present invention provides a construction engineering index division method based on an improved clustering algorithm, the method comprising the following steps:

[0010] Step 1: Determine the indicators of the construction project to be divided and its reference characteristics for division, obtain the survey data and summarize them into a multi-dimensional feature matrix;

[0011] Step 2: Perform a preliminary cluster analysis on the multidimensional feature matrix to determine the number of interval divisions of the construction engineering indicators to be divided;

[0012] Step 3: Based on the interval division number, the characteristic dimension of the multidimensional characteristic matrix is ​​transformed to realize the improved clustering of the multidimensional data with the index dimension to be divided as the core and the division reference characteristic dimension as the auxiliary;

[0013] Step 4: According to the results obtained by the improved clustering method, determine the interval division results of the indicators to be divided.

[0014] Further, step 1: determine the indicators of the construction project to be divided and their reference characteristics for division, obtain the survey data and summarize them into a multi-dimensional feature matrix, including:

[0015] For a construction project indicator that needs to be standardized by interval, determine one or more reference indicators to assist in the interval division of the construction project indicator. Extensively survey completed construction projects, summarize the survey data into a multi-dimensional feature matrix, clean the data and perform unbiased normalization on each feature dimension.

[0016] Further, step 2: performing a preliminary cluster analysis on the multidimensional feature matrix to determine the number of interval divisions of the construction engineering indicators to be divided, including:

[0017] The multidimensional feature matrix is ​​repeatedly run with a clustering algorithm suitable for the problem under different classification numbers. For each classification number, the highest value of the silhouette coefficient of all running results is taken as the silhouette coefficient corresponding to the classification number. Within the range of classification numbers that meet the requirements of the problem, the classification number with the highest corresponding silhouette coefficient is selected as the interval division number of the index to be divided.

[0018] Further, step 3: based on the interval division number, the characteristic dimension of the multidimensional characteristic matrix is ​​transformed to realize the improved clustering of the multidimensional data with the to-be-divided index dimension as the core and the division reference characteristic dimension as the auxiliary, including:

[0019] Step 3-1: Implement the interval separation judgment function. This function is used to judge whether the given clustering result satisfies the separation of the storage intervals corresponding to each category on the dimension to be divided (hereinafter referred to as interval clustering);

[0020] Step 3-2: Transform the feature dimensions of the multidimensional feature matrix, including linear transformation of the index dimension to be divided and free transformation of the reference feature dimension to be divided. Among them, linear transformation of the index dimension to be divided is necessary, which is used to increase the influence of the index dimension to be divided on clustering, and its transformation parameters are objectively determined by binary search; free transformation of the reference feature dimension to be divided is not necessary, and free transformation includes linear transformation and nonlinear transformation. Linear transformation is used to change the relative influence of different reference feature dimensions on clustering, and nonlinear transformation is used to change the internal data distribution of the reference feature dimension to be divided, and its transformation parameters are subjectively determined by the decision maker based on the understanding of the problem. If free transformation of the reference feature dimension to be divided is to be applied, it should be placed before the linear transformation step of the index dimension to be divided;

[0021] Step 3-3: Based on the transformed multi-dimensional feature matrix, complete the improved clustering with the indicator dimension to be divided as the core and the division reference feature dimension as the auxiliary.

[0022] Furthermore, step 3-1: realizing the interval separation judgment function includes:

[0023] Initialize the storage interval corresponding to each category in the specified dimension, where the right endpoint of the interval is initialized to 0 and the left endpoint is initialized to a value exceeding the upper limit of the data;

[0024] Traversing the sample data, and modifying the storage interval corresponding to the corresponding class according to the class to which each sample point belongs;

[0025] If the value of the sample point on the specified dimension is greater than the right endpoint of the storage interval of the category to which it belongs, the right endpoint is updated to the sample point value; if the value of the sample point on the specified dimension is less than the left endpoint of the storage interval of the category to which it belongs, the left endpoint is updated to the sample point value;

[0026] Determine whether there is overlap between each collection interval. If so, it is determined that the clustering result does not satisfy interval-type clustering. If not, it is determined that the clustering result satisfies interval-type clustering. The method for determining whether there is overlap between each collection interval is as follows: (1) For any two intervals, the method for determining whether there is overlap is as follows: if the left and right endpoint values ​​of the first interval are both greater than or equal to the right endpoint of the second interval, or the left and right endpoint values ​​of the first interval are both less than or equal to the left endpoint of the second interval, then it is considered that the two intervals do not overlap. (2) For any n intervals, the method for determining whether there is overlap is as follows: judge each interval in turn with the interval behind it. If each interval does not overlap with all the intervals behind it, then it is considered that these n intervals do not overlap with each other.

[0027] Further, step 3-2: transforming the characteristic dimension of the multidimensional characteristic matrix, including linear transformation of the index dimension to be divided and free transformation of the reference characteristic dimension to be divided, including:

[0028] If necessary, apply a free transformation to the partition reference feature dimension, and determine the free transformation parameters of the partition reference feature dimension subjectively based on the problem.

[0029] Binary search is used to determine the linear transformation parameters of the index dimension to be divided, that is, the scaling factor of the dimension data. The specific search method is:

[0030] Determine the initial scaling factor. Update the multidimensional feature matrix according to the preset original scaling factor, perform cluster analysis on the updated multidimensional feature matrix, and determine whether the clustering result satisfies the interval separation; if not, update the original scaling factor according to the preset multiple; if so, use the current original scaling factor as the initial scaling factor.

[0031] Implement the binary search function and perform multiple rounds of binary search on the scaling factor. The left endpoint of the binary search is 1, and the right endpoint is the initial scaling factor. Each round searches for a minimum scaling factor that enables the clustering result to pass the interval separation judgment. Record the scaling factor obtained in each round of search and its corresponding silhouette coefficient.

[0032] A multi-objective optimization problem is constructed so that the silhouette coefficient is as large as possible while the scaling factor is as small as possible. The format of the objective function is as follows:

[0033] ,in is the scaling factor, is the silhouette coefficient, It is a custom hyperparameter, and the scaling factor with the largest objective function value is selected as the linear transformation parameter of the final indicator dimension to be divided.

[0034] Furthermore, step 4: determining the interval division result of the index to be divided according to the result obtained by the improved clustering method, including:

[0035] Extract the classification results obtained by improved cluster analysis and record the narrowest inclusion interval of each category on the specified dimension. If the number of categories is , the corresponding storage intervals of various categories in the specified dimension are , then the final index interval division method is: a total of The values ​​are used as breakpoints to divide the indicator into n intervals with different characteristics, which are:

[0036] ,

[0037] in For the breakpoint value.

[0038] In the second aspect, a construction engineering index classification system based on an improved clustering algorithm is provided, comprising:

[0039] A data acquisition and sorting module is used to acquire sample data and summarize the sample data into a multi-dimensional feature matrix;

[0040] The clustering calculation module is used to perform improved clustering analysis on the multi-dimensional feature matrix.

[0041] The characteristic matrix transformation parameter calculation module is used to input the free transformation parameters of the partition reference dimension and the linear transformation parameters of the binary search index dimension to be partitioned;

[0042] The indicator division module is used to determine the interval division results of the corresponding indicators according to the results obtained by the improved cluster analysis.

[0043] Furthermore, the clustering calculation module includes:

[0044] The clustering analysis module is used to run a clustering algorithm suitable for the problem on the multi-dimensional feature matrix.

[0045] The interval partition number evaluation module is used to evaluate the interval partition number using the silhouette coefficient. For each classification number, the highest value of the silhouette coefficient of all running results is taken as the silhouette coefficient corresponding to the classification number. Within the range of classification numbers that meet the requirements of the problem, the classification number with the highest corresponding silhouette coefficient is selected as the interval partition number of the indicator to be divided.

[0046] Furthermore, the feature matrix transformation parameter calculation module includes the following submodules:

[0047] A partition reference dimension free transformation parameter input module is used to receive the partition reference dimension free transformation parameters and update the multidimensional feature matrix according to the parameters;

[0048] The interval separation judgment module is used to judge whether the clustering results meet the definition of interval clustering;

[0049] An initial scaling factor calculation module, used to determine an initial scaling factor;

[0050] Binary search module, used to implement binary search function to perform multiple rounds of binary search, the left endpoint of the binary search is set to 1 by default, and the right endpoint is set to the initial scaling factor. Record the search results of each round in the memory;

[0051] An optimal zoom factor selection module is used to select the optimal zoom factor in each round of search results;

[0052] Furthermore, the interval separation judgment module includes:

[0053] Initialize the storage interval corresponding to each type of sample in the specified dimension, traverse the sample data, and modify the storage interval corresponding to the corresponding class according to the category to which each sample point belongs;

[0054] If the value of the sample point on the specified dimension is greater than the right endpoint of the category storage interval to which it belongs, the right endpoint is updated to the sample point value;

[0055] If the value of the sample point on the specified dimension is less than the left endpoint of the category storage interval to which it belongs, the left endpoint is updated to the sample point value;

[0056] It is determined whether the minimum storage intervals overlap or not. If so, it is determined that the clustering result does not conform to the interval type clustering. If not, it is determined that the clustering result conforms to the interval type clustering.

[0057] Furthermore, the optimal scaling factor calculation module includes:

[0058] Selecting the smallest scaling factor among the initial scaling factors that conform to interval-type clustering as the optimal scaling factor; or,

[0059] A multi-objective optimization problem is constructed so that the silhouette coefficient is as large as possible while the scaling factor is as small as possible. The format of the objective function is as follows:

[0060] ,in is the scaling factor, is the silhouette coefficient, It is a custom hyperparameter, and the scaling factor with the largest objective function value is selected as the linear transformation parameter of the final indicator dimension to be divided.

[0061] The initial scaling factor with the largest objective function value is selected as the optimal scaling factor.

[0062] Furthermore, the indicator division module includes:

[0063] Extract the classification results obtained by cluster analysis under the optimal scaling factor, and record the narrowest inclusion interval of each category on the specified dimension. If the number of categories is , the corresponding storage intervals of various categories in the specified dimension are , then the final index interval division method is: a total of The values ​​are used as breakpoints to divide the indicator into n intervals with different characteristics, which are:

[0064] ,

[0065] in For the breakpoint value.

[0066] In a third aspect, an electronic device is provided, including:

[0067] One or more processors; and a memory associated with the one or more processors, the memory being used to store program instructions, and when the program instructions are read and executed by the one or more processors, executing a construction engineering index division method based on an improved clustering algorithm.

[0068] In a fourth aspect, a computer-readable medium is provided, on which a computer program is stored, wherein when the program is executed by a processor, a method for dividing construction project indicators based on an improved clustering algorithm is implemented.

[0069] The technical solution provided by the embodiment of the present invention has the following beneficial effects:

[0070] The embodiment of the present invention discloses a construction engineering index division method based on an improved clustering algorithm. Based on the improvement of the basic clustering algorithm principle, it can complete the interval clustering of the specified dimension under the multi-dimensional data source, and then can efficiently solve the division problem of construction engineering indexes through completely objective calculations, avoiding subjective assumptions. In addition, it can also be extended to the division of indicators in other fields with similar structural problems, or the division of other objects with similar characteristics to the indicators;

[0071] The present invention proposes for the first time to complete the index division under multidimensional data sources based on the principle of clustering. Although the clustering idea is highly compatible with the division of construction engineering indexes or other similar indexes, the existing clustering algorithms cannot adapt to the data structure of this type of problem. The present invention proposes an improved clustering algorithm specifically for this type of problem through a large number of algorithm improvement tests, achieving a breakthrough in the clustering algorithm to complete single-dimensional targeted clustering under multidimensional data, thereby providing a more objective and effective method for the index division problem.

[0072] The construction engineering index division method based on the improved clustering algorithm disclosed in the present invention can achieve the single-dimensional clustering goal while making full use of the information of the remaining auxiliary dimensions as much as possible through linear and nonlinear transformation of multi-dimensional data source data; that is, it can make the information of the division reference dimension fully assist the interval division of the construction engineering index;

[0073] The interval clustering analysis method disclosed in the embodiment of the present invention is highly flexible and adaptable. On the one hand, the method disclosed in the present invention is applicable to data sources of any dimension; on the other hand, the present invention focuses on providing a new computing framework and system, in which some computing modules can be freely replaced in combination with actual problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 It is a schematic diagram of the flow of the interval clustering analysis method provided by an embodiment of the present invention;

[0075] Figure 2 It is a schematic diagram of the process of the interval separation test method provided by an embodiment of the present invention;

[0076] Figure 3 Schematic diagram of a binary search scaling factor process provided by an embodiment of the present invention;

[0077] Figure 4 This is the principle description of the algorithm proposed by the present invention. Figure 1 , where (a) is an example of sample point attribution before dimensionality scaling, and (b) is an example of sample point attribution after dimensionality scaling;

[0078] Figure 5 This is the principle description of the algorithm proposed by the present invention. Figure 2 ;

[0079] Figure 6 It is an example diagram of the nonlinear transformation of the reference feature dimension proposed by the present invention;

[0080] Figure 7 It is a sample data distribution diagram of residential outdoor space quality control provided by an embodiment of the present invention;

[0081] Figure 8 It is a schematic diagram of classification number recording provided by an embodiment of the present invention;

[0082] Fig. 9 It is a clustering result diagram under the K-Means algorithm provided by an embodiment of the present invention;

[0083] Fig.10 is a final clustering result diagram provided by an embodiment of the present invention;

[0084] Fig.11 is a final indicator division result diagram provided by an embodiment of the present invention;

[0085] Fig.12 It is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0086] In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0087] The specific technical solutions of the present invention are as follows:

[0088] like Figure 1 As shown, a construction engineering index division method based on an improved clustering algorithm includes:

[0089] S1: Determine the indicators of the construction project to be divided and its reference characteristics for division, obtain the survey data and summarize them into a multi-dimensional feature matrix.

[0090] Determine the feature dimension to be divided (i.e., construction project index) and the reference feature dimension for division. That is, for the research sample, analyze and determine the feature items to be extracted, where there is only one feature dimension to be divided and there can be one or more reference dimensions for division. Extensively survey data samples and summarize the samples into a multi-dimensional feature matrix.

[0091] Perform data cleaning on sample data, including data normalization, missing value processing, and outlier processing;

[0092] Among them, data normalization adopts an unbiased normalization method, and the specific calculation formula is as follows:

[0093] ,

[0094] in For the The sample in The values ​​in the dimensions, is the total sample size, is the total number of dimensions, For the sample in The minimum value in the dimension, For the sample in The maximum value in each dimension is used to normalize the data. This method maps the data completely to the range of 0-1.

[0095] Missing value processing, that is, checking whether there are missing values ​​in the data matrix. If there are missing values, the sample is directly deleted when the sample size is sufficient, and the filling method is used when the sample size is insufficient;

[0096] Outlier processing, that is, checking whether there are erroneous data points. First, all outliers are screened out. If there are erroneous data points among the outliers, the points are directly deleted; for outliers that are not recorded or calculated incorrectly, the selection should be made according to the problem type.

[0097] S2: The multi-dimensional feature matrix is ​​subjected to a preliminary cluster analysis to determine the number of interval divisions for the construction project indicator to be divided.

[0098] The multidimensional feature matrix is ​​repeatedly run with a clustering algorithm suitable for the problem under different classification numbers. The optional clustering algorithms include but are not limited to the K-Means clustering algorithm, the mean shift clustering algorithm, and the DBSCAN clustering algorithm. For each classification number, the highest value of the silhouette coefficient of all running results is taken as the silhouette coefficient corresponding to the classification number. Within the range of classification numbers that meet the requirements of the problem, the classification number with the highest corresponding silhouette coefficient is selected as the interval division number of the index to be divided.

[0099] In one embodiment, step S2 includes:

[0100] Run a clustering algorithm suitable for the problem requirements on the multidimensional feature matrix according to the number of classifications;

[0101] The silhouette coefficient is used to evaluate the number of classifications. Within the range of classification numbers that meet the requirements of the problem, the number of classifications with the highest silhouette coefficient is selected as the optimal number of classifications, and the optimal number of classifications is used as the interval division number of the indicator.

[0102] The above problem mainly refers to the limit range of the number of classifications. The Silhouette Coefficient is used to evaluate the quality of clustering results. The calculation formula of the Silhouette Coefficient is as follows:

[0103] ,

[0104] in For sample The average distance to other samples in class A. For sample The minimum value of the average distance to other class samples, that is:

[0105] ,

[0106] in For sample points and sample points distance.

[0107] The silhouette coefficient is an indicator for evaluating the quality of clustering results, and is generally selected in the range of , the closer it is to 1, the stronger the commonality within each classification group, the weaker the commonality between different groups, and the better the clustering effect.

[0108] For a certain number of classifications, considering the instability of some clustering algorithms, run the conventional clustering algorithm multiple times, and take the maximum silhouette coefficient among all classification results as the silhouette coefficient corresponding to the number of classifications. Within a certain range of classifications that meets the requirements of the problem, select the classification number with the highest silhouette coefficient as the optimal classification number for the current sample set, and the optimal classification number is the interval division number of the indicator.

[0109] It should be noted that when determining the number of interval divisions, whether to use the traditional clustering algorithm or directly use the improved clustering algorithm proposed in the present invention can be selected in combination with actual conditions. It is generally not recommended to skip this step, but the clustering algorithm used to obtain the silhouette coefficient is replaceable.

[0110] S3: Based on the interval division number, the characteristic dimension of the multidimensional characteristic matrix is ​​transformed to achieve improved clustering of multidimensional data with the to-be-divided index dimension as the core and the division reference characteristic dimension as the auxiliary.

[0111] In the above, step S3 specifically includes:

[0112] S31: Implement the interval separation judgment function, which is used to judge whether the given clustering result satisfies the separation of the storage intervals corresponding to each category on the dimension to be divided. This function is implemented by writing an interval separation judgment function, such as Figure 2 As shown. The interval separation judgment function receives the original data and the category vector and returns a bool value. The specific execution content of this function includes:

[0113] Data preprocessing, including integrating the category vector into the original data matrix and analyzing the number of categories in the category vector; initializing the storage interval corresponding to each category in the specified dimension, where the right endpoint of the interval is initialized to 0 and the left endpoint is initialized to a value exceeding the upper limit of the data;

[0114] Traversing the sample data, and modifying the storage interval corresponding to the corresponding class according to the class to which each sample point belongs;

[0115] If the value of the sample point on the specified dimension is greater than the right endpoint of the storage interval of the category to which it belongs, the right endpoint is updated to the sample point value; if the value of the sample point on the specified dimension is less than the left endpoint of the storage interval of the category to which it belongs, the left endpoint is updated to the sample point value;

[0116] Determine whether there is overlap between the collected intervals. If so, it is determined that the clustering result does not satisfy interval-type clustering. If not, it is determined that the clustering result satisfies interval-type clustering. Finally, a bool value is returned, that is, if it exists, 1 is returned, if not, 0 is returned. The method for determining whether there is overlap between the collected intervals is as follows: (1) For any two intervals, the method for determining whether there is overlap is as follows: if the left and right endpoint values ​​of the first interval are both greater than or equal to the right endpoint of the second interval, or if the left and right endpoint values ​​of the first interval are both less than or equal to the left endpoint of the second interval, then it is considered that the two intervals do not overlap. (2) For any n intervals, the method for determining whether there is overlap is as follows: judge each interval in turn with the intervals behind it. If each interval does not overlap with all the intervals behind it, then it is considered that these n intervals do not overlap with each other.

[0117] S32: transforming the characteristic dimension of the multidimensional characteristic matrix, including linear transformation of the index dimension to be divided and free transformation of the reference characteristic dimension to be divided.

[0118] Among them, the linear transformation of the index dimension to be divided is necessary to increase the influence of the index dimension to be divided on the clustering, and its transformation parameters are objectively determined by binary search; the free transformation of the partition reference feature dimension is not necessary, and the free transformation includes linear transformation and nonlinear transformation. The linear transformation is used to change the relative influence of different partition reference feature dimensions on the clustering, and the nonlinear transformation is used to change the internal data distribution of the partition reference feature dimension. Its transformation parameters are determined subjectively by the decision maker based on the understanding of the problem. If the free transformation of the partition reference feature dimension is to be applied, it should be placed before the linear transformation step of the index dimension to be divided. Specifically include:

[0119] If necessary, apply free transformation to the partition reference feature dimension, and determine the free transformation parameters of the partition reference feature dimension subjectively based on the problem. Free transformation includes linear transformation and nonlinear transformation, in which the additional nonlinear transformation cannot change the value range of the dimension data. The focus is on changing the internal numerical distribution, such as expanding or contracting with a point as the center. For example, if there is an important critical value in other dimensions (such as a qualified standard), the value of the dimension can be nonlinearly expanded with the critical value as the center to reflect the important influence of the critical value on clustering. The expansion equation can be constructed using a polynomial function and cubic spline interpolation. If the critical value is 0.5, the nonlinear transformation function of the partition reference variable can be constructed as follows Figure 6 .

[0120] Use binary search to determine the linear transformation parameter of the dimension to be partitioned, that is, the scaling factor for the data in this dimension.

[0121] The "scaling factor" involves the core principle of the present invention: for the normalized multi-dimensional feature matrix, by stretching the number axis of the dimension to be partitioned, the influence of the values in the dimension to be partitioned on the classification result is increased until the intervals corresponding to all categories on this dimension do not overlap exactly, so as to achieve interval clustering for this dimension. The principle of the scaling factor is schematically shown in Figure 4 、 Figure 5 。

[0122] In Figure 4 , the horizontal and vertical axes are respectively Feature 1 and Feature 2 for clustering, as shown in (a) of Figure 4 . (a) is an example of the sample point attribution before dimension scaling. If A and B are two clustering centers, when the magnitudes of the horizontal and vertical axes are the same, the distances from the sample point P to the clustering centers A and B are L1 and L2 (L1 < L2) respectively. The sample point P is closer to point A and thus belongs to class A; as shown in (b) of Figure 4 . (b) is an example of the sample point attribution after dimension scaling; after stretching the horizontal axis to 100 times its original length, the distances from the sample point P to the clustering centers A and B can be approximated as L3 and L4 (L3 > L4). The sample point P is closer to point B and the class attribution will be changed to class B. This shows that stretching the dimension will change the class attribution of the sample points, and the fundamental reason for the change is that: the magnitude differences in different dimensions will lead to differences in the influence weights of each dimension on the sample point attribution. The larger the magnitude, the greater the influence weight.

[0123] In Figure 5 , if the horizontal axis is stretched to an infinite multiple of its original length, the class attribution of the sample points will be completely determined by the horizontal axis and will not be affected by the data in other dimensions, which is equivalent to flattening the data onto the horizontal axis.

[0124] By stretching the dimension to be partitioned, no matter the "distance" in the operation is the common Euclidean distance, Manhattan distance or other classical distance definition methods, the influence of the values in this dimension on the class attribution of each sample point can be increased. Taking the most commonly used Euclidean distance as an example, let A and B be two points in an n-dimensional space, and their coordinates are respectively , . According to the Euclidean distance, the distance between A and B is defined as:

[0125] ,

[0126] If the dimension specified for partitioning in the problem faced is the first dimension, and now the coordinate axis of the first dimension is stretched to times its original length, then the distance between points A and B is updated to:

[0127] ,

[0128] when As it approaches infinity:

[0129] ,

[0130] From this we can see that with As the distance increases, the influence of the value of the specified dimension also increases. When it tends to infinity, it is equivalent to flattening the data along the specified dimension, and the multidimensional data source is reduced to one dimension. In this case, the data in other dimensions are completely invalid and have no effect on the clustering. Although this completes the interval clustering of the specified dimension, the data in the auxiliary dimension cannot be used and cannot produce a more ideal result state. In summary: Specifying the dimension scaling factor The smaller the value, the greater the impact of other dimensional data on the clustering results, and the more fully the data in other dimensions can be used; specify the dimension scaling factor The larger the value is, the smaller the influence of other dimensional data on the clustering results. In fact, the data of other dimensions is gradually discarded, which has an adverse effect.

[0131] Therefore, one of the cores of the present invention is to search for an optimal scaling factor of a specified dimension (i.e., a dimension with divided construction engineering indicators) value, so that while completing interval clustering, it can also make full use of data in other dimensions. Theoretically, there is a critical minimum If the scaling factor is lower than this value, interval clustering cannot be completed. If the scaling factor is higher than this value, not only interval clustering can be completed, but also multiple clustering results that meet the conditions may be generated. This method can complete the optimal The search and determination of the value can take into account the silhouette coefficient of the clustering results and seek a lower scaling factor Balanced unity of value and higher silhouette coefficient.

[0132] How to search for the best zoom factor The present invention chooses to transform based on the traditional binary search method, because the scaling factor The range itself is , there is no definite right boundary, so it is not suitable to use step-by-step search. The specific search steps include:

[0133] Determine the initial scaling factor. Update the multidimensional feature matrix according to the preset original scaling factor, perform cluster analysis on the updated multidimensional feature matrix, and determine whether the clustering result satisfies the interval separation; if not, update the original scaling factor according to the preset multiple; if so, use the current original scaling factor as the initial scaling factor.

[0134] Implement the binary search function and perform multiple rounds of binary search on the scaling factor, where the left endpoint of the binary search is 1 and the right endpoint is the initial scaling factor. Each round searches for a minimum scaling factor that enables the clustering result to pass the interval separation judgment. Record the scaling factor obtained in each round of search and its corresponding silhouette coefficient.

[0135] The binary search function is implemented by the binary search function, such as Figure 3 As shown. This function receives normalized data, initial scaling factor, and number of clusters, and returns the minimum scaling factor, silhouette coefficient, category vector, and cluster center found in this function execution search; the function's hyperparameters include error threshold, maximum number of iterations, and number of cluster categories.

[0136] First, define the binary search auxiliary variable Record the minimum zoom factor that can be passed at present. Record the maximum zoom factor that cannot be passed at present, and check the zoom factor in each cycle The test method is to cluster multiple times to get the case with the largest silhouette coefficient (due to the instability of the results of the K-Means algorithm), and determine whether the case with the largest silhouette coefficient can pass the interval separation test. If it can, reset is the current test value, if not reset The above steps are repeated until any of the following exit conditions is met: (1) the distance between the current left and right endpoints is less than the preset threshold; (2) the number of iterations reaches the preset number.

[0137] It should be noted that for a scaling factor , it is necessary to run the clustering algorithm multiple times to determine whether it is feasible. This is due to the instability of traditional clustering algorithms. As long as one of the runs can pass, the scaling factor is considered It is feasible; the number of repeated runs of the clustering algorithm is also a hyperparameter of this algorithm.

[0138] Use the above implemented scaling factor binary search function to perform multiple rounds of search, recording the scaling factor obtained in each run and silhouette coefficient The reason why multiple rounds of search are needed is that the K-Means algorithm itself has a large amount of randomness. Therefore, the minimum scaling factor and the corresponding maximum silhouette coefficient obtained in each round of binary search are different. The general rule is: the smaller the minimum scaling factor searched, the smaller the corresponding maximum silhouette coefficient.

[0139] Regarding how to select the final scaling factor, the present invention believes that the smallest scaling factor is not necessarily the best, and the excellence of the clustering results also needs to be considered. After multiple application experiments on specific sample groups, it is found that as the scaling factor increases, the upper limit of the silhouette coefficient of the clustering result will generally increase. Therefore, the selection scheme provided by the present invention is as follows:

[0140] Construct a multi-objective optimization problem. The scaling factor is as small as possible (i.e., the other dimensional data is used as fully as possible) and the silhouette coefficient of the clustering result is as large as possible as two parallel and contradictory goals. For the sake of simplicity, this invention does not recommend solving the Pareto front solution set, but uses a custom weight coefficient method to convert it into a single-objective optimization problem. The format of the objective function is as follows:

[0141] ,in is the scaling factor, is the silhouette coefficient, It is a custom hyperparameter, and its most appropriate value needs to be determined through empirical judgment or running experiments. It should be noted that the silhouette coefficient will be affected by the magnitude of the data. Therefore, no matter what the scaling factor is, the calculation object of the silhouette coefficient is the original data (that is, completely normalized data). The general calculation process is: a certain scaling factor The clustering results under are saved and the silhouette coefficient is calculated on the original data. The scaling factor with the largest objective function value is selected as the linear transformation parameter of the final index dimension to be divided.

[0142] S4: Determine the interval division result of the index to be divided according to the result obtained by the improved clustering method.

[0143] Extract the classification results obtained under the multi-dimensional feature matrix transformation parameters, and record the narrowest inclusion interval of each category on the specified dimension. , the corresponding storage intervals of various categories in the specified dimension are , then the final index interval division method is: a total of The indicator is divided into The intervals with different characteristics are:

[0144] ,

[0145] in For the breakpoint value.

[0146] The interval clustering method disclosed in the embodiment of the present invention is described in detail below in combination with specific practical scenarios:

[0147] A batch of data from real surveys was selected. The research object of each sample in this batch of data is a residential area. The sample characteristics include two dimensions, namely a new indicator used to measure the quality of the residential outdoor space and the average satisfaction of the residents of the residential area with the quality of the residential outdoor space. The goal is to use the average satisfaction dimension to assist in segmenting the new indicator dimension, forming intervals representing different characteristics, and revealing the impact mechanism of the difference in the new indicator on the quality of the residential outdoor space. The data distribution is as follows: Figure 7 shown.

[0148] The above problem constitutes a construction project index division problem under a multi-dimensional data source. The embodiment of the present invention proposes to solve the problem by improving the clustering algorithm, including the following steps:

[0149] S1: Determine the indicators of the construction project to be divided and its reference characteristics for division, obtain the survey data and summarize them into a multi-dimensional feature matrix.

[0150] Determine the characteristic dimension to be divided (i.e., construction project index) and the auxiliary reference characteristic dimension. The index dimension to be divided in this practical problem is the newly built index used to measure the quality of outdoor space in residential areas, and the reference characteristic dimension is the average satisfaction with the quality of outdoor space in residential areas.

[0151] The data samples are extensively investigated, and the summarized samples are a multi-dimensional feature matrix. In this embodiment, a total of 101 residential areas are investigated, and the summarized samples are a two-dimensional matrix with 101 rows and 2 columns.

[0152] After data cleaning, the data matrix was normalized and checked to find no missing values ​​or outliers.

[0153] S2: Perform a preliminary cluster analysis on the multi-dimensional feature matrix to determine the number of interval divisions for the construction project indicators to be divided.

[0154] The traditional K-Means clustering algorithm is run on the sample data. For a certain number of categories, the algorithm is run multiple times to take the maximum silhouette coefficient among all classification results as the silhouette coefficient corresponding to the number of categories in this study; the calculation is continuously performed backward from the number of categories 2, and the final calculated number of categories-highest silhouette coefficient line graph is as follows Figure 8 As shown in , the optimal number of clusters for this batch of samples is determined to be 3. The indicators to be divided can be initially divided into 3 intervals. The results obtained by using the traditional K-Means algorithm under the clustering category number 3 are as follows Fig. 9 shown.

[0155] S3: Based on the interval division number, the characteristic dimension of the multidimensional characteristic matrix is ​​transformed to achieve improved clustering of multidimensional data with the to-be-divided index dimension as the core and the division reference characteristic dimension as the auxiliary.

[0156] S31: realize the interval separation judgment function,

[0157] S32: transforming the characteristic dimension of the multidimensional characteristic matrix, including linear transformation of the index dimension to be divided and free transformation of the reference characteristic dimension to be divided.

[0158] In view of the actual problem of this embodiment, the initial scaling factor obtained by searching is 25.021.

[0159] The optimal scaling factor is selected based on the search results of each round. The multi-objective optimization function is constructed as follows:

[0160] ,

[0161] Finally, through multiple rounds of binary search, the scaling factor selected under the above objective function is The value is 2.832.

[0162] S33: Based on the transformed multidimensional feature matrix, complete the improved clustering with the index dimension to be divided as the core and the reference feature dimension as the auxiliary

[0163] S4: Determine the interval division result of the index to be divided according to the result obtained by the improved clustering method.

[0164] As mentioned above, the final clustering result obtained in the embodiment of the present invention is as follows: Fig.10 As shown, Fig. 9 The comparison can significantly reflect the difference between this method and the traditional clustering algorithm. First, the interval of the new index is divided into three intervals from left to right, namely the low-quality interval, the reasonable interval and the inefficient interval; due to the needs of the problem, the first interval (low-quality interval) is further divided into two intervals, namely the prohibited interval and the strong control interval, thereby completing the complete interval division of the new index. The results obtained mainly include: stipulating that the value of any residential area on the new index shall not be less than 8.04; it is recommended that the value of any residential area on the new index be between 18.20 and 39.57. The final results are as follows: Fig.11 shown.

[0165] Based on the improved clustering algorithm disclosed in the embodiment of the present invention, the embodiment of the present invention also provides a construction engineering index classification system using an improved clustering algorithm, including:

[0166] A data acquisition and sorting module is used to acquire sample data and summarize the sample data into a multi-dimensional feature matrix;

[0167] A clustering calculation module is used to perform improved clustering analysis on the multidimensional feature matrix.

[0168] The characteristic matrix transformation parameter calculation module is used to input the free transformation parameters of the partition reference dimension and the linear transformation parameters of the binary search index dimension to be partitioned;

[0169] The indicator division module is used to determine the interval division results of the corresponding indicators based on the results of the improved cluster analysis.

[0170] Furthermore, the clustering calculation module includes:

[0171] The clustering analysis module is used to run a clustering algorithm suitable for the problem on the multi-dimensional feature matrix.

[0172] The interval partition number evaluation module is used to evaluate the interval partition number using the silhouette coefficient. For each classification number, the highest value of the silhouette coefficient of all running results is taken as the silhouette coefficient corresponding to the classification number. Within the range of classification numbers that meet the requirements of the problem, the classification number with the highest corresponding silhouette coefficient is selected as the interval partition number of the indicator to be divided.

[0173] Furthermore, the feature matrix transformation parameter calculation module includes the following submodules:

[0174] The partition reference dimension free transformation parameter input module is used to receive the free transformation parameters of the partition reference dimension and update the multi-dimensional feature matrix according to the parameters.

[0175] The interval separation judgment module is used to judge whether the clustering results meet the definition of interval clustering.

[0176] The initial scaling factor calculation module is used to determine the initial scaling factor.

[0177] The binary search module is used to implement the binary search function to perform multiple rounds of binary search. The left endpoint of the binary search is set to 1 by default, and the right endpoint is set to the initial scaling factor. The search results of each round are recorded in the memory.

[0178] The optimal zoom factor selection module is used to select the optimal zoom factor in each round of search results.

[0179] Furthermore, the interval separation judgment module includes:

[0180] Initialize the storage interval corresponding to each type of sample in the specified dimension, traverse the sample data, and modify the storage interval corresponding to the corresponding class according to the category to which each sample point belongs;

[0181] If the value of the sample point on the specified dimension is greater than the right endpoint of the category storage interval to which it belongs, the right endpoint is updated to the sample point value;

[0182] If the value of the sample point on the specified dimension is less than the left endpoint of the category storage interval to which it belongs, the left endpoint is updated to the sample point value;

[0183] It is determined whether the minimum storage intervals overlap or not. If so, it is determined that the clustering result does not conform to the interval type clustering. If not, it is determined that the clustering result conforms to the interval type clustering.

[0184] Furthermore, the optimal scaling factor calculation module includes:

[0185] Selecting the smallest scaling factor among the initial scaling factors that conform to interval-type clustering as the optimal scaling factor; or,

[0186] A multi-objective optimization problem is constructed so that the silhouette coefficient is as large as possible while the scaling factor is as small as possible. The format of the objective function is as follows:

[0187] ,in is the scaling factor, is the silhouette coefficient, is a custom hyperparameter,

[0188] The initial scaling factor with the largest objective function value is selected as the optimal scaling factor.

[0189] Furthermore, the indicator division module includes:

[0190] Extract the classification results obtained by cluster analysis under the optimal scaling factor, and record the narrowest inclusion interval of each category on the specified dimension. If the number of categories is , the corresponding storage intervals of various categories in the specified dimension are , then the final index interval division method is: a total of The indicator is divided into The intervals with different characteristics are:

[0191] ,

[0192] in For the breakpoint value.

[0193] In addition, the embodiment of the present invention may also add a classification result visualization module for generating visualization results such as cluster analysis diagrams and index interval division diagrams to help the computer intuitively determine whether interval clustering has been completed.

[0194] In addition, an embodiment of the present invention further provides an electronic device, including:

[0195] One or more processors; and a memory associated with the one or more processors, the memory being used to store program instructions, and when the program instructions are read and executed by the one or more processors, the method for dividing construction project indicators based on the improved clustering algorithm is executed.

[0196] Among them, Fig.12 As shown, the computer device 12 is in the form of a general-purpose computing device. The components of the computer device 12 include: one or more processors or processing units 16, a system memory 28, and a bus 18 that connects different system components (including the system memory 28 and the processing unit 16). The bus 18 represents one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, a graphics acceleration port, a processor or a local bus using any of a variety of bus structures. For example, these architectures include an Industry Standard Architecture (ISA) bus, a Micro Channel Architecture (MAC) bus, an Enhanced ISA bus, a Video Electronics Standards Association (VESA) local bus, and a Peripheral Component Interconnect (PCI) bus.

[0197] The computer device 12 typically includes a variety of computer system readable media. These media can be any available media that can be accessed by the computer device 12, including volatile and non-volatile media, removable and non-removable media.

[0198] The system memory 28 may include computer system readable media in the form of volatile memory, such as random access memory, i.e., RAM 30 and / or cache memory 32. The computer device 12 may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, the storage system 34 may be used to read and write non-removable, non-volatile magnetic media (not shown in the figure, commonly referred to as a "hard drive"). Although not shown in the drawings, a disk drive for reading and writing to a removable non-volatile disk (e.g., a "floppy disk"), and an optical disk drive for reading and writing to a removable non-volatile optical disk (e.g., a CD-ROM, DVD-ROM, or other optical media) may be provided. In these cases, each drive may be connected to the bus 18 via one or more data media interfaces. The system memory 28 may include at least one program product having a set (e.g., at least one) of program modules that are configured to perform the functions of various embodiments of the present invention.

[0199] A program / utility 40 having a set (at least one) of program modules 42 may be stored, for example, in system memory 28, such program modules 42 including an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment. Program modules 42 generally perform the functions and / or methods of the embodiments described herein.

[0200] The computer device 12 may also communicate with one or more external devices 14 (e.g., keyboards, pointing devices, displays 24, etc.), and may also communicate with one or more devices that enable a user to interact with the computer device 12, and / or communicate with any device that enables the computer device 12 to communicate with one or more other computing devices (e.g., network cards, modems, etc.). Such communication may be performed through an input / output, or I / O, interface 22. In addition, the display 24 of the computer device 12 in this embodiment does not exist as an independent individual, but is embedded in a mirror surface. When the display surface of the display 24 is not displayed, the display surface of the display 24 is visually integrated with the mirror surface. Furthermore, the computer device 12 may also communicate with one or more networks (e.g., a local area network (LAN), a wide area network (WAN), and / or a public network, such as the Internet) through a network adapter 20. Fig.12 As shown, network adapter 20 communicates with the other modules of computer device 12 via bus 18 .

[0201] The processing unit 16 executes various functional applications and data processing by running programs stored in the system memory 28 .

[0202] The technical solution provided by the present application is described in detail above. The principle and implementation method of the present application are described in detail using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present application. At the same time, for those skilled in the art, according to the idea of ​​the present application, there will be changes in the specific implementation method and application scope. In summary, the content of this specification should not be understood as limiting the present application.

Claims

1. A construction engineering index division method based on an improved clustering algorithm, characterized in that: The method comprises the following steps: Step 1: Determine the indicators of the construction project to be divided and its reference characteristics for division, obtain the survey data and summarize them into a multi-dimensional feature matrix; Step 2: Conduct a preliminary cluster analysis on the multidimensional feature matrix to determine the number of interval divisions for the construction engineering indicators to be divided; Step 3: Based on the interval division number, the characteristic dimension of the multidimensional characteristic matrix is ​​transformed to realize the improved clustering of the multidimensional data with the index dimension to be divided as the core and the division reference characteristic dimension as the auxiliary; Step 4: Determine the interval division results of the indicators to be divided according to the results obtained by the improved clustering method; wherein, step 2: perform preliminary clustering analysis on the multidimensional feature matrix to determine the number of interval divisions of the construction engineering indicators to be divided, including: Run the clustering algorithm suitable for the problem for multiple times under different classification numbers for the multidimensional feature matrix. For each classification number, take the highest value of the silhouette coefficient of all running results as the silhouette coefficient corresponding to the classification number. Within the range of classification numbers that meet the requirements of the problem, select the classification number with the highest corresponding silhouette coefficient as the interval division number of the index to be divided. Among them, step 3: based on the interval division number, the characteristic dimension of the multidimensional characteristic matrix is ​​transformed to realize the improved clustering of the multidimensional data with the to-be-divided index dimension as the core and the division reference characteristic dimension as the auxiliary, including: Step 3-1: Implement the interval separation judgment function, which is used to judge whether the given clustering result satisfies the separation of the storage intervals corresponding to each category on the dimension to be divided. Step 3-2: Transform the feature dimension of the multidimensional feature matrix, including linear transformation of the partition index dimension and free transformation of the partition reference feature dimension. Step 3-3: Based on the transformed multidimensional feature matrix, complete the improved clustering with the indicator dimension to be divided as the core and the reference feature dimension as the auxiliary; The step 3-1: realizing the interval separation judgment function includes: Initialize the storage interval corresponding to each category in the specified dimension, where the right endpoint of the interval is initialized to 0 and the left endpoint is initialized to a value exceeding the upper limit of the data; Traverse the sample data and modify the collection interval corresponding to the corresponding class according to the category to which each sample point belongs; If the value of the sample point on the specified dimension is greater than the right endpoint of the storage interval of the category to which it belongs, the right endpoint is updated to the sample point value; if the value of the sample point on the specified dimension is less than the left endpoint of the storage interval of the category to which it belongs, the left endpoint is updated to the sample point value; Determine whether there is overlap between the included intervals. If so, determine that the clustering result does not satisfy interval-type clustering. If not, determine that the clustering result satisfies interval-type clustering. The method for determining whether there is overlap between the included intervals is as follows: (1) For any two intervals, the method for determining whether there is overlap is as follows: if the left and right endpoint values ​​of the first interval are both greater than or equal to the right endpoint of the second interval, or the left and right endpoint values ​​of the first interval are both less than or equal to the left endpoint of the second interval, then it is considered that the two intervals do not overlap. (2) For any n intervals, the method for determining whether there is overlap is as follows: judge each interval in turn with the interval behind it. If each interval does not overlap with any of the intervals behind it, then it is considered that the n intervals do not overlap with each other. The step 3-2: transforming the feature dimension of the multi-dimensional feature matrix includes: Binary search is used to determine the linear transformation parameters of the index dimension to be divided, that is, the scaling coefficient of the dimensional data. The specific search method is: Determine the initial scaling factor, update the multidimensional feature matrix according to the preset original scaling factor, perform cluster analysis on the updated multidimensional feature matrix, and determine whether the clustering result satisfies the interval separation; if not, update the original scaling factor according to the preset multiple; if satisfied, use the current original scaling factor as the initial scaling factor, Implement the binary search function, perform multiple rounds of binary search on the scaling factor, where the left endpoint of the binary search is 1, and the right endpoint is the initial scaling factor. Each round searches for a minimum scaling factor that enables the clustering result to pass the interval separation judgment, and records the scaling factor obtained in each round of search and its corresponding silhouette coefficient. Construct a multi-objective optimization problem. The format of the objective function is as follows: F(k, sc) = -k + a*sc, where k is the scaling factor, sc is the silhouette coefficient, and a is a custom hyperparameter. The scaling factor with the largest objective function value is selected as the linear transformation parameter of the final indicator dimension to be divided.

2. The construction engineering index division method based on the improved clustering algorithm according to claim 1 is characterized in that: Step 1: Determine the indicators of the construction project to be divided and its reference indicators, obtain the survey data and summarize them into a multi-dimensional feature matrix, including: For construction engineering indicators that need to be standardized according to intervals, one or more reference indicators are determined to assist in the interval division of construction engineering indicators. Completed construction engineering projects are surveyed, and the survey data are summarized into a multi-dimensional feature matrix. The data is cleaned and unbiased normalization is performed on each feature dimension.

3. The construction engineering index division method based on the improved clustering algorithm according to claim 1 is characterized in that: Step 4: According to the results obtained by the improved clustering method, the interval division results of the index to be divided are determined, including: Extract the classification results obtained by the improved cluster analysis and record the narrowest storage interval of each category on the specified dimension. If the number of categories is n, the corresponding storage interval of each category on the specified dimension is [a1, b1], [a2, b2], ..., [a n , b n ], the final index interval division method is: a total of n-1 values ​​are used as breakpoints to divide the index into n intervals with different characteristics, which are: Where Di is the i-th breakpoint value.

4. A construction engineering index classification system based on an improved clustering algorithm, characterized in that: The method for dividing construction project indicators based on the improved clustering algorithm for implementing any one of claims 1 to 3 comprises: The data acquisition and sorting module is used to acquire sample data and summarize the sample data into a multi-dimensional feature matrix. The clustering calculation module is used to perform cluster analysis on the multi-dimensional feature matrix. The characteristic matrix transformation parameter calculation module is used to input the free transformation parameters of the reference dimension and the linear transformation parameters of the index dimension to be divided in the binary search. The indicator division module is used to determine the interval division results of the corresponding indicators according to the results obtained by the improved cluster analysis.

5. An electronic device, characterized in that: include: one or more processors; And a memory associated with the one or more processors, the memory is used to store program instructions, and when the program instructions are read and executed by the one or more processors, the method for dividing construction project indicators based on the improved clustering algorithm as described in any one of claims 1 to 3 is executed.

6. A computer-readable medium, characterized in that A computer program is stored on a readable medium, wherein: When the program is executed by a processor, the method for dividing construction engineering indicators based on an improved clustering algorithm as described in any one of claims 1 to 3 is implemented.

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