A multi-dimensional correlation market research data intelligent analysis method

Abstract

This invention discloses an intelligent analysis method for multi-dimensional correlations in market research data, belonging to the field of data processing and analysis technology. The method includes: collecting raw data containing respondent attributes, questionnaire items, timestamps, and geographical locations; constructing a fourth-order raw research tensor; performing multi-dimensional correlation entropy calculation to obtain a correlation entropy coefficient matrix, and filtering high-correlation dimension pairs; extracting tensor slices from each high-correlation dimension pair and performing local topological analysis to generate local manifold structures; inputting all local manifold structures into a hierarchical adversarial network to output an enhanced correlation manifold tensor; fusing it with the original tensor to obtain a fused research tensor; performing nonlinear dimensionality reduction mapping to obtain a data representation in a low-dimensional embedding space; performing density peak clustering to identify research data clusters; and outputting the boundary description and center point coordinates of each cluster. This invention can efficiently mine deep correlation structures between multiple dimensions, improving the accuracy and interpretability of market research data analysis.

Description

Technical Field

[0001] This invention relates to the field of data processing and analysis technology, specifically to a multi-dimensional correlation intelligent analysis method for market research data. Background Technology

[0002] Existing market research data analysis methods typically employ traditional statistical techniques such as cross-tabulation analysis, correlation analysis, and principal component analysis. These techniques are based on the assumption of low-dimensional data and can only handle simple associations in a few dimensions, such as respondent attributes, questionnaire items, time, or geographic location. As market research data becomes increasingly complex, the raw data contains four high-dimensional discrete dimensions: respondent attributes, questionnaire items, timestamps, and geographic location. These dimensions are coupled to form complex nonlinear association structures, making it difficult for traditional methods to accurately extract high-order interactions between dimensions from this four-dimensional tensor structure. Conventional correlation measures can only characterize the linear dependence between pairs of dimensions and cannot capture the joint distribution information under multi-dimensional combinations, leading to the neglect of many strongly correlated dimension pairs hidden in local data regions. Furthermore, existing techniques often use global statistics when analyzing dimensional associations, lacking the ability to fine-tune the local manifold structure within the data subspace corresponding to highly correlated dimensions. This makes it impossible to effectively characterize nonlinear topological features in the data (such as local clustering and gradient changes). In data fusion and enhancement, traditional methods typically only perform simple tensor concatenation or weighted averaging, failing to consider learning richer correlation information from local manifold structures. This results in the fused data representation lacking the ability to deeply reconstruct potential correlation patterns in the original data. To address these issues, this invention proposes two core steps: multidimensional correlation entropy calculation and high-correlation dimension pair screening; and local topology analysis and hierarchical generative adversarial network enhancement. These steps aim to overcome the shortcomings of existing technologies, such as insufficient exploitation of deep multidimensional correlation structures, incomplete extraction of local manifold features, and inadequate data enhancement capabilities. Summary of the Invention

[0003] This invention aims to provide a multi-dimensional correlation intelligent analysis method for market research data, in order to solve the problems of existing market research data analysis methods that are unable to accurately identify high-order correlations between dimensions from a four-dimensional tensor structure containing respondent attributes, questionnaire items, timestamps, and geographical locations, are unable to perform fine topological modeling of the local data subspaces corresponding to highly correlated dimensions, and lack the ability to utilize local manifold structures to generate enhanced correlation information to improve the quality of data representation.

[0004] The objective of this invention can be achieved through the following technical solutions: A multi-dimensional correlation intelligent analysis method for market research data includes: collecting raw market research data, wherein the raw market research data includes respondent attribute dimensions, questionnaire item dimensions, timestamp dimensions, and geographic location dimensions; performing a multi-dimensional tensor construction operation on the raw market research data to generate a fourth-order raw research tensor; performing multi-dimensional correlation entropy calculation on the fourth-order raw research tensor to obtain a correlation entropy coefficient matrix between each dimension combination; selecting dimension combinations with correlation entropy coefficients exceeding a preset threshold as high-correlation dimension pairs based on the correlation entropy coefficient matrix; and for each high-correlation dimension pair, extracting the tensor slice corresponding to the high-correlation dimension pair and performing local correlation analysis. Topological analysis is performed to generate the local manifold structure of the highly correlated dimensional pairs. The local manifold structures of all highly correlated dimensional pairs are input into a hierarchical generative adversarial network (GAN), which outputs an enhanced correlated manifold tensor. This enhanced correlated manifold tensor is fused with the original fourth-order survey tensor to generate a fused survey tensor. Nonlinear dimensionality reduction mapping is performed on the fused survey tensor to obtain a survey data representation in a low-dimensional embedding space. Density peak clustering is performed in this low-dimensional embedding space to identify multiple survey data clusters. The boundary description and centroid coordinates of each survey data cluster are output as the multidimensional analysis results of the market research data.

[0005] Preferably, the step of performing a multi-dimensional tensor construction operation on the original market research data to generate a fourth-order original research tensor specifically includes: treating each respondent in the original market research data as an independent entity record; extracting the age range label, income level label, and occupation category label for each respondent entity record, and combining these labels into a respondent attribute vector; extracting the respondent's selection results for each questionnaire item for each respondent entity record, and combining all selection results into a questionnaire item response vector; extracting the timestamp of the respondent's questionnaire submission for each respondent entity record, and converting the timestamp into a sequential time window index value; extracting the geographical coordinates of the respondent's location for each respondent entity record, and mapping the geographical coordinates to a discrete grid encoding value; constructing a four-dimensional sparse tensor structure with different values ​​of the respondent attribute vector as the first dimension, different values ​​of the questionnaire item response vector as the second dimension, different values ​​of the sequential time window index value as the third dimension, and different values ​​of the discrete grid encoding value as the fourth dimension; and filling the response intensity value corresponding to each respondent entity record into the corresponding tensor unit in the four-dimensional sparse tensor structure to obtain the fourth-order original research tensor. This construction method enables the discrete and heterogeneous multidimensional information in the original survey data to be uniformly mapped into a structured tensor space, preserving the original correspondence between each dimension and providing a data foundation for subsequent correlation analysis and manifold learning.

[0006] Preferably, the step of performing multidimensional correlation entropy calculation on the fourth-order original survey tensor to obtain the correlation entropy coefficient matrix between each dimension combination specifically includes: projecting the fourth-order original survey tensor along a first dimension to generate a marginal probability distribution function for the first dimension; projecting the fourth-order original survey tensor along a second dimension to generate a marginal probability distribution function for the second dimension; projecting the fourth-order original survey tensor along a third dimension to generate a marginal probability distribution function for the third dimension; projecting the fourth-order original survey tensor along a fourth dimension to generate a marginal probability distribution function for the fourth dimension; extracting the joint projection of the first and second dimensions from the fourth-order original survey tensor to generate a joint probability distribution function for the first and second dimensions; and extracting the joint projection of the first and third dimensions from the fourth-order original survey tensor to generate a joint probability distribution function for the first and third dimensions. The joint probability distribution function is obtained by extracting the joint projection of the first and fourth dimensions from the fourth-order original survey tensor to generate the joint probability distribution function of the first and fourth dimensions; extracting the joint projection of the second and third dimensions from the fourth-order original survey tensor to generate the joint probability distribution function of the second and third dimensions; extracting the joint projection of the second and fourth dimensions from the fourth-order original survey tensor to generate the joint probability distribution function of the second and fourth dimensions; extracting the joint projection of the third and fourth dimensions from the fourth-order original survey tensor to generate the joint probability distribution function of the third and fourth dimensions; for each dimension combination, the joint probability distribution function of the dimension combination is divided by the product of the marginal probability distribution functions of the two dimensions in the dimension combination, and then the logarithm is taken to the base of the natural constant to obtain the correlation entropy coefficient of the dimension combination, specifically including: for dimension combinations ,in and The correlation entropy coefficient is calculated according to the following formula. :

[0007] in, Representing dimensions The total number of discrete values; Representing dimensions The total number of discrete values; For dimension The Each discrete value; For dimension The Each discrete value; For dimension Value With dimension Value The joint probability distribution function value; For dimension Value The marginal probability distribution function value; For dimension Value The marginal probability distribution function value; Represented by natural constant The natural logarithm with base 0; That is, dimensional combination The correlation entropy coefficients of all dimensions are calculated; the correlation entropy coefficients of all dimensions are organized into a symmetric matrix, which serves as the correlation entropy coefficient matrix. This step quantifies the nonlinear dependence between dimension pairs by calculating the relative entropy between the joint and independent distributions of dimensions, providing an objective statistical basis for subsequent screening of key correlation pairs.

[0008] Preferably, the step of selecting dimension combinations with correlation entropy coefficients exceeding a preset threshold as highly correlated dimension pairs based on the correlation entropy coefficient matrix specifically includes: traversing each matrix element outside the diagonal of the correlation entropy coefficient matrix; comparing the value of the currently traversed matrix element with a preset correlation entropy threshold; when the value of the currently traversed matrix element is greater than the correlation entropy threshold, marking the two dimensions corresponding to that matrix element as a candidate dimension pair; when the value of the currently traversed matrix element is less than or equal to the correlation entropy threshold, skipping that matrix element and continuing to traverse the next matrix element; collecting all marked candidate dimension pairs to form a candidate dimension pair list; deleting duplicate dimension pairs from the candidate dimension pair list, ensuring that each dimension pair appears only once in the list; and selecting each dimension pair in the deduplicated candidate dimension pair list as the highly correlated dimension pair. Threshold filtering can automatically identify truly strongly correlated dimension combinations in the data, reducing redundant calculations and focusing on core correlation structures.

[0009] Preferably, for each highly correlated dimension pair, the step of extracting the tensor slice corresponding to the highly correlated dimension pair and performing local topological analysis to generate the local manifold structure of the highly correlated dimension pair specifically includes: for the currently processed highly correlated dimension pair, fixing the index values ​​of all dimensions other than the two dimensions involved in the highly correlated dimension pair from the fourth-order original survey tensor; after fixing the index values ​​of the other dimensions, extracting a two-dimensional matrix as the tensor slice corresponding to the highly correlated dimension pair; performing a logarithmic transformation on each matrix element value in the tensor slice to obtain a logarithmically transformed pair. The tensor slice matrix is ​​generated by calculating the difference between each element and its neighboring elements to create a difference gradient field. Local maxima and minima of the gradient magnitude are searched within this difference gradient field, and these extreme points are used as the keypoint set for the tensor slice. The points in the keypoint set are connected into a triangular mesh structure using the Delaunay triangulation method. The weight of each edge in the triangular mesh structure is set to the absolute value of the gradient difference between the two endpoints of that edge. The weighted triangular mesh structure is then used as the local manifold structure for the highly correlated dimensional pair. By transforming the tensor slice into a triangular mesh manifold, the non-uniform distribution pattern in the local geometry between dimensions is preserved, providing structured input for subsequent generative adversarial networks.

[0010] Preferably, the step of inputting the local manifold structures of all highly correlated dimension pairs into a hierarchical generative adversarial network (GAN), wherein the GAN outputs an enhanced correlated manifold tensor, specifically includes: converting the local manifold structure of each highly correlated dimension pair into a two-dimensional image matrix, wherein the pixel values ​​of the two-dimensional image matrix correspond to the weights of the triangular mesh nodes in the local manifold structure; grouping all the converted two-dimensional image matrices according to the corresponding highly correlated dimension pairs to form a multi-channel input tensor; and inputting the multi-channel input tensor into the first-stage generator of the hierarchical GAN, wherein the first-stage... The generator outputs a first-level enhanced image matrix; this first-level enhanced image matrix is ​​input into the second-level generator of the hierarchical generative adversarial network, which outputs a second-level enhanced image matrix; this process continues, with the enhanced image matrices output from the previous level generator being input into the next level generator, until the final level generator outputs a final-level enhanced image matrix; the pixel values ​​in the final-level enhanced image matrix are extracted and reorganized into a multidimensional array according to the spatial arrangement of the original high-association dimension pairs; this multidimensional array is used as the tensor of the enhanced associative manifold. Through multi-level adversarial learning, this network can learn from the local manifold structure and synthesize a smoother, more faithful global associative manifold, improving the quality of subsequent fusion.

[0011] Preferably, the step of fusing the enhanced correlation manifold tensor with the fourth-order original survey tensor to generate a fused survey tensor specifically includes: checking whether the dimensional structure of the enhanced correlation manifold tensor is consistent with the dimensional structure of the fourth-order original survey tensor; when the dimensional structures are inconsistent, performing a linear interpolation resampling operation on the enhanced correlation manifold tensor so that the dimensional structure of the resampled enhanced correlation manifold tensor is exactly the same as the dimensional structure of the fourth-order original survey tensor; performing a weighted summation of each tensor element value in the resampled enhanced correlation manifold tensor with the tensor element value at the corresponding position in the fourth-order original survey tensor, wherein the weight coefficient of the weighted summation is determined by a preset fusion parameter; filling each tensor element value obtained after weighted summation into the tensor unit at the corresponding position in a new four-dimensional tensor structure; and using the new four-dimensional tensor structure as the fused survey tensor. The fusion operation combines the true statistical distribution of the original data with the correlation manifold information extracted by the generative network, enhancing the overall structural consistency and noise resistance of the data.

[0012] Preferably, the specific steps for performing nonlinear dimensionality reduction mapping on the fused survey tensor to obtain a survey data representation in a low-dimensional embedding space include: expanding the fused survey tensor into a two-dimensional matrix, wherein the rows of the two-dimensional matrix correspond to all dimension combinations in the fused survey tensor except for the first dimension, and the columns of the two-dimensional matrix correspond to the values ​​of the first dimension of the fused survey tensor; performing a centering process on the two-dimensional matrix to obtain a centered matrix; randomly selecting a preset number of sample points from the centered matrix as an anchor point set; calculating the geodesic distance between each sample point in the centered matrix and each anchor point in the anchor point set to obtain a distance matrix; performing a double-centering operation on the distance matrix to obtain a double-centered distance matrix; calculating the eigenvector corresponding to the largest eigenvalue of the double-centered distance matrix, and using each component of the eigenvector as the first coordinate value of the corresponding sample point in the low-dimensional embedding space, specifically including: Let the bi-centered distance matrix be... Its dimensions are ,in Given the total number of sample points, solve the following characteristic equation:

[0013] in, For feature vectors; For the corresponding eigenvalues; find the maximum value among all eigenvalues. and obtain its corresponding feature vector. Then the first in the low-dimensional embedding space The first coordinate value of each sample point Calculate using the following formula:

[0014] in, The result obtained after performing a bicentering operation on the distance matrix matrix; for The largest eigenvalue; The eigenvector corresponding to the largest eigenvalue The first in One component; For the first The first coordinate value of each sample point in the low-dimensional embedding space is calculated; the eigenvector corresponding to the second largest eigenvalue of the bi-centered distance matrix is ​​calculated, and each component of the eigenvector is used as the second coordinate value of the corresponding sample point in the low-dimensional embedding space; the two-dimensional point set composed of the first and second coordinate values ​​is used as the survey data representation in the low-dimensional embedding space. Through nonlinear dimensionality reduction, high-dimensional tensor data can be compressed into an intuitive and visual low-dimensional space while preserving the global geometric structure of the data, which facilitates subsequent clustering analysis.

[0015] Preferably, the specific steps for performing density peak clustering in the low-dimensional embedding space to identify multiple survey data clusters include: for each data point in the low-dimensional embedding space, calculating the Euclidean distance between the data point and its nearest neighbor data point, as the local density value of the data point; for each data point in the low-dimensional embedding space, calculating the minimum Euclidean distance between the data point and all data points with a local density value higher than the data point's, as the distance deviation value of the data point; marking data points whose local density values ​​and distance deviation values ​​both exceed their respective preset thresholds as candidate cluster centers; and sorting the candidate cluster centers in descending order of their local density values. The method obtains an ordered sequence of cluster centers. For each data point that is not a candidate cluster center in the low-dimensional embedding space, the data point is assigned to the cluster to which the nearest candidate cluster center belongs. When the same candidate cluster center is assigned to multiple data points, these data points, along with the candidate cluster center itself, are grouped into the same temporary cluster. The method checks whether the number of data points in each temporary cluster exceeds a preset minimum cluster size threshold. All data points in temporary clusters with a number of data points below the minimum cluster size threshold are reassigned to adjacent temporary clusters. Each remaining temporary cluster after reassignment is considered as a survey data cluster. This method does not require pre-specifying the number of clusters and can automatically discover cluster structures of different densities and shapes, making it suitable for scenarios involving natural respondent grouping in market research.

[0016] Preferably, the step of outputting the boundary description and center point coordinates of each survey data cluster as the multidimensional analysis result of the market research data specifically includes: for each survey data cluster, collecting the coordinate values ​​of all data points in the low-dimensional embedding space; calculating the arithmetic mean of the coordinate values ​​of all data points in the survey data cluster to obtain the cluster center coordinates of the survey data cluster; calculating the Euclidean distance from each data point in the survey data cluster to the cluster center coordinates, and finding the maximum distance value; constructing a circular region with the cluster center coordinates as the center and the maximum distance value as the radius, and using the circumference equation of the circular region as the boundary description of the survey data cluster; organizing the cluster center coordinates and the boundary description of each survey data cluster into an output record; arranging the output records of all survey data clusters in descending order of cluster size to form an output list; and returning the output list as the multidimensional analysis result of the market research data. By outputting the cluster center and circular boundary, the characteristic range and core location of each market segment can be intuitively presented to the user, assisting in decision support.

[0017] The beneficial effects of this invention are: By performing multidimensional correlation entropy calculations, the correlation entropy coefficient matrix between each dimension combination is obtained, and dimension combinations with correlation entropy coefficients exceeding a preset threshold are selected as highly correlated dimension pairs. This scheme uses the ratio of the product of the joint probability distribution and the marginal probability distribution, and takes the logarithm, to measure the degree of nonlinear dependence between dimensions. It can comprehensively capture the joint information between any two dimensions in a four-dimensional tensor. Compared with the traditional linear correlation coefficient, it is more sensitive to complex high-order interactions between dimensions, thus accurately identifying potentially important dimension pairs in the data. This avoids missing local strongly correlated structures due to relying solely on global statistics, allowing subsequent analysis to focus on dimension combinations with truly high information density, improving the computational efficiency and relevance of the analysis. For each highly correlated dimension pair, tensor slices are extracted and local topological analysis is performed, including logarithmic transformation, difference gradient field calculation, extremum detection, Delaunay triangulation, and edge weight setting, generating a triangular mesh structure with gradient differences as a local manifold structure. All local manifold structures are then converted into two-dimensional image matrices and grouped into multi-channel input tensors, which are input to a hierarchical generative adversarial network (GAN). After being progressively enhanced by a multi-level generator, an enhanced correlated manifold tensor is output. This scheme performs refined topological modeling of the local data subspace for each highly correlated dimension pair, preserving the gradient changes and geometric connectivity within the data, and avoiding the destruction of local nonlinear features by global smoothing. The hierarchical GAN, by progressively learning the distribution patterns of the local manifold structure, can generate more representative and complete correlation information from limited input data, ensuring that the enhanced correlated manifold tensor not only contains the topological features of the original highly correlated dimension pairs but also supplements missing or weakened correlation details. Attached Figure Description

[0018] The invention will now be further described with reference to the accompanying drawings.

[0019] Figure 1 This is a flowchart of the intelligent analysis method for multi-dimensional correlation market research data described in this invention; Figure 2 This is a flowchart constructed based on the correlation entropy matrix of the edge and joint probability distribution; Figure 3 This is a flowchart of the survey tensor augmentation fusion under hierarchical generative adversarial networks. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] See Figure 1 This invention provides a method for intelligent analysis of market research data with multi-dimensional correlation, comprising: collecting raw market research data, wherein the raw market research data includes respondent attribute dimensions, questionnaire item dimensions, timestamp dimensions, and geographic location dimensions; performing a multi-dimensional tensor construction operation on the raw market research data to generate a fourth-order raw research tensor; performing multi-dimensional correlation entropy calculation on the fourth-order raw research tensor to obtain a correlation entropy coefficient matrix between each dimension combination; selecting dimension combinations with correlation entropy coefficients exceeding a preset threshold as high-correlation dimension pairs based on the correlation entropy coefficient matrix; and for each high-correlation dimension pair, extracting the tensor slice corresponding to the high-correlation dimension pair and performing... Local topology analysis is performed to generate the local manifold structure of the highly correlated dimensional pairs. The local manifold structures of all highly correlated dimensional pairs are input into a hierarchical generative adversarial network (GAN), which outputs an enhanced correlated manifold tensor. This enhanced correlated manifold tensor is fused with the original fourth-order survey tensor to generate a fused survey tensor. Nonlinear dimensionality reduction mapping is performed on the fused survey tensor to obtain a survey data representation in a low-dimensional embedding space. Density peak clustering is performed in this low-dimensional embedding space to identify multiple survey data clusters. The boundary description and centroid coordinates of each survey data cluster are output as the multidimensional analysis results of the market research data.

[0022] Example 1: In specific implementation, a multi-dimensional tensor construction operation is performed on the original market research data to generate a fourth-order original research tensor. Each respondent in the original market research data is treated as an independent entity record. For each respondent entity record, age range labels, income level labels, and occupation category labels are extracted and combined into a respondent attribute vector. The age range labels are taken from a predefined set of age ranges, the income level labels from a predefined set of income levels, and the occupation category labels from a predefined set of occupation categories. For each respondent entity record, the respondent's selection results for each questionnaire item are extracted and combined into a questionnaire item response vector. Each component in the questionnaire item response vector corresponds to a selection result for a questionnaire item, represented by an integer value. For each respondent entity record, the timestamp of the respondent submitting the questionnaire is extracted and converted into a sequential time window index value. The sequential time window index value is obtained by mapping the timestamp to a window number in a pre-divided continuous time window, with each time window having a fixed duration. For each respondent entity record, the geographic location coordinates of the respondent are extracted and mapped to a discrete grid code value. The discrete grid code value is obtained by gridding the geographic location coordinates, dividing the geographic space into multiple grid cells, with each grid cell corresponding to a unique code value.

[0023] A four-dimensional sparse tensor structure is constructed, using different values ​​of the respondent attribute vector as the first dimension, different values ​​of the questionnaire item response vector as the second dimension, different values ​​of the sequential time window index value as the third dimension, and different values ​​of the discrete grid encoding value as the fourth dimension. The dimensions of the four-dimensional sparse tensor structure are determined by the total number of values ​​of the respondent attribute vector, the total number of values ​​of the questionnaire item response vector, the total number of values ​​of the sequential time window index value, and the total number of values ​​of the discrete grid encoding value, respectively. The response intensity value corresponding to each respondent entity record is filled into the corresponding tensor unit in the four-dimensional sparse tensor structure to obtain the fourth-order original survey tensor. The response intensity value refers to the numerical value corresponding to the respondent's selection result for each questionnaire item. For each respondent entity record, its corresponding tensor unit is jointly determined by the respondent's respondent attribute vector value, the respondent's questionnaire item response vector value, the respondent's sequential time window index value, and the respondent's discrete grid encoding value.

[0024] Example 2: In specific implementation, refer to Figure 2Multidimensional correlation entropy calculation is performed on the fourth-order original survey tensor to obtain the correlation entropy coefficient matrix between each dimension combination. The fourth-order original survey tensor is then marginally projected along the first dimension to generate a marginal probability distribution function for the first dimension. This marginal probability distribution function is obtained by summing all tensor element values ​​corresponding to the first dimension index values ​​along the second, third, and fourth dimensions, and then dividing by the sum of all tensor element values ​​in the fourth-order original survey tensor. The fourth-order original survey tensor is then marginally projected along the second dimension to generate a marginal probability distribution function for the second dimension. The fourth-order original survey tensor is then marginally projected along the third dimension to generate a marginal probability distribution function for the third dimension. Finally, the fourth-order original survey tensor is marginally projected along the fourth dimension to generate a marginal probability distribution function for the fourth dimension. The marginal probability distribution functions for the second, third, and fourth dimensions are generated in the same way as those for the first dimension, by summing and normalizing along their respective other three dimensions.

[0025] The joint projection of the first and second dimensions is extracted from the fourth-order original survey tensor to generate a joint probability distribution function for the first and second dimensions. This joint probability distribution function is obtained by summing the tensor element values ​​in the fourth-order original survey tensor that correspond to both the first and second dimension indices along the third and fourth dimensions, and then dividing by the sum of all tensor element values ​​in the fourth-order original survey tensor. The joint projection of the first and third dimensions is extracted from the fourth-order original survey tensor to generate a joint probability distribution function for the first and third dimensions. The joint projection of the second and third dimensions is extracted from the fourth-order original survey tensor to generate a joint probability distribution function for the second and third dimensions. The joint projection of the second and fourth dimensions is extracted from the fourth-order original survey tensor to generate a joint probability distribution function for the second and fourth dimensions. The joint projection of the third and fourth dimensions is extracted from the fourth-order original survey tensor to generate a joint probability distribution function for the third and fourth dimensions. The above six joint probability distribution functions are all generated in the same way: the index values ​​of the corresponding two dimensions are fixed, and the summation and normalization are performed along the other two dimensions.

[0026] For each dimension combination, the joint probability distribution function of that combination is divided by the product of the marginal probability distribution functions of the two dimensions in that combination, and then the logarithm is taken to the base of the natural constant to obtain the association entropy coefficient of that dimension combination. Specifically, for dimension combinations... ,in and The correlation entropy coefficient is calculated according to the following formula. :

[0027] in, Representing dimensions The total number of discrete values, Representing dimensions The total number of discrete values, For dimension The A discrete value, For dimension The A discrete value, For dimension Value With dimension Value The joint probability distribution function value, For dimension Value The marginal probability distribution function value, For dimension Value The marginal probability distribution function value, Represented by natural constant The natural logarithm with base 0. That is, dimensional combination The correlation entropy coefficient.

[0028] The correlation entropy coefficients of all dimension combinations are organized into a symmetric matrix, which is taken as the correlation entropy coefficient matrix. The dimension of the correlation entropy coefficient matrix is... The matrix located at the th Line 1 The elements of the column correspond to the dimension combination correlation entropy coefficient And the matrix satisfies symmetry, that is Diagonal elements It does not participate in the calculation and can be set to zero or any value.

[0029] Example 3: In specific implementation, dimension combinations with correlation entropy coefficients exceeding a preset threshold are selected as high-correlation dimension pairs based on the correlation entropy coefficient matrix. Each matrix element outside the diagonal of the correlation entropy coefficient matrix is ​​traversed. The value of the currently traversed matrix element is compared with a preset correlation entropy threshold. When the value of the currently traversed matrix element is greater than the correlation entropy threshold, the two dimensions corresponding to that matrix element are marked as a candidate dimension pair. When the value of the currently traversed matrix element is less than or equal to the correlation entropy threshold, that matrix element is skipped and the traversal continues to the next matrix element. All marked candidate dimension pairs are collected to form a candidate dimension pair list. Duplicate dimension pairs are removed from the candidate dimension pair list, ensuring that each dimension pair appears only once in the list. Each dimension pair in the deduplicated candidate dimension pair list is selected as the high-correlation dimension pair.

[0030] For each highly correlated dimension pair, a tensor slice corresponding to that pair is extracted and local topological analysis is performed to generate the local manifold structure of that pair. For the currently processed highly correlated dimension pair, the index values ​​of all dimensions other than the two dimensions involved in the highly correlated pair are fixed from the fourth-order original survey tensor. After fixing the index values ​​of the other dimensions, a two-dimensional matrix is ​​extracted as the tensor slice corresponding to that highly correlated dimension pair. A logarithmic transformation is performed on each matrix element value in the tensor slice to obtain a logarithmically transformed logarithmic slice matrix. The logarithmic transformation uses natural constants. The natural logarithm function with base 0, for each matrix element value in the tensor slice. calculate To avoid cases where the logarithmic value is zero, the corresponding element values ​​in the logarithmic slice matrix are obtained. The difference between each matrix element and its adjacent matrix elements is calculated to generate a difference gradient field. The adjacent matrix elements include those above, below, to the left, and to the right of the matrix element; if the matrix element is located on a boundary, adjacent elements in missing directions are ignored. The difference is the value of the matrix element minus the value of its adjacent matrix elements. Local maxima and minima of the gradient magnitude are searched in the difference gradient field, and these extreme points are used as the keypoint set for the tensor slice. The gradient magnitude is the square root of the sum of the squares of the differences in the four directions at each matrix element. The points in the keypoint set are connected into a triangular mesh structure using the Delaunay triangulation method. The weight of each edge in the triangular mesh structure is set to the absolute value of the gradient difference between the two endpoints of that edge. The absolute value of the gradient difference is obtained by calculating the difference between the gradient magnitudes of the two endpoints at their corresponding positions in the difference gradient field and taking the absolute value. The weighted triangular mesh structure is used as the local manifold structure for this highly correlated dimension pair.

[0031] Example 4: In specific implementation, refer to Figure 3 The local manifold structures of all highly correlated dimension pairs are input into a hierarchical generative adversarial network (GAN), which outputs an enhanced correlated manifold tensor. Each highly correlated dimension pair's local manifold structure is converted into a two-dimensional image matrix, where the pixel values ​​of the two-dimensional image matrix correspond to the weights of triangular mesh nodes in the local manifold structure. The conversion process involves arranging the weights of the triangular mesh nodes in the local manifold structure according to their spatial positions within the mesh and filling them into corresponding positions in a two-dimensional matrix. The size of the matrix is ​​determined by the maximum number of rows and columns of the triangular mesh nodes; positions without nodes are filled with zeros. All the converted two-dimensional image matrices are grouped according to their corresponding highly correlated dimension pairs to form a multi-channel input tensor. The number of channels in the multi-channel input tensor is equal to the number of highly correlated dimension pairs, with each channel corresponding to a two-dimensional image matrix of a highly correlated dimension pair. The multi-channel input tensor is then input into the first-level generator of the hierarchical GAN, which outputs a first-level enhanced image matrix. The first-level generator consists of a convolutional neural network with an encoder-decoder structure. The encoder part contains multiple convolutional and pooling layers, and the decoder part contains multiple deconvolutional and upsampling layers. The encoder and decoder are connected via skip connections. The input to the first-level generator is the multi-channel input tensor, and the output is a single-channel first-level enhanced image matrix. The first-level enhanced image matrix is ​​then input into the second-level generator of the hierarchical generative adversarial network, which outputs a second-level enhanced image matrix. The second-level generator uses the same network structure as the first-level generator, with the enhanced image matrix output from the previous level as input and a single-channel enhanced image matrix as output. This process continues, with the enhanced image matrix output from the previous level being input into the next level generator, until the final level generator outputs a final-level enhanced image matrix. The total number of levels in the hierarchical generative adversarial network is determined by a preset level parameter, which is set to 3. This is based on the premise that when the number of highly correlated dimensional pairs does not exceed 6, a 3-level generator can sufficiently amplify the correlated features in the local manifold structure. The pixel values ​​in the final enhanced image matrix are extracted and reorganized into a multidimensional array according to the spatial arrangement order of the original highly correlated dimension pairs. The spatial arrangement order of the original highly correlated dimension pairs refers to the order of each channel when the multi-channel input tensor is formed in the previous step. This multidimensional array is used as the enhanced correlated manifold tensor.

[0032] The enhanced correlated manifold tensor is fused with the fourth-order original survey tensor to generate a fused survey tensor. The dimensional structure of the enhanced correlated manifold tensor is checked to ensure consistency with that of the fourth-order original survey tensor. If the dimensional structures are inconsistent, a linear interpolation resampling operation is performed on the enhanced correlated manifold tensor to ensure that the dimensional structure of the resampled enhanced correlated manifold tensor is identical to that of the fourth-order original survey tensor. The linear interpolation resampling operation adjusts the size of each dimension of the enhanced correlated manifold tensor to the target dimension size by applying one-dimensional linear interpolation to each dimension. Each tensor element value in the resampled enhanced correlated manifold tensor is then weighted and summed with the corresponding tensor element value in the fourth-order original survey tensor. The weighting coefficients for the summation are determined by a preset fusion parameter. The fusion parameter is set to 0.5, indicating that the weight of both the resampled enhanced correlated manifold tensor and the fourth-order original survey tensor is 0.5, ensuring that the two tensors contribute equally during fusion. Each tensor element value obtained after weighted summation is filled into the corresponding tensor unit in a new four-dimensional tensor structure. This new four-dimensional tensor structure is used as the fusion survey tensor.

[0033] Example 5: In a specific implementation, a nonlinear dimensionality reduction mapping is performed on the fused survey tensor to obtain a survey data representation in a low-dimensional embedding space. The fused survey tensor is expanded into a two-dimensional matrix, where the rows of the two-dimensional matrix correspond to all dimension combinations in the fused survey tensor except for the first dimension, and the columns of the two-dimensional matrix correspond to the values ​​of the first dimension of the fused survey tensor. The first dimension is the respondent attribute dimension. All dimension combinations except for the first dimension include all possible value combinations of the second, third, and fourth dimensions. Each combination corresponds to a row of the two-dimensional matrix, and each value of the first dimension corresponds to a column of the two-dimensional matrix. A centering process is performed on the two-dimensional matrix to obtain a centered matrix. The centering process is as follows: calculate the mean of each column of the two-dimensional matrix, and then subtract the mean of the column from each element in that column to obtain the centered matrix. A preset number of sample points are randomly selected from the centered matrix as an anchor point set. The preset number is set to 100, based on the fact that when the total number of sample points exceeds 10,000, 100 anchor points can ensure the stability of geodesic distance calculation. Calculate the geodesic distance between each sample point in the centered matrix and each anchor point in the anchor point set to obtain a distance matrix. The geodesic distance is obtained by constructing a k-nearest neighbor graph between sample points and running Dijkstra's algorithm on the k-nearest neighbor graph, with k set to 15. Perform a bi-centering operation on the distance matrix to obtain a bi-centered distance matrix. The bi-centering operation includes: squaring each element in the distance matrix, then subtracting the mean from each row and column of the squared matrix, adding the global mean, and multiplying by -0.5 to obtain the bi-centered distance matrix. Calculate the eigenvector corresponding to the largest eigenvalue of the bi-centered distance matrix, and use each component of this eigenvector as the first coordinate value of the corresponding sample point in the low-dimensional embedding space. Specifically, this includes: Let the bi-centered distance matrix be... Its dimensions are ,in Given the total number of sample points, solve the following characteristic equation:

[0034] in, For feature vectors, Let each be a corresponding eigenvalue. Find the maximum value among all eigenvalues. and obtain its corresponding feature vector. Then the first in the low-dimensional embedding space The first coordinate value of each sample point Calculate using the following formula:

[0035] in, The result obtained after performing a bicentering operation on the distance matrix matrix, for The largest eigenvalue, The eigenvector corresponding to the largest eigenvalue The first in One portion, For the first The first coordinate value of each sample point in the low-dimensional embedding space. Calculate the eigenvector corresponding to the second largest eigenvalue of the bi-centered distance matrix, and use each component of this eigenvector as the second coordinate value of the corresponding sample point in the low-dimensional embedding space. The second largest eigenvalue... The corresponding eigenvector is denoted as Then the first The second coordinate value of each sample point Calculate using the following formula:

[0036] The two-dimensional point set consisting of the first coordinate value and the second coordinate value is used as the survey data representation in the low-dimensional embedding space.

[0037] Density peak clustering is performed in the low-dimensional embedding space to identify multiple survey data clusters. For each data point in the low-dimensional embedding space, the Euclidean distance between the data point and its nearest neighbor is calculated as the local density value of the data point. The nearest neighbor refers to the other data point with the smallest Euclidean distance to the data point. For each data point in the low-dimensional embedding space, the minimum Euclidean distance between the data point and all data points with a local density value higher than the data point is calculated as the distance deviation value of the data point. If the local density value of a data point is the largest among all data points, the distance deviation value of the data point is set as the maximum Euclidean distance from the data point among all data points. Data points whose local density value and distance deviation value both exceed their respective preset thresholds are marked as candidate cluster centers. The preset threshold for the local density value is set to the median of the local density values ​​of all data points, and the preset threshold for the distance deviation value is set to the median of the distance deviation values ​​of all data points. The candidate cluster centers are sorted in descending order of local density value to obtain an ordered cluster center sequence. For each data point that is not a candidate cluster center in the low-dimensional embedding space, the data point is assigned to the cluster to which the nearest candidate cluster center belongs. The distance refers to Euclidean distance. When the same candidate cluster center is assigned to multiple data points, these data points, along with the candidate cluster center itself, are grouped into the same temporary cluster. It is checked whether the number of data points in each temporary cluster exceeds a preset minimum cluster size threshold. All data points in temporary clusters with a number of data points below the minimum cluster size threshold are reassigned to adjacent temporary clusters. The minimum cluster size threshold is set to 5, based on the fact that statistically significant clusters cannot be formed when the number of data points is less than 5. Reassignment to adjacent temporary clusters means assigning each data point in the temporary cluster to the candidate cluster center of the next temporary cluster closest to the data point. Each remaining temporary cluster after reassignment is considered as one of the survey data clusters.

[0038] Output the boundary description and center point coordinates of each survey data cluster as the multidimensional analysis result of the market research data. For each survey data cluster, collect the coordinate values ​​of all data points in the low-dimensional embedding space. Calculate the arithmetic mean of the coordinate values ​​of all data points in the survey data cluster to obtain the cluster center coordinates. The arithmetic mean is obtained by summing the first coordinate values ​​of all data points and dividing by the number of data points, and by summing the second coordinate values ​​of all data points and dividing by the number of data points. Use the first and second coordinate averages as the cluster center coordinates. Calculate the Euclidean distance from each data point in the survey data cluster to the cluster center coordinates and find the maximum distance value. Construct a circular region with the cluster center coordinates as the center and the maximum distance value as the radius. Use the equation of the circumference of this circular region as the boundary description of the survey data cluster. The circumference equation is... ,in The coordinates of the cluster center The maximum distance value is used. The cluster center coordinates and boundary descriptions of each survey data cluster are organized into an output record. All output records for all survey data clusters are arranged in descending order of cluster size, forming an output list. The cluster size refers to the number of data points contained in the cluster. This output list is returned as the multidimensional analysis result of the market research data.

[0039] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.

Claims

1. A multi-dimensional associated market research data intelligent analysis method, characterized in that, The method comprises the following steps: Collecting original market research data, which includes respondent attribute dimensions, questionnaire item dimensions, timestamp dimensions, and geographic location dimensions; Performing a multi-dimensional tensor construction operation on the original market research data to generate a four-order original research tensor; Performing multi-dimensional correlation entropy calculation on the four-order original research tensor to obtain a correlation entropy coefficient matrix between each dimension combination; Filtering out dimension combinations with correlation entropy coefficients exceeding a preset threshold as high-correlation dimension pairs according to the correlation entropy coefficient matrix; For each high-correlation dimension pair, extracting the tensor slice corresponding to the high-correlation dimension pair and performing local topological analysis to generate the local manifold structure of the high-correlation dimension pair; Inputting the local manifold structures of all high-correlation dimension pairs into a hierarchical generative adversarial network, which outputs an enhanced correlation manifold tensor; Fusing the enhanced correlation manifold tensor with the four-order original research tensor to generate a fused research tensor; Performing nonlinear dimension reduction mapping on the fused research tensor to obtain a research data representation in a low-dimensional embedding space; Performing density peak clustering in the low-dimensional embedding space to identify multiple research data clusters; Outputting the boundary description and center point coordinates of each research data cluster as the multi-dimensional analysis result of the market research data.

2. The method of claim 1, wherein, The step of performing a multi-dimensional tensor construction operation on the original market research data to generate a four-order original research tensor comprises the following steps: Regarding each respondent in the original market research data as an independent entity record; Extracting the age interval label, income level label, and occupation category label of each respondent entity record, and combining these labels into a respondent attribute vector; Extracting the selection results of each respondent on each questionnaire item, and combining the selection results of all items into a questionnaire item response vector; Extracting the timestamp of each respondent submitting the questionnaire, and converting the timestamp into a sequential time window index value; Extracting the geographic location coordinates of each respondent, and mapping the geographic location coordinates to a discrete grid encoding value; Constructing a four-dimensional sparse tensor structure with different values of the respondent attribute vector as the first dimension, different values of the questionnaire item response vector as the second dimension, different values of the sequential time window index value as the third dimension, and different values of the discrete grid encoding value as the fourth dimension; Filling the response intensity value corresponding to each respondent entity record into the corresponding tensor unit of the four-dimensional sparse tensor structure to obtain the four-order original research tensor.

3. The method of claim 2, wherein the method further comprises: The step of performing multi-dimensional correlation entropy calculation on the four-order original research tensor to obtain a correlation entropy coefficient matrix between each dimension combination comprises the following steps: Performing edge projection on the four-order original research tensor along the first dimension to generate an edge probability distribution function of the first dimension; Performing edge projection on the four-order original research tensor along the second dimension to generate an edge probability distribution function of the second dimension; The fourth-order original survey tensor is projected along the third dimension to generate the edge probability distribution function of the third dimension. The fourth-order original survey tensor is projected along the fourth dimension to generate the edge probability distribution function of the fourth dimension. Extract the joint projection of the first and second dimensions from the fourth-order original survey tensor to generate the joint probability distribution function of the first and second dimensions; Extract the joint projection of the first and third dimensions from the fourth-order original survey tensor to generate the joint probability distribution function of the first and third dimensions; Extract the joint projection of the first and fourth dimensions from the fourth-order original survey tensor to generate the joint probability distribution function of the first and fourth dimensions; Extract the joint projection of the second and third dimensions from the fourth-order original survey tensor to generate the joint probability distribution function of the second and third dimensions; Extract the joint projection of the second and fourth dimensions from the fourth-order original survey tensor to generate the joint probability distribution function of the second and fourth dimensions; Extract the joint projection of the third and fourth dimensions from the fourth-order original survey tensor to generate the joint probability distribution function of the third and fourth dimensions; For each dimension combination, the joint probability distribution function of the dimension combination is divided by the product of the marginal probability distribution functions of the two dimensions in the dimension combination, and then the logarithm is taken to the base of the natural constant to obtain the correlation entropy coefficient of the dimension combination. The correlation entropy coefficients of all dimension combinations are organized into a symmetric matrix, which is used as the correlation entropy coefficient matrix.

4. The multi-dimensional associated market research data intelligent analysis method according to claim 3, characterized in that, The step of selecting dimension pairs with correlation entropy coefficients exceeding a preset threshold as high-correlation dimension pairs based on the correlation entropy coefficient matrix specifically includes: Iterate through every element of the correlation entropy coefficient matrix that is outside the diagonal; The value of the currently traversed matrix element is compared with a pre-set associative entropy threshold. When the value of the currently traversed matrix element is greater than the association entropy threshold, the two dimensions corresponding to the matrix element are marked as a candidate dimension pair. When the value of the currently traversed matrix element is less than or equal to the associated entropy threshold, skip the matrix element and continue traversing the next matrix element; Collect all labeled candidate dimension pairs to form a candidate dimension pair list; Remove duplicate dimension pairs from the candidate dimension pair list so that each dimension pair appears only once in the list; Each dimension pair in the deduplicated candidate dimension pair list is taken as the highly correlated dimension pair.

5. The multi-dimensional associated market research data intelligent analysis method according to claim 4, characterized in that, For each highly correlated dimension pair, the steps of extracting the tensor slice corresponding to that highly correlated dimension pair and performing local topological analysis to generate the local manifold structure of that highly correlated dimension pair specifically include: For the currently processed highly correlated dimension pair, fix the index values ​​of all other dimensions except the two dimensions involved in the highly correlated dimension pair from the fourth-order original survey tensor; After fixing the index values ​​of other dimensions, a two-dimensional matrix is ​​extracted as the tensor slice corresponding to the highly correlated dimension pair; Perform a logarithmic transformation on each matrix element value in the tensor slice to obtain a logarithmically transformed logarithmic slice matrix; Calculate the difference between each element of the logarithmic slice matrix and its adjacent elements to generate a difference gradient field; Search for local maxima and local minima of the gradient magnitude in the difference gradient field, and use these extreme points as the key point set of the tensor slice; The points in the key point set are connected into a triangular mesh structure using the Delaunay triangulation method; The weight of each edge in the triangular mesh structure is set to the absolute value of the gradient difference between the two endpoints of that edge; The weighted triangular mesh structure is used as the local manifold structure for this highly correlated dimension pair.

6. The multi-dimensional, correlated market research data intelligent analysis method of claim 5, wherein, The step of inputting the local manifold structure of all highly correlated dimension pairs into a hierarchical generative adversarial network (GAN), which outputs an enhanced correlated manifold tensor, specifically includes: The local manifold structure of each highly correlated dimension pair is transformed into a two-dimensional image matrix, where the pixel values ​​of the two-dimensional image matrix correspond to the weights of the triangular mesh nodes in the local manifold structure. All the converted two-dimensional image matrices are grouped according to their corresponding highly correlated dimensions to form a multi-channel input tensor. The multi-channel input tensor is input into the first-level generator of the hierarchical generative adversarial network, and the first-level generator outputs a first-level enhanced image matrix. The first-level enhanced image matrix is ​​input into the second-level generator of the hierarchical generative adversarial network, and the second-level generator outputs a second-level enhanced image matrix. In this way, the enhanced image matrix output by the previous stage generator is input into the next stage generator until the final stage generator processes it and outputs a final stage enhanced image matrix. The pixel values ​​in the final enhanced image matrix are extracted and reorganized into a multidimensional array according to the spatial arrangement order of the original highly correlated dimension pairs; The multidimensional array is used as the enhanced associative manifold tensor.

7. The multi-dimensional, correlated market research data intelligent analysis method of claim 6, wherein, The step of fusing the enhanced correlated manifold tensor with the fourth-order original survey tensor to generate a fused survey tensor specifically includes: Check whether the dimensional structure of the enhanced correlated manifold tensor is consistent with the dimensional structure of the fourth-order original survey tensor; When the dimensional structure is inconsistent, a linear interpolation resampling operation is performed on the enhanced correlated manifold tensor so that the dimensional structure of the resampled enhanced correlated manifold tensor is exactly the same as the dimensional structure of the fourth-order original survey tensor. The tensor element value in the resampled enhanced correlated manifold tensor is weighted and summed with the tensor element value at the corresponding position in the fourth-order original survey tensor, wherein the weight coefficient of the weighted summation is determined by a preset fusion parameter. Each tensor element value obtained after weighted summation is filled into the corresponding tensor unit in a new four-dimensional tensor structure; The new four-dimensional tensor structure is used as the fusion survey tensor.

8. The multi-dimensional associated market research data intelligent analysis method according to claim 7, characterized in that, The specific steps for performing nonlinear dimensionality reduction mapping on the fused survey tensor to obtain a survey data representation in a low-dimensional embedding space include: The fusion survey tensor is expanded into a two-dimensional matrix, wherein the rows of the two-dimensional matrix correspond to all combinations of dimensions in the fusion survey tensor except for the first dimension, and the columns of the two-dimensional matrix correspond to the values ​​of the first dimension of the fusion survey tensor. The two-dimensional matrix is ​​centered to obtain a centered matrix; A predetermined number of sample points are randomly selected from the centralized matrix as the anchor point set; Calculate the geodesic distance between each sample point in the centered matrix and each anchor point in the anchor point set to obtain a distance matrix; Perform a bicentering operation on the distance matrix to obtain a bicentered distance matrix; Calculate the eigenvector corresponding to the largest eigenvalue of the dual-centering distance matrix, and use each component of the eigenvector as the first coordinate value of the corresponding sample point in the low-dimensional embedding space; Calculate the eigenvector corresponding to the second largest eigenvalue of the dual-centering distance matrix, and use each component of the eigenvector as the second coordinate value of the corresponding sample point in the low-dimensional embedding space; The two-dimensional point set consisting of the first coordinate value and the second coordinate value is used as the survey data representation in the low-dimensional embedding space.

9. The multi-dimensional associated market research data intelligent analysis method according to claim 8, characterized in that, The specific steps for performing density peak clustering in the low-dimensional embedding space to identify multiple survey data clusters include: For each data point in the low-dimensional embedding space, calculate the Euclidean distance between the data point and its nearest neighbor data point, and use it as the local density value of the data point. For each data point in the low-dimensional embedding space, calculate the minimum Euclidean distance between the data point and all data points with a higher local density value than the data point, and use this distance as the distance deviation value of the data point. Data points whose local density value and distance deviation value both exceed their respective preset thresholds are marked as candidate cluster centers; Candidate cluster centers are sorted in descending order of local density values ​​to obtain an ordered cluster center sequence. For each data point that is not a candidate cluster center in the low-dimensional embedding space, the data point is assigned to the cluster to which the nearest candidate cluster center belongs; When the same candidate cluster center is assigned to multiple data points, these data points, along with the candidate cluster center itself, are grouped into the same temporary cluster. Check whether the number of data points in each temporary cluster exceeds the preset minimum cluster size threshold, and reallocate all data points in temporary clusters with a number of data points lower than the minimum cluster size threshold to adjacent temporary clusters. Each of the remaining temporary clusters after redistribution will be considered as one of the survey data clusters.

10. The method of claim 9, wherein the method further comprises: The steps for outputting the boundary descriptions and center point coordinates of each survey data cluster as the results of multidimensional analysis of market research data specifically include: For each survey data cluster, collect the coordinate values ​​of all data points in the survey data cluster in the low-dimensional embedding space; Calculate the arithmetic mean of the coordinates of all data points in the survey data cluster to obtain the coordinates of the cluster center of the survey data cluster; Calculate the Euclidean distance from each data point in the survey data cluster to the coordinates of the cluster center, and find the maximum distance value among them; A circular region is constructed with the cluster center coordinates as the center and the maximum distance value as the radius. The circumference equation of this circular region is used as the boundary description of the survey data cluster. The cluster center coordinates and boundary descriptions of each survey data cluster are organized into an output record. Arrange the output records of all survey data clusters in descending order of cluster size to form an output list; The output list is returned as the result of a multidimensional analysis of the market research data.

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