Feature Constraint-based Primary Curve Optimization Method and Device

Abstract

This application is applicable to the field of data processing technology, and provides a method and device for optimizing a principal curve based on feature constraints. The method includes: obtaining high-dimensional non-linear data to be analyzed and mapping it to a target Riemannian manifold; the high-dimensional non-linear data has specific attributes; constructing an initial principal curve to be optimized through the data points of the target Riemannian manifold; determining a target projection point where the target data point is projected to the target position; determining a joint contribution factor of the target data point according to a spatial constraint coefficient and at least one data attribute feature constraint coefficient; updating the principal curve to be optimized by minimizing the target optimization error to obtain a final target principal curve. This application introduces a data attribute feature constraint coefficient on the basis of the spatial constraint coefficient to jointly determine the joint contribution factor of the data points of the high-dimensional non-linear data, solves the fitting error problem caused by the traditional principal curve method ignoring the data attribute features, and improves the fitting accuracy of the principal curve.

Description

Technical Field

[0001] This application relates to the technical field of data processing, and in particular, to a method and device for optimizing a principal curve based on feature constraints. Background Art

[0002] With the rapid development of artificial intelligence and data science, the application of high-dimensional non-linear data is becoming increasingly widespread in many fields. Such data not only contains complex spatial structures but may also have specific attribute features, such as time-series characteristics, density distribution features, or velocity change features. For example, human motion data, as typical high-dimensional non-linear data, not only contains complex spatial structures but also has strong time-series characteristics and three-dimensional rotation information. Accurately and effectively analyzing and modeling high-dimensional non-linear data is of great significance for promoting the development of related fields.

[0003] Currently, the principal curve method, as an important non-linear dimensionality reduction technique, has been widely studied and applied. This method captures the main trends and potential structures of data by fitting a smooth curve on the data manifold, providing a basis for subsequent analysis and modeling. However, existing principal curve methods face two key technical problems when dealing with high-dimensional non-linear data with specific attributes:

[0004] First, the problem of feature misalignment. Existing principal curve methods only rely on the Riemannian distance to optimize the curve during the update process, completely ignoring the specific attribute features that the data may have. For example, when dealing with data with strong time-series characteristics (such as human motion data), if traditional methods treat data points as an unordered set and ignore the time correlation between data points, it will lead to the destruction of the time structure of the data during the fitting process, making the principal curve unable to accurately capture the true evolution process of the data. For example, when the start phase of an action is spatially similar to the end phase of another action, existing principal curve methods may wrongly confuse these phases, resulting in an incoherent fitting result; or for periodic motion, it is unable to effectively distinguish similar configurations in adjacent periods, often wrongly classifying similar points in different periods into the same fitting group, leading to the destruction of the periodic structure, thus seriously affecting the fitting accuracy of the principal curve.

[0005] Second, when dealing with data containing rotation information, there is a problem of unstable rotation axis selection. Traditional methods usually use predefined fixed rotation axes (such as the X, Y, or Z axes) to process rotation data. This method ignores the geometric characteristics of the data distribution and is prone to direction instability when dealing with equivalent rotations (for example, rotating 90° to the left is equivalent to rotating 270° to the right mathematically), which in turn affects the convergence of the optimization process and the global consistency of the fitting result. Especially when there are measurement errors or depth estimation biases in the rotation data, this instability will be further amplified, resulting in a significant reduction in the fitting quality of the principal curve and introducing unnecessary computational complexity. Summary of the Invention

[0006] The embodiments of the present application provide an optimization method, device, electronic device and medium for a principal curve based on feature constraints, which can solve the problem of low fitting accuracy of traditional principal curve methods. The present application provides an optimization method, device and medium for a principal curve based on feature constraints.

[0007] In a first aspect, the embodiments of the present application provide an optimization method for a principal curve based on feature constraints, including:

[0008] Obtain high-dimensional non-linear data to be analyzed, and map the high-dimensional non-linear data to a target Riemannian manifold; the high-dimensional non-linear data has specific attributes;

[0009] Construct an initial principal curve to be optimized through the data points of the target Riemannian manifold;

[0010] Determine a target projection point for the target data point projected to a target position; the target data point is any data point on the target Riemannian manifold, and the target position is any position on the principal curve to be optimized;

[0011] Determine a joint contribution factor of the target data point according to a spatial constraint coefficient and at least one data attribute feature constraint coefficient; wherein, the spatial constraint coefficient is determined based on the Riemannian distance between the target projection point and the target curve point, the data attribute feature constraint coefficient is determined based on the specific attribute, and the target curve point is the point on the principal curve to be optimized at the target position;

[0012] Update the principal curve to be optimized by minimizing the target optimization error to obtain the final target principal curve; wherein, the target optimization error is weighted by the joint contribution factor.

[0013] The beneficial effects of the embodiments of the present application compared with the prior art are:

[0014] By introducing a data attribute feature constraint coefficient on the basis of the existing spatial constraint coefficient to jointly determine the joint contribution factor of the data points of the high-dimensional non-linear data, the subsequent update of the principal curve is not only affected by the Riemannian distance correlation coefficient, but also affected by the data attribute feature correlation coefficient, so as to be able to maintain the specific attribute structure of the data, solve the fitting error problem caused by the traditional principal curve method relying only on spatial distance and ignoring data attribute features, and improve the principal curve fitting accuracy and adaptability of the high-dimensional non-linear data. <>

[0015] In a possible implementation manner of the first aspect, the specific attributes include a time sequence attribute and a distribution attribute, the time sequence attribute corresponds to at least a time feature, and the distribution attribute corresponds to at least a density feature.

[0016] In the above solution, different data attribute feature constraints can be flexibly selected according to different specific attributes of the data, which makes this method have wide applicability and can adapt to the analysis requirements of various complex data. For time series data with strong time series characteristics, time feature constraints can be selected; for distributed data with uneven distribution, density feature constraints can be selected.

[0017] In a possible implementation manner of the first aspect, when the high-dimensional non-linear data is human motion data, the steps of obtaining the high-dimensional non-linear data to be analyzed and mapping the high-dimensional non-linear data to the target Riemannian manifold include:

[0018] Obtain the joint point information and joint limb information of the human skeleton;

[0019] Obtain the rotation data of two adjacent joint points at the same moment from the human motion data, and convert the rotation data into the rotation matrix of the joint limb;

[0020] Determine all the rotation matrices at the same moment as a set of rotation matrix sequences; among them, multiple sets of rotation matrix sequences at different moments have sequentiality in time;

[0021] Map the multiple sets of rotation matrix sequences to the target Riemannian manifold.

[0022] In the above solution, when processing human motion data, the human motion is described by using the human skeleton information and the rotation matrix. The rotation matrix sequence can not only accurately and intuitively describe the posture of the joint limb, but also describe the dynamic changes of the joint limb at different moments, and can avoid the inherent singularity problem of representation methods such as Euler angles, thus comprehensively and accurately reflecting the geometric characteristics of human motion. In addition, by emphasizing the sequentiality of data in time during the processing, the time series attribute of the data is increased, laying a foundation for introducing time feature constraints in the subsequent update of the principal curve.

[0023] In a possible implementation manner of the first aspect, the step of constructing the principal curve to be optimized through the data points of the target Riemannian manifold includes:

[0024] Divide the data points on the Riemannian manifold into multiple data groups;

[0025] Based on Riemannian geometry, determine the mean points of the data groups respectively;

[0026] Between two adjacent mean points, generate intermediate points by using geodesic interpolation;

[0027] Fit the principal curve to be optimized according to the mean points and the intermediate points.

[0028] In the above solution, the Riemann mean points obtained by calculation are used as the representative nodes of the principal curve to form the initial trajectory, thereby preserving the true characteristics of the data, reducing the dependence on hyperparameters, enhancing the generalization ability on different data types, and then smoothing the initial trajectory through geodesic interpolation to generate a continuous and smooth principal curve. Compared with random selection or linear interpolation, this principal curve has significantly lower fitting errors, thereby improving the fitting efficiency and fitting accuracy in the subsequent principal curve update process.

[0029] In a possible implementation manner of the first aspect, when the data points correspond to rotation matrices, the step of respectively determining the mean points of the data groups based on Riemannian geometry includes:

[0030] Using logarithmic mapping to map each rotation matrix in the data group to a rotation vector in the Lie algebra;

[0031] Calculating the average vector based on the rotation vectors;

[0032] Using exponential mapping to map the average vector back to the Lie group to obtain the initial candidate mean point;

[0033] Calculating the Riemannian distance from each rotation matrix in the data group to the candidate mean point;

[0034] Updating the candidate mean point by minimizing the objective function to obtain the final mean point of the data group, and the objective function to be minimized is: ;

[0035] Wherein, represents the mean point, R represents the candidate mean point, represents the rotation matrix in the data group, SO(3) represents the three-dimensional special rotation group, represents the Riemannian distance from the rotation matrix to the candidate mean point.

[0036] In the above solution, by dynamically selecting the data points closest to the center as the initial candidate mean points, the overall distribution of the data can be more accurately reflected, thereby reducing the subsequent number of iterations and obtaining results closer to the true mean faster and more accurately. For high-dimensional non-linear data, by utilizing the correspondence between Lie groups and Lie algebras, the optimization problem on the high-dimensional manifold space is reduced to an optimization on a low-dimensional space, greatly improving the computational efficiency. Especially for data processing containing rotation information, the computational complexity is reduced from O(n³) to O(n), making it more suitable for real-time applications or computationally resource-constrained environments.

[0037] In a possible implementation manner of the first aspect, the joint contribution factor of the target data point is determined by the following formula: ;

[0038] Among them, t represents the position parameter of the main curve, and n represents the identification parameter of the data point. represents the joint contribution factor. represents the spatial constraint coefficient. represents the data attribute feature constraint coefficient. represents the smoothing kernel function.

[0039] In the above solution, the joint contribution factor is calculated by designing a joint smoothing kernel function that simultaneously considers spatial factors and data attribute features. This way of introducing data attribute feature constraints is easy to apply to optimize the main curve fitting process of various different types of data.

[0040] In a possible implementation manner of the first aspect, when the specific attribute is a time series attribute, the joint contribution factor of the target data point is determined by the following formula:

[0041] ;

[0042] Among them, represents the time feature constraint coefficient. represents the curve point at parameter t on the main curve. represents the data point the projection point of the data point on the main curve at parameter t. represents the Riemannian distance between the projection point and the curve point. represents the spatial scale factor. represents the time scale factor. represents the time deviation between the data point and the curve point. represents the time corresponding to the curve point with parameter t on the main curve. represents the data point the time corresponding to the data point.

[0043] In a possible implementation manner of the first aspect, when the high-dimensional non-linear data contains rotation information, the main curve optimization method based on feature constraints further includes determining the adaptive rotation axis direction of the high-dimensional non-linear data. The steps of determining the adaptive rotation axis direction of the high-dimensional non-linear data include:

[0044] Converting the high-dimensional non-linear data into at least one set of rotation matrix data; the set of rotation matrix data includes multiple rotation matrices; for any set of rotation matrix data, determining the mean matrix of the set of rotation matrix data based on Riemannian geometry;

[0045] Obtaining the deviation vectors of the mean matrix and each rotation matrix in the set of rotation matrix data;

[0046] Constructing a covariance matrix based on the deviation vectors;

[0047] Perform eigenvalue decomposition on the covariance matrix to obtain eigenvalues and corresponding eigenvectors; the eigenvalues represent the amount of change in the direction of the corresponding eigenvectors, and the eigenvectors are used to represent the change directions of the rotation matrix dataset;

[0048] Select the eigenvector corresponding to the smallest eigenvalue and determine it as the rotation axis direction of the rotation matrix dataset;

[0049] Determine the adaptive rotation axis direction of the high-dimensional non-linear data based on the rotation axis directions of all different rotation matrix datasets.

[0050] In the above solution, for high-dimensional non-linear data containing rotation information, the determination of the adaptive rotation axis is carried out, getting rid of the limitations of the traditional fixed-axis method, and being able to automatically determine the optimal rotation axis according to the change characteristics in the data distribution. The direction corresponding to the smallest eigenvalue in the covariance matrix represents the direction with the least change in the dataset. By selecting this direction as the rotation axis, it can effectively avoid the mirror ambiguity and direction instability problems caused by equivalent rotation, ensuring the global consistency and reliability of the rotation representation. In addition, for the rotation matrix, by constraining a suitable rotation axis in the dataset, the high-dimensional optimization problem can be reduced to an optimization problem in a low-dimensional space, greatly reducing the computational cost and improving the computational efficiency.

[0051] In a second aspect, an embodiment of the present application provides a principal curve optimization device based on feature constraints, including:

[0052] A data acquisition module, configured to acquire high-dimensional non-linear data to be analyzed and map the high-dimensional non-linear data to a target Riemannian manifold; the high-dimensional non-linear data has specific attributes;

[0053] A curve construction module, configured to construct an initial principal curve to be optimized through the data points of the target Riemannian manifold;

[0054] A projection module, configured to determine a target projection point where a target data point is projected to a target position; the target data point is any data point of the target Riemannian manifold, and the target position is any position of the principal curve to be optimized;

[0055] A contribution calculation module, configured to determine a joint contribution factor of the target data point according to a spatial constraint coefficient and at least one data attribute feature constraint coefficient; wherein, the spatial constraint coefficient is determined based on the Riemannian distance between the target projection point and the target curve point, the data attribute feature constraint coefficient is determined based on the specific attribute, and the target curve point is the point on the principal curve to be optimized at the target position;

[0056] A curve update module, configured to update the main curve to be optimized by minimizing an objective optimization error, so as to obtain a final target main curve; wherein, the objective optimization error is weighted by the joint contribution factor.

[0057] In a third aspect, an embodiment of the present application provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method for optimizing a main curve based on feature constraints according to any one of the above first aspects is implemented.

[0058] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for optimizing a main curve based on feature constraints according to any one of the above first aspects is implemented.

[0059] In a fifth aspect, an embodiment of the present application provides a computer program product. When the computer program product runs on a terminal device, the terminal device is enabled to execute the method for optimizing a main curve based on feature constraints according to any one of the above first aspects.

[0060] It can be understood that the beneficial effects of the above second aspect to the fifth aspect can refer to the relevant descriptions in the above first aspect, and will not be elaborated here. Description of the Drawings

[0061] Figure 1 is a flowchart of a method for optimizing a main curve based on feature constraints provided by an embodiment of the present application;

[0062] Figure 2 is a schematic diagram of a main curve of the prior art;

[0063] Figure 3 is a schematic diagram of a main curve of an embodiment of the present application;

[0064] Figure 4 is a schematic diagram of a main curve of another embodiment of the present application;

[0065] Figure 5 is a schematic diagram of a human body skeleton provided by an embodiment of the present application;

[0066] Figure 6 is a flowchart of determining an adaptive rotation axis provided by an embodiment of the present application;

[0067] Figure 7 is a schematic structural diagram of a device for optimizing a main curve based on feature constraints provided by an embodiment of the present application;

[0068] Figure 8 is a schematic structural diagram of an electronic device provided by an embodiment of the present application. Detailed implementation manners

[0069] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments may be combined with each other.

[0070] In the following description, for the purpose of illustration rather than limitation, specific details such as specific system architectures and technologies are proposed to thoroughly understand the embodiments of the present application. However, those skilled in the art should clearly understand that the present application can also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid unnecessary details from interfering with the description of the present application.

[0071] It should be understood that when used in the specification of the present application and the appended claims, the term "comprising" indicates the presence of the described features, wholes, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components, and / or their combinations.

[0072] It should also be understood that the term "and / or" used in the specification of the present application and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0073] As used in the specification of the present application and the appended claims, the term "if" may be interpreted as "when", "once", "in response to determining", or "in response to detecting" according to the context. Similarly, the phrase "if determined" or "if [the described condition or event] is detected" may be interpreted as meaning "once determined", "in response to determining", "once [the described condition or event] is detected", or "in response to detecting [the described condition or event]" according to the context.

[0074] In addition, in the description of the specification of the present application and the appended claims, the terms "first", "second", "third", etc. are only used for distinguishing descriptions and cannot be understood as indicating or implying relative importance.

[0075] See Figure 1 , the embodiments of the present application provide a flowchart of a method for optimizing a principal curve based on feature constraints. As an example rather than a limitation, the method may include the following steps:

[0076] S11. Obtain high-dimensional non-linear data to be analyzed and map the high-dimensional non-linear data to a target Riemannian manifold.

[0077] Among them, the high-dimensional non-linear data has specific attributes. In a possible implementation, the specific attributes include temporal attributes and distribution attributes. Among them, the temporal attributes correspond to at least time features, and the distribution attributes correspond to at least density features. Of course, this embodiment is not limited to the above two attributes and also includes dynamic attributes, which correspond to at least speed features.

[0078] In this embodiment, each data point of the target Riemannian manifold represents the geometric characteristics of a data point. In a possible implementation, when processing data containing rotation information (such as human motion data), the target Riemannian manifold is SO(3). SO(3) can be used as both a three-dimensional special rotation group and a three-dimensional Riemannian manifold. Its group characteristics reflect the algebraic structure of the rotation relationship, while the manifold characteristics reveal its geometric topological properties, providing a basis for the construction and optimization of the subsequent principal curve.

[0079] Of course, the target Riemannian manifold of this embodiment is not limited to SO(3). An appropriate Riemannian manifold can be selected according to the data characteristics of the high-dimensional non-linear data, application requirements, and the geometric properties of the manifold. For example, for electroencephalogram signal analysis data, the covariance matrix between data points is relatively important, and the SPD manifold (symmetric positive definite matrix manifold) can be selected; for another example, for word vector data, to capture the hierarchical semantic relationship of words, the hyperbolic space can be selected, etc.

[0080] S12. Construct an initial principal curve to be optimized through the data points of the target Riemannian manifold.

[0081] S13. Determine the target projection point where the target data point is projected to the target position.

[0082] Among them, the target data point is any data point of the target Riemannian manifold, and the target position is any position of the principal curve to be optimized.

[0083] S14. Determine the joint contribution factor of the target data point according to the spatial constraint coefficient and at least one data attribute feature constraint coefficient.

[0084] Among them, the spatial constraint coefficient is determined based on the Riemannian distance between the target projection point and the target curve point, the data attribute feature constraint coefficient is determined based on the specific attributes, and the target curve point is the point on the principal curve to be optimized at the target position.

[0085] S15. Update the principal curve to be optimized by minimizing the target optimization error to obtain the final target principal curve.

[0086] Among them, the target optimization error is weighted by the joint contribution factor. Specifically, when the target optimization error reaches the minimum value, the principal curve to be optimized is determined as the target principal curve; otherwise, based on the projection point, fit the principal curve to be optimized for the next iteration optimization, and then return to execute step S3.

[0087] A method for optimizing a principal curve based on feature constraints provided in this embodiment determines a joint contribution factor of data points of high-dimensional non-linear data by introducing a data attribute feature constraint coefficient on the basis of an existing spatial constraint coefficient, so that the subsequent update of the principal curve is affected not only by the Riemann distance correlation coefficient, but also by the data attribute feature correlation coefficient, thereby being able to maintain the specific attribute structure of the data, solving the fitting error problem caused by the traditional principal curve method relying only on spatial distance and ignoring data attribute features, and improving the principal curve fitting accuracy and adaptability of high-dimensional non-linear data.

[0088] In one implementation manner of step S4, the joint contribution factor of the target data point is determined by the following formula:

[0089] ;

[0090] where t represents the position parameter of the principal curve, that is, the independent variable in the parametric representation of the principal curve, used to locate points on the curve, n represents the identification parameter of the data point, represents the joint contribution factor, represents the spatial constraint coefficient, represents the data attribute feature constraint coefficient, represents the smoothing kernel function.

[0091] The spatial distance constraint coefficient c(t, n) is calculated by the following formula:

[0092] ;

[0093] where represents the Riemann distance between the projection point and the curve point, represents the curve point at parameter t on the principal curve (that is, at position t), represents the data point, represents the data point at the projection position on the principal curve, represents the data point at the projection point at parameter t on the principal curve, represents the spatial scale factor, indicates that this formula holds for all parameters n and parameter t.

[0094] A method for optimizing a principal curve based on feature constraints provided in this embodiment calculates the joint contribution factor by designing a joint smoothing kernel function that simultaneously considers spatial factors and data attribute features. This way of introducing data attribute feature constraints is easy to apply to the principal curve fitting process for optimizing various different types of data.

[0095] In a possible implementation, when the specific attribute is a timing attribute, step S14 includes determining the combined contribution factor of the target data point through the following formula:

[0096] ;

[0097] where, represents the time feature constraint coefficient, represents the time deviation between the data point and the curve point. Specifically, represents the time corresponding to the curve point with parameter t on the main curve, represents the data point in the time dimension, that is, the time corresponding to the data point ; represents the time scale factor. When the time deviation exceeds the preset threshold, even if the data point is close to the curve point in space, its combined contribution factor will be significantly reduced, thereby maintaining the timing consistency of curve updates.

[0098] The following is an example with reference to Figure 2 and Figure 3 . As shown in Figure 2 , the curve update in the existing main curve fitting method only depends on the Riemannian distance. Under this mechanism, the update of the data point is likely to be affected by data points that are far in time distance but close in space distance. For example, Figure 2 the third point on the curve in wrongly classifies the data point into the same fitting group, resulting in the updated point

[0099] deviating from the correct time evolution trajectory. Figure 3 By jointly updating the main curve with spatial constraints and time constraints simultaneously, as shown in , since the data point exceeds the time constraint, although it is close to the data point in space, it is excluded from the update range when updating the data point , thus classifying the data point and the data point Figure 3 into the same fitting group. Therefore, the updated data point in

[0100] meets both the spatial constraint and the time constraint, thus conforming to the correct time evolution trajectory. ;

[0101] where, represents the density constraint coefficient, represents the number of neighboring data points of each curve point within a certain range, [[ID=,4]]represents the density scale factor.

[0102] As Figure 4 shown, under the constraint of density, the weights of data points in high-density regions are higher, and the main curve actively focuses on the data trend with higher density, so that the main curve better reflects the main change direction of the data.

[0103] Optionally, an implementation manner of step S14 may include: determining the joint contribution factor of the target data point according to at least two of the spatial constraint coefficient, the time constraint coefficient, and the density constraint coefficient, which are data attribute feature constraint coefficients. This multi-constraint combination method makes the method have a wider applicability and can flexibly select and combine different types of constraints according to different characteristics of the data.

[0104] It should be noted that in addition to the three data attribute feature constraint coefficients shown in this embodiment, step S14 can also set other feature constraint coefficients based on requirements, such as the speed constraint coefficient or the distribution constraint coefficient, etc., to adapt to the characteristics and analysis requirements of different types of data. Specifically, for data with strong time series, time constraint can be selected; for data with uneven distribution, density constraint can be selected; for data sensitive to the change rate, speed constraint can be selected. This flexible constraint selection mechanism enables the method to adapt to the analysis requirements of various complex data, and when the data has a combination of multiple specific attributes, multiple data attribute feature constraint coefficients can be introduced.

[0105] Optionally, an implementation manner of step S15 may include:

[0106] Based on the joint contribution factor of each data point and the Riemannian distance between the corresponding projection point and the curve point calculate the target optimization error , specifically:

[0107] ;

[0108] The target optimization error represents the sum of the weighted squared distances between all curve points on the main curve and the projection points of the data points on the main curve. When this value reaches the minimum, this main curve is the finally determined main curve. Before that, the shape of the main curve can be continuously adjusted according to the projection points. The specific formula is as follows: ;

[0109] As an example but not a limitation, when the high-dimensional non-linear data is human motion data, the high-dimensional non-linear data can be converted into multiple sets of rotation matrix series. Optionally, one implementation of step S11 may include:

[0110] S111. Obtain the joint point information and joint limb information of the human skeleton.

[0111] S112. Obtain the rotation data of two adjacent joint points at the same moment from the human motion data, and convert the rotation data into the rotation matrix of the joint limb.

[0112] S113. Aggregate the rotation matrices between all limb pairs at the same moment into a set of rotation matrix sequences.

[0113] Among them, multiple sets of rotation matrix sequences at different moments are sequential in time.

[0114] S114. Map the multiple sets of rotation matrix sequences to the target Riemannian manifold.

[0115] In a possible implementation, the joint point information is defined as , the joint limb information is defined as , where n represents the subscript parameter of the joint point, represents the nth joint point, m represents the subscript parameter of the joint limb, represents the mth joint limb; define and as two adjacent joint points. At the same time, and can also be regarded as the two endpoints of the joint limb . Represent the rotation data of and at time s as the rotation matrix of the joint limb . The rotation matrix R is a 3×3 orthogonal matrix, satisfying and , where is the transpose matrix of R, I is the 3×3 identity matrix, and det(R)=1 means the determinant of the rotation matrix is 1; aggregate all rotation matrices to obtain the rotation matrix sequence .

[0116] The following is an example with reference to Figure 5 . Figure 5 shows that there are 20 joint points in the skeleton model, connected by 19 joint limbs. The rotation data of the human body can be regarded as the rotation matrix sequence . In a possible implementation, when the human motion is limited to some joint limbs, a rotation matrix sequence can be established only for some joint limbs. For example,Figure 5 Only the right - hand actions are shown. Figure 5 In Figure 5 , the left skeleton model is equivalent to the initialized right - hand action, and the right skeleton model is equivalent to the changed right - hand action. The sequence of rotation matrices can be used to represent human motion data.

[0117] It should be noted that all the sequences of rotation matrices are arranged in chronological order, so that the human motion data has the specific property of temporal characteristics.

[0118] A method for optimizing the principal curve based on feature constraints provided in this embodiment, when processing human motion data, uses human skeleton information and rotation matrices to describe human motion. The sequence of rotation matrices can not only accurately and intuitively describe the postures of joint limbs, but also describe the dynamic changes of joint limbs at different times, and can avoid the inherent singularity problems of representation methods such as Euler angles, thus comprehensively and accurately reflecting the geometric characteristics of human motions. In addition, by emphasizing the sequentiality of data in time during the processing, the temporal attribute of the data is increased, laying a foundation for introducing constraints on time features in the subsequent principal curve update.

[0119] Optionally, one implementation of step S12 may include:

[0120] S121: Divide the data points on the Riemannian manifold into multiple data groups.

[0121] In a possible implementation, for data with temporal attributes, it can be divided according to time steps. For example, in human motion data, a sequence of rotation matrices at one moment is a data group. Of course, other division methods can also be adopted.

[0122] S122: Respectively determine the mean points of the data groups based on Riemannian geometry.

[0123] S123: Generate intermediate points by geodesic interpolation between two adjacent mean points.

[0124] S124: Fit the principal curve to be optimized according to the mean points and intermediate points.

[0125] A method for optimizing the principal curve based on feature constraints provided in this embodiment uses the calculated Riemannian mean points as the representative nodes of the principal curve to form an initial trajectory, thus retaining the true features of the data, reducing the dependence on hyperparameters, enhancing the generalization ability on different data types, and then smoothing the initial trajectory through geodesic interpolation to generate a continuous and smooth principal curve. Compared with random selection or linear interpolation, this principal curve has significantly lower fitting errors, thereby improving the fitting efficiency and fitting accuracy in the subsequent principal curve update process.

[0126] As an example rather than a limitation, when the data points correspond to rotation matrices, the data grouping is represented as a series of rotation matrix groups composed of multiple rotation matrices. Optionally, one implementation of step S121 may include:

[0127] S1211. Use logarithmic mapping to map each rotation matrix in the data grouping to a rotation vector in the Lie algebra.

[0128] Specifically, given a sequence of rotation matrices , representing all the rotation matrices in the data grouping, according to the properties of SO(3), each rotation matrix is mapped to the Lie algebra . is a vector space composed of three-dimensional skew-symmetric matrices . The skew-symmetric matrix corresponds one-to-one with the rotation vector . The formula for logarithmic mapping is: ;

[0129] In one possible implementation, the rotation vector is given by the product of the rotation angle and the unit rotation axis :

[0130] ;

[0131] In one possible implementation, the rotation angle is related to the trace of the rotation matrix . The trace of the rotation matrix is the sum of the elements on the main diagonal of the matrix. The rotation angle and the rotation axis can be calculated using the following formula. Specifically:

[0132] ;

[0133] ;

[0134] ;

[0135] ;

[0136] S1212. Calculate the average vector based on the rotation vectors.

[0137] In one possible implementation, the average vector can be calculated using the following formula:

[0138] ;

[0139] S1213. Map the average vector back to the Lie group using the exponential map to obtain the initial candidate mean point.

[0140] In one possible implementation, the exponential map can map the average vector back to the rotation matrix (i.e., the candidate mean point), specifically:

[0141] ;

[0142] where is the skew-symmetric matrix of the average vector , represents the rotation angle, and can be expressed as:

[0143] ;

[0144] ;

[0145] S1214. Calculate the Riemannian distance from each rotation matrix in the data group to the candidate mean point.

[0146] In one possible implementation, the Riemannian distance can be calculated in the following way, specifically:

[0147] ;

[0148] where represents the rotation matrix in the data group, represents the candidate mean point, represents the Riemannian distance from the rotation matrix to the candidate mean point, represents the Frobenius norm, i.e., the square root of the sum of the squares of all elements of the matrix.

[0149] The calculation of the Frobenius norm can be to sum the squares of all elements of the matrix and then take the square root. For example, for a matrix , its Frobenius norm is .

[0150] S1215. Update the candidate mean point by minimizing the objective function to obtain the mean point of the final rotation matrix sequence.

[0151] where the objective function to be minimized is: ;

[0152] where represents the finally determined mean point. By continuously adjusting , the The value reaches the minimum, and the determined is the finally determined mean point .

[0153] A method for optimizing a principal curve based on feature constraints provided by this embodiment can more accurately reflect the overall distribution of data by dynamically selecting the data point closest to the center as the initial candidate mean point, thereby reducing the subsequent number of iterations and obtaining a result closer to the true mean faster and more accurately. For high-dimensional non-linear data, by utilizing the correspondence between Lie groups and Lie algebras, the optimization problem on the high-dimensional manifold space is reduced to an optimization on a low-dimensional space, greatly improving the computational efficiency. Especially for data processing involving rotation information, the computational complexity is reduced from O(n³) to O(n), making it more suitable for real-time applications or computational environments with limited resources.

[0154] Optionally, an implementation manner of step S122 specifically includes:

[0155] On the SO(3) manifold, each rotation matrix corresponds to a tangent space . Assuming two mean matrices and , calculate the tangent vector from to based on the logarithmic mapping. Specifically:

[0156] ;

[0157] Generate an interpolation path (i.e., geodesic from to ) through the following geodesic formula:

[0158]

[0159] Among them, by selecting different t values (e.g., t = 0, 0.1, 0.2, …, 1), a series of interpolation points (i.e., intermediate points) can be generated.

[0160] Optionally, an implementation manner of step S123 specifically includes: using the above mean point and intermediate point as curve points on the principal curve, and generating an initial principal curve to be optimized by connecting the curve points.

[0161] When processing rotation data, equivalent rotations on the SO(3) manifold (e.g., 90° left rotation and 270° right rotation) may cause unstable mean calculation and affect the optimization process of the principal curve. Especially in human motion data, the instability of joint rotation representation will directly affect the accuracy and consistency of motion modeling.

[0162] The reference to a fixed rotation axis can solve the problem of rotational instability and also significantly reduce the computational complexity. After the data is projected onto the fixed rotation axis, the rotation matrix can be decomposed into the rotation angle around this axis, thereby simplifying the data representation from high-dimensional rotation to scalar angle representation. However, the choice of the rotation axis largely determines the quality of data dimensionality reduction. When different actions involve different rotation trends, a fixed rotation axis may lead to the problem of local information loss. For example, in actions mainly moving along the Z-axis such as "jumping" and "squatting", fixing the Z-axis helps to maximize the retention of their key features. For actions involving multi-directional rotation (such as "waving" or "moving an object"), the choice of a single axis may result in the loss of some motion information. Therefore, it is necessary to select an appropriate rotation axis according to different types of human motion data.

[0163] In one possible implementation, when the high-dimensional non-linear data contains rotation information, the method for optimizing the principal curve based on feature constraints further includes determining the adaptive rotation axis direction of the high-dimensional non-linear data, such as Figure 6 shown, the steps for determining the adaptive rotation axis direction of the high-dimensional non-linear data include:

[0164] S21. Convert the high-dimensional non-linear data into at least one rotation matrix dataset.

[0165] Among them, the rotation matrix dataset includes multiple rotation matrices. For complex high-dimensional non-linear data, a pre-partitioning process can be performed in advance. Each rotation matrix dataset is represented as , represents the rotation matrix, and SO(3) represents the three-dimensional special rotation group.

[0166] S22. For any one rotation matrix dataset, determine the mean matrix of the rotation matrix dataset based on Riemannian geometry.

[0167] In this embodiment, the implementation manner of step S22 is basically the same as that of step S121. The rotation matrix dataset corresponds to the rotation matrix sequence, and the mean matrix corresponds to the mean point, which will not be elaborated here.

[0168] S23. Obtain the deviation vectors of the mean matrix and each rotation matrix in the rotation matrix dataset.

[0169] In one possible implementation, through the logarithmic mapping , each rotation matrix can be converted into an anti-symmetric matrix in the Lie algebra, establishing a close connection between the Lie group and its Lie algebra. The Lie algebra consists of all anti-symmetric matrices. The Lie algebra is the tangent space of the SO(3) manifold (Lie group) at the rotation matrix R (identity element). Then each rotation matrix The deviation from the mean is logarithmically mapped to the tangent space as:

[0170] ;

[0171] where is the rotation vector in the tangent space, represents the rotation matrix with respect to the deviation vector from the mean matrix, that is, it represents the direction of the rotation deviation on the manifold.

[0172] S24. Construct a covariance matrix based on the deviation vector.

[0173] where the covariance matrix C describes the variations of the rotation matrix dataset in different directions. Optionally, the covariance matrix C of the series of rotation matrices is: ;

[0174] S25. Perform eigenvalue decomposition on the covariance matrix to obtain eigenvalues and corresponding eigenvectors.

[0175] where the eigenvalues represent the amounts of variation in the directions of the corresponding eigenvectors, and the eigenvectors are used to represent the directions of variation of the rotation matrix dataset. Specifically, . Where is the eigenvalue, representing the variance of the variation along different directions, is the corresponding eigenvector, representing the direction of variation in the rotation matrix sequence.

[0176] S26. Select the eigenvector corresponding to the smallest eigenvalue and determine it as the rotation axis direction of the rotation matrix dataset.

[0177] where the eigenvector corresponding to the smallest eigenvalue represents the direction with the least variation, that is, the most stable direction, in the rotation matrix dataset. Selecting this direction as the rotation axis can effectively avoid the problem of direction instability caused by equivalent rotations.

[0178] S27. Determine the adaptive rotation axis direction of the high-dimensional non-linear data based on the rotation axis directions of all different rotation matrix datasets.

[0179] A method for optimizing the principal curve based on feature constraints provided in this embodiment determines an adaptive rotation axis for high-dimensional non-linear data containing rotation information, getting rid of the limitations of traditional fixed-axis methods and being able to automatically determine the optimal rotation axis according to the changing characteristics in the data distribution. The direction corresponding to the minimum eigenvalue in the covariance matrix represents the direction with the least change in the dataset. By selecting this direction as the rotation axis, it can effectively avoid the mirror ambiguity and direction instability problems caused by equivalent rotation, ensuring the global consistency and reliability of the rotation representation. In addition, for the rotation matrix, by constraining a suitable rotation axis in the dataset, the high-dimensional optimization problem can be reduced to an optimization problem in a low-dimensional space, greatly reducing the computational cost and improving the computational efficiency.

[0180] It should be understood that the magnitudes of the sequence numbers of the steps in the above embodiments do not mean the order of execution is prior or posterior. The execution order of each process should be determined according to its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of this application.

[0181] Corresponding to the method for optimizing the principal curve based on feature constraints described in the above embodiments, Figure 7 The structural block diagram of the device for optimizing the principal curve based on feature constraints provided by the embodiments of this application is shown. For the sake of convenience of description, only the parts related to the embodiments of this application are shown.

[0182] Referring to Figure 7 , the device for optimizing the principal curve based on feature constraints includes:

[0183] A data acquisition module 11, configured to acquire high-dimensional non-linear data to be analyzed and map the high-dimensional non-linear data to a target Riemannian manifold; the high-dimensional non-linear data has specific attributes.

[0184] A curve construction module 12, configured to construct an initial principal curve to be optimized through the data points of the target Riemannian manifold.

[0185] A projection module 13, configured to determine a target projection point for projecting a target data point to a target position. The target data point is any data point of the target Riemannian manifold, and the target position is any position of the principal curve to be optimized.

[0186] A contribution calculation module 14, configured to determine a joint contribution factor of the target data point according to a spatial constraint coefficient and at least one data attribute feature constraint coefficient. Among them, the spatial constraint coefficient is determined based on the Riemannian distance between the target projection point and the target curve point, the data attribute feature constraint coefficient is determined based on the specific attribute, and the target curve point is the point on the principal curve to be optimized at the target position.

[0187] The curve update module 15 is configured to update the main curve to be optimized by minimizing the target optimization error, so as to obtain the final target main curve. The target optimization error is weighted by the joint contribution factor.

[0188] In some embodiments of the present application, the specific attributes include a timing attribute and a distribution attribute. The timing attribute corresponds to at least a time feature, and the distribution attribute corresponds to at least a density feature.

[0189] In some embodiments of the present application, the data acquisition module 11 may be specifically configured to, when the high-dimensional non-linear data is human motion data, acquire the joint point information and joint limb information of the human skeleton; acquire the rotation data of two adjacent joint points at the same moment from the human motion data, and convert the rotation data into a rotation matrix of the joint limb; determine all the rotation matrices at the same moment as a set of rotation matrix sequences; wherein, multiple sets of rotation matrix sequences at different moments are sequential in time; map the multiple sets of rotation matrix sequences to the target Riemannian manifold.

[0190] In some embodiments of the present application, the curve construction module 12 may be specifically configured to divide the data points on the Riemannian manifold into multiple data groups; respectively determine the mean points of the data groups based on Riemannian geometry; between two adjacent mean points, generate intermediate points by geodesic interpolation; fit the main curve to be optimized according to the mean points and the intermediate points.

[0191] In some embodiments of the present application, the curve construction module 12 may also be specifically configured to, when the data points correspond to rotation matrices, use logarithmic mapping to map each rotation matrix in the data group to a rotation vector in the Lie algebra; calculate the average vector based on the rotation vectors; use exponential mapping to map the average vector back to the Lie group to obtain an initial candidate mean point; calculate the Riemannian distance from each rotation matrix in the data group to the candidate mean point; update the candidate mean point by minimizing the objective function to obtain the final mean point of the data group.

[0192] In some embodiments of the present application, the main curve optimization device based on feature constraints further includes a rotation axis determination module, which is configured to convert the high-dimensional non-linear data into at least one rotation matrix dataset when the high-dimensional non-linear data contains rotation information; for any one of the rotation matrix datasets, determine the mean matrix of the rotation matrix dataset based on Riemannian geometry; obtain the deviation vectors of the mean matrix and each rotation matrix in the rotation matrix dataset; construct a covariance matrix based on the deviation vectors; perform eigenvalue decomposition on the covariance matrix to obtain eigenvalues and corresponding eigenvectors; the eigenvalues represent the amount of change in the direction of the corresponding eigenvectors, and the eigenvectors are used to represent the change direction of the rotation matrix dataset; select the eigenvector corresponding to the minimum eigenvalue and determine it as the rotation axis direction of the rotation matrix dataset; determine the adaptive rotation axis direction of the high-dimensional non-linear data based on the rotation axis directions of all different rotation matrix datasets.

[0193] It should be noted that the information interaction, execution process, etc. between the above-mentioned devices / units, due to being based on the same concept as the method embodiments of the present application, for their specific functions and the technical effects brought, reference can be specifically made to the method embodiment part, and details will not be elaborated here.

[0194] Those skilled in the art can clearly understand that, for the convenience and conciseness of description, only the above-mentioned division of each functional unit and module is used as an example. In actual applications, the above-mentioned functions can be allocated to different functional units and modules according to needs, that is, the internal structure of the device is divided into different functional units or modules to complete all or part of the functions described above. Each functional unit and module in the embodiment can be integrated in a processing unit, or each unit can exist physically alone, or two or more units can be integrated in one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of a software functional unit. In addition, the specific names of each functional unit and module are only for the convenience of mutual distinction and do not limit the protection scope of the present application. The specific working process of the units and modules in the above-mentioned device can refer to the corresponding process in the foregoing method embodiments, and details will not be elaborated here.

[0195] Figure 8 It is a schematic structural diagram of an electronic device provided by an embodiment of the present application. As Figure 8 shown, the electronic device 2 in the embodiment includes: at least one processor 20 ( Figure 8 only one is shown in the figure), a processor, a memory 21, and a computer program 22 stored in the memory 21 and executable on the at least one processor 20. When the processor 20 executes the computer program 22, the steps in each of the above-mentioned main curve optimization method embodiments based on feature constraints are implemented.

[0196] The electronic device 2 can be a computing device such as a desktop computer, a notebook, a palm computer, and a cloud server. The electronic device 2 may include, but is not limited to, a processor 20 and a memory 21. Those skilled in the art can understand that Figure 8 merely examples of the electronic device 2, which do not constitute a limitation on the electronic device 2, may include more or fewer components than shown in the figure, or combine certain components, or different components. For example, it may also include input / output devices, network access devices, etc.

[0197] The processor 20 may be a central processing unit (CPU), and the processor 20 may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0198] In some embodiments, the memory 21 may be an internal storage unit of the electronic device 2, such as the hard disk or memory of the electronic device 2. In other embodiments, the memory 21 may also be an external storage device of the electronic device 2, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. equipped on the electronic device 2. Further, the memory 21 may also include both the internal storage unit and the external storage device of the electronic device 2. The memory 21 is used to store an operating system, application programs, a boot loader, data, and other programs, such as the program code of a computer program. The memory 21 may also be used to temporarily store data that has been output or will be output.

[0199] The embodiment of the present application also provides a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the steps in the above-mentioned embodiments of the main curve optimization method based on various feature constraints can be implemented.

[0200] The embodiment of the present application provides a computer program product, and when the computer program product runs on a mobile terminal, the mobile terminal is enabled to execute the steps in the above-mentioned embodiments of the main curve optimization method based on various feature constraints.

[0201] In the above embodiments, the descriptions of the respective embodiments each have their own focus. For parts not described in detail or recorded in a certain embodiment, reference may be made to the relevant descriptions of other embodiments.

[0202] Those of ordinary skill in the art can realize that the units and algorithm steps of the examples described in combination with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. A professional technician can use different methods for each specific application to implement the described functions, but such implementation should not be considered to exceed the scope of this application.

[0203] In the embodiments provided in this application, it should be understood that the disclosed device / network device and method can be implemented in other ways. For example, the device / network device embodiments described above are merely illustrative. For example, the division of the modules or units is only a logical function division. In actual implementation, there may be other division methods. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed coupling or direct coupling or communication connection to each other can be through some interfaces. The indirect coupling or communication connection of the device or unit can be in an electrical, mechanical or other form.

[0204] The above-described embodiments are only used to illustrate the technical solutions of this application, rather than to limit them; although this application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for optimizing a principal curve based on feature constraints, characterized in that Including: Obtain high-dimensional non-linear data to be analyzed and map the high-dimensional non-linear data to a target Riemannian manifold; The high-dimensional non-linear data has specific attributes; Construct an initial principal curve to be optimized through data points of the target Riemannian manifold; Determine a target projection point where a target data point is projected to a target position; The target data point is any data point of the target Riemannian manifold, and the target position is any position of the principal curve to be optimized; Determine a joint contribution factor of the target data point according to a spatial constraint coefficient and at least one data attribute feature constraint coefficient; wherein, the spatial constraint coefficient is determined based on the Riemannian distance between the target projection point and a target curve point, the data attribute feature constraint coefficient is determined based on the specific attribute, and the target curve point is the point on the principal curve to be optimized at the target position; Update the principal curve to be optimized by minimizing a target optimization error to obtain a final target principal curve; wherein, the target optimization error is weighted by the joint contribution factor; When the high-dimensional non-linear data is human motion data, the step of obtaining the high-dimensional non-linear data to be analyzed and mapping the high-dimensional non-linear data to the target Riemannian manifold includes: Obtain joint point information and joint limb information of a human skeleton; Obtain rotation data of two adjacent joint points at the same moment from the human motion data and convert the rotation data into a rotation matrix of a joint limb; Determine all rotation matrices at the same moment as a set of rotation matrix sequences; wherein, multiple sets of rotation matrix sequences at different moments are sequential in time; Map the multiple sets of rotation matrix sequences to the target Riemannian manifold; The step of determining the joint contribution factor of the target data point according to the spatial constraint coefficient and at least one data attribute feature constraint coefficient includes determining the joint contribution factor of the target data point through the following formula: ； where t represents the position parameter of the main curve, and n represents the identification parameter of the data points, represents the combined contribution factor, represents the spatial constraint coefficient, represents the data attribute feature constraint coefficient, represents the smoothing kernel function; When the specific attribute is a temporal attribute, the step of determining the joint contribution factor of the target data point according to the spatial constraint coefficient and at least one data attribute feature constraint coefficient further includes determining the joint contribution factor of the target data point through the following formula: ； Among them, represents the time feature constraint coefficient, represents the curve point at parameter t on the main curve, represents the data point the projection point of the data point on the main curve at parameter t, represents the Riemannian distance between the projection point and the curve point, represents the spatial scale factor, represents the time scale factor, represents the time deviation between the data point and the curve point, represents the time corresponding to the curve point with parameter t on the main curve, represents the data point the corresponding time.

2. The method for optimizing the main curve based on feature constraints according to claim 1, wherein The specific attributes include a temporal attribute and a distribution attribute, the temporal attribute corresponds to at least time characteristics, and the distribution attribute corresponds to at least density characteristics.

3. The method for optimizing a principal curve based on feature constraints according to claim 1, wherein The step of constructing a principal curve to be optimized through data points of the target Riemannian manifold includes: Divide data points on the Riemannian manifold into multiple data groups; Respectively determine mean points of the data groups based on Riemannian geometry; Generate intermediate points by geodesic interpolation between two adjacent mean points; Fit the principal curve to be optimized according to the mean points and the intermediate points.

4. The main curve optimization method based on feature constraints according to claim 3, wherein When the data points correspond to rotation matrices, the step of respectively determining mean points of the data groups based on Riemannian geometry includes: Use logarithmic mapping to map each rotation matrix in the data group to a rotation vector in Lie algebra; Calculate an average vector based on the rotation vectors; Use exponential mapping to map the average vector back to Lie group to obtain an initial candidate mean point; Calculate the Riemannian distance from each rotation matrix in the data packet to the candidate mean point; Update the candidate mean point by minimizing the objective function to obtain the mean point of the final data packet. The objective function to be minimized is: ； Among them, represents the mean point, represents the candidate mean point, represents the rotation matrix in the data grouping, represents the three-dimensional rotation group, represents the Riemannian distance from the rotation matrix to the candidate mean point.

5. The method for optimizing a principal curve based on feature constraints according to claim 1, wherein When the high-dimensional non-linear data contains rotation information, the method for optimizing the principal curve based on feature constraints further includes determining the adaptive rotation axis direction of the high-dimensional non-linear data. The steps for determining the adaptive rotation axis direction of the high-dimensional non-linear data include: Convert the high-dimensional non-linear data into at least one rotation matrix data set; the rotation matrix data set includes multiple rotation matrices; For any one rotation matrix data set, determine the mean matrix of the rotation matrix data set based on Riemannian geometry; Obtain the deviation vectors between the mean matrix and each rotation matrix in the rotation matrix data set; Construct a covariance matrix based on the deviation vectors; Perform eigenvalue decomposition on the covariance matrix to obtain eigenvalues and corresponding eigenvectors; the eigenvalues represent the amount of change in the direction of the corresponding eigenvectors, and the eigenvectors are used to represent the change direction of the rotation matrix data set; Select the eigenvector corresponding to the minimum eigenvalue and determine it as the rotation axis direction of the rotation matrix data set; Determine the adaptive rotation axis direction of the high-dimensional non-linear data based on the rotation axis directions of all different rotation matrix data sets.

6. An apparatus for optimizing a principal curve based on feature constraints, characterized in that, It includes: A data acquisition module, configured to acquire high-dimensional non-linear data to be analyzed and map the high-dimensional non-linear data to a target Riemannian manifold; The high-dimensional non-linear data has specific attributes; A curve construction module, configured to construct an initial principal curve to be optimized through the data points of the target Riemannian manifold; A projection module, configured to determine a target projection point where a target data point is projected to a target position; The target data point is any data point on the target Riemannian manifold, and the target position is any position on the principal curve to be optimized; A contribution calculation module, configured to determine the joint contribution factor of the target data point according to the spatial constraint coefficient and at least one data attribute feature constraint coefficient; wherein, the spatial constraint coefficient is determined based on the Riemannian distance between the target projection point and the target curve point, the data attribute feature constraint coefficient is determined based on the specific attribute, and the target curve point is the point on the principal curve to be optimized at the target position; A curve update module, configured to update the principal curve to be optimized by minimizing the target optimization error to obtain the final target principal curve; wherein, the target optimization error is weighted by the joint contribution factor; When the high-dimensional non-linear data is human motion data, the data acquisition module is specifically configured to acquire the joint point information and joint limb information of the human skeleton; acquire the rotation data of two adjacent joint points at the same moment from the human motion data, and convert the rotation data into the rotation matrix of the joint limb; determine all the rotation matrices at the same moment as a set of rotation matrix sequences; wherein, multiple sets of rotation matrix sequences at different moments have sequentiality in time; map the multiple sets of rotation matrix sequences to the target Riemannian manifold; The contribution calculation module is specifically configured to determine the combined contribution factor of the target data point through the following formula: ； where t represents the position parameter of the main curve, and n represents the identification parameter of the data points, represents the combined contribution factor, represents the spatial constraint coefficient, represents the data attribute feature constraint coefficient, represents the smoothing kernel function; When the specific attribute is a time series attribute, the contribution calculation module is specifically configured to determine the combined contribution factor of the target data point through the following formula: ； Among them, represents the time feature constraint coefficient, represents the curve point at parameter t on the main curve, represents the data point the projection point of the data point at parameter t on the main curve, represents the Riemannian distance between the projection point and the curve point, represents the spatial scale factor, represents the time scale factor, represents the time deviation between the data point and the curve point, represents the time corresponding to the curve point with parameter t on the main curve, represents the data point the corresponding time.

7. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, the method for optimizing the principal curve based on feature constraints according to any one of claims 1 to 5 is implemented.

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