A multi-scale structure preserving optimal transport depth kernel clustering method

Abstract

The application discloses a multi-scale structure preserving optimal transmission depth kernel clustering method, and belongs to the technical field of unsupervised machine learning, pattern recognition and data mining, and comprises the following steps: S1, multi-layer coding is performed on input unlabeled single-view data to obtain hierarchical hidden representation; S2, each layer of normalized kernel matrix is obtained based on the step S1; S3, a fusion kernel matrix is obtained based on the step S2; S4, the fusion kernel matrix obtained based on the step S2; S5, a multi-scale structure preserving regularization term of the step S3 is taken as a core constraint; and S6, after the final fusion kernel matrix is obtained after model training convergence, a multi-scale structure preserving regularization is constructed from the local neighborhood distribution consistency and the global geometric correlation, the geometric deviation of the kernel space relative to the input space is explicitly constrained, and the excessive geometric distortion and structure degradation in the kernel learning process are inhibited.

Description

Technical Field

[0001] This invention belongs to the fields of unsupervised machine learning, pattern recognition and data mining technology, and specifically relates to a multi-scale structure-preserving optimal transmission depth kernel clustering method. Background Technology

[0002] Unsupervised clustering aims to discover latent class structures in unlabeled data and is one of the fundamental tasks in fields such as pattern recognition, text analysis, image understanding, and graph data mining. With the development of deep representation learning, clustering research has gradually shifted from a two-stage paradigm of learning features first and then performing clustering to a deep clustering framework that couples representation learning with cluster structure estimation. Recent reviews indicate that the current focus of deep clustering research is no longer limited to improving the separability of the embedding space, but has further shifted to issues such as pseudo-supervised quality, self-training stability, utilization of structural priors, and robust optimization in complex scenarios.

[0003] The representative method DEC (Deep Kernel Clustering) is the first to directly embed the clustering target into the deep representation learning process. It achieves joint adjustment of representation and cluster centers by iteratively optimizing the target distribution. Deep kernel clustering combines kernel methods with deep networks, and learns the adaptive kernel representation of data through neural networks to achieve nonlinear relationship modeling and clustering co-optimization. However, existing deep kernel clustering methods have the following drawbacks: the kernel learning process is prone to destroying the original geometric structure of the input space, resulting in the loss of local neighborhood relationships and global geometric distortion, which reduces the robustness of clustering; the structure update in the training phase lacks explicit constraints, and soft assignment is prone to problems such as cluster size imbalance, structural oscillation, and accumulation of pseudo-supervision noise. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-scale structure-preserving optimal transmission depth kernel clustering method to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a multi-scale structure-preserving optimal transmission depth kernel clustering method, comprising the following steps: S1: Perform multi-layer encoding on the input unlabeled single-view data to obtain hierarchical hidden representations. Based on each layer of hidden representations, perform projection mapping and kernel feature mapping in sequence to construct multi-layer explicit kernel features. Then, calculate the Gram kernel within the layer based on the explicit kernel features and apply unified kernel normalization to obtain the normalized kernel matrix of each layer. S2: Based on the normalized kernel matrices of each layer obtained in step S1, learnable weights are introduced to complete adaptive cross-layer fusion. After applying unified kernel normalization again, the data adaptive fusion kernel matrix is ​​obtained, which provides the basic kernel representation for subsequent structural constraints and clustering updates. S3: Based on the fusion kernel matrix obtained in step S2, construct a multi-scale structure-preserving regularization term that couples the consistency of local neighborhood distribution and global geometric correlation, constrain the geometric offset of the kernel space relative to the input space, and suppress the structural distortion in the kernel learning process; S4: Based on the fusion kernel matrix obtained in step S2, a soft kernel k-means structure update mechanism inspired by the optimal transmission margin constraint is designed. A controlled soft assignment matrix that satisfies the margin constraint is generated by Sinkhorn normalization, and the target structure matrix is ​​smoothly updated in an adaptive momentum manner to provide dynamic structure supervision for kernel learning. S5: Using the multi-scale structure preservation regularization term in step S3 as the core constraint, and combining the reconstruction loss and kernel consistency loss based on the fusion kernel matrix to construct the overall learning objective, the model training is completed using the optimization framework of alternating parameter updates and periodic structure updates supported by steps S1-S4. S6: After the model training converges and the final fusion kernel matrix is ​​obtained, perform independent post-processing based on the final fusion kernel matrix to obtain the final clustering label and complete the single-view unsupervised deep kernel clustering.

[0006] As a preferred implementation, the unified kernel normalization in steps S1 and S2 involves performing standardization operations of symmetry normalization, dual centering, and trace normalization in sequence to unify the numerical scale of the layer kernel, fusion kernel, and target structure matrix, thereby reducing instability caused by scale drift during training.

[0007] As a preferred implementation, the adaptive cross-layer fusion in step S2 calculates the learnable weights of the normalized kernel matrix of each layer using the softmax function, performs unified kernel normalization again after weighted summation of the multi-layer kernel matrices, and realizes adaptive weighted integration of kernel representations at different levels.

[0008] As a preferred implementation, the multi-scale structure preservation regularization term in step S3 depends on the fusion kernel matrix in step S2 and the original input data, specifically including local structure preservation loss: constructing a multi-scale k-nearest neighbor graph in the input space to obtain the target neighborhood distribution, converting the fusion kernel matrix into a soft neighborhood distribution in the kernel space, and constraining the consistency of the multi-scale neighborhood distribution through KL divergence; global structure preservation loss: Calculate the bicentering correlation between the Euclidean distance matrix of the input space and the induced distance matrix of the fusion kernel, and use 1 minus this correlation as a global geometric consistency constraint.

[0009] As a preferred implementation, the soft-kernel k-means structure update mechanism in step S4 directly relies on the fusion kernel matrix output in step S2 to calculate the soft-kernel k-means distance from the sample to the cluster. Specifically, it includes: constructing an unnormalized similarity matrix based on the distance matrix and dynamically updating the target cluster size edge constraints using an exponential sliding method. An approximate coupling matrix is ​​obtained by performing a finite-step Sinkhorn alternating scaling, and the soft assignment matrix is ​​obtained after row normalization. Based on the soft assignment matrix, an instantaneous structure matrix is ​​constructed, and the target structure matrix is ​​updated using an exponential moving average of the adaptive momentum coefficient. In a preferred embodiment, the adaptive momentum coefficient is correlated with the sample average confidence level of the soft assignment matrix. In the low confidence stage, the momentum is increased to suppress structural oscillations, while in the high confidence stage, the momentum is decreased to improve the structural update responsiveness.

[0010] As a preferred implementation, the total learning objective in step S5 is to integrate the multi-scale structure preservation regularization term in step S3, the target structure matrix in step S4, and the fusion kernel matrix in step S2, specifically: Total loss = Reconstruction loss + Kernel consistency weight × Kernel consistency loss + Structure preservation weight × Multi-scale structure preservation loss. Among them, the reconstruction loss is the input data reconstruction error based on the row relation representation of the fusion kernel matrix, and the kernel consistency loss includes the confidence-weighted alignment loss between the centralized fusion kernel matrix and the target structure matrix, and the representation consistency loss between the multi-layer encoding representation and the fusion kernel.

[0011] As a preferred implementation, the alternating optimization framework described in step S5, with the fusion kernel matrix of step S2 and the target structure matrix of step S4 as the interaction core, is divided into: Parameter update step: With the target structure matrix fixed, optimize the parameters of the encoder, projector head, kernel feature head and decoder through backpropagation, and update the fusion kernel matrix synchronously; Periodic structure update step: Fix the fusion kernel matrix, execute the soft kernel k-means structure update in step S4 at set intervals, and refresh the soft assignment matrix and the target structure matrix.

[0012] As a preferred implementation, in step S5, a dynamic segmented scheduling strategy is adopted for the core consistency weight and the structure preservation weight. The weights are fixed during the preheating phase and gradually decay or are linearly adjusted according to preset rules after the preheating is completed, which is coordinated and adapted with the structure update cycle in step S4.

[0013] As a preferred implementation, the independent post-processing in step S6 uses a spectral rounding algorithm to discretize the final fusion kernel matrix obtained in step S5. The soft assignment matrix in the training phase is only used as dynamic structure supervision in step S5 and does not directly participate in the final clustering label generation.

[0014] Compared with the prior art, the beneficial effects of the present invention are: This invention constructs a multi-scale structure-preserving regularity from two levels: local neighborhood distribution consistency and global geometric correlation. It explicitly constrains the geometric offset of the kernel space relative to the input space, suppressing excessive geometric distortion and structural degradation during kernel learning. Ablation experiments confirm that removing this module results in an average decrease in clustering performance. This invention introduces a soft-kernel k-means structure update mechanism with optimal transmission margin constraints and Sinkhorn normalization, which can explicitly control the cluster size distribution and avoid cluster collapse, cluster imbalance and structural oscillation. Combined with adaptive momentum smoothing update of the target structure matrix, it significantly reduces the error accumulation caused by unreliable pseudo-supervision in the early stage of training. The training dynamic curve shows that the total loss converges smoothly, the trajectory is highly consistent under different random seeds, there is no divergence and violent oscillation, and the empirical stability is significantly better than traditional self-training clustering methods.

[0015] This invention transforms multi-layer deep representation into a data adaptive fusion kernel while retaining nonlinear fitting ability and sample relationship structure, thereby continuously improving the kernel similarity of classes and significantly reducing the similarity between classes. The separability of kernel representation steadily increases with training. The fusion kernel simultaneously serves three constraints: reconstruction, kernel consistency, and structure preservation, achieving integrated coupling optimization of "feature learning - kernel learning - clustering structure", which is superior to the two-stage paradigm of feature learning followed by clustering. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the overall framework of the MSPOT-DKC invention; Figure 2 This is a schematic diagram of the post-construction inspection of the Nemenyi method of the present invention; Figure 3 This is a schematic diagram comparing the clustering performance of the MSPOT-DKC and its ablation variants on 12 datasets. Figure 4 This is a schematic diagram showing the performance difference distribution of each ablation variant of the present invention relative to the complete model MSPOT-DKC; Figure 5 This is a schematic diagram of the parameter sensitivity analysis of the MSPOT-DKC of the present invention under different hyperparameter settings; Figure 6 This is a schematic diagram illustrating the controlled load scaling results of the MSPOT-DKC of the present invention on the Basehock dataset; Figure 7 This is a schematic diagram illustrating the training dynamics and empirical stability results on the BBC dataset of this invention; Figure 8 This is a schematic diagram illustrating the steps of the multi-scale structure-preserving-optimal-transmission-depth-kernel clustering method of the present invention. Detailed Implementation

[0017] The present invention will be further described below with reference to embodiments.

[0018] The following embodiments are used to illustrate the present invention, but should not be used to limit the scope of protection of the present invention. The conditions in the embodiments can be further adjusted according to specific conditions, and simple improvements to the method of the present invention under the premise of the concept of the present invention are all within the scope of protection claimed by the present invention.

[0019] Please see Figure 1 - Figure 8 This invention provides a multi-scale structure-preserving optimal transmission depth kernel clustering method. This application collaboratively designs kernel representation learning, structure-preserving constraints, and controlled structure update mechanisms within an alternating optimization framework. Given input data X, the model first obtains hierarchical representations through a multi-layer encoder, then constructs layer kernels through projection mapping and explicit kernel feature mapping, and subsequently obtains a unified kernel matrix K through learnable weight fusion. During the training phase, the fused kernel K is simultaneously used for kernel row reconstruction, kernel consistency constraints, periodic structure updates, and multi-scale structure-preserving regularization; during the inference phase, the final clustering label is determined by the converged fused kernel. Obtained through independent post-processing.

[0020] The training of MSPOT-DKC consists of alternating parameter update steps and periodic structure update steps. In the parameter update step, with the target structure matrix V fixed, the network parameters are optimized and the fusion kernel K is updated through backpropagation. In the structure update step, with the current kernel matrix K fixed, a soft assignment matrix S is generated using a soft-kernel k-means algorithm based on OT-Sinkhorn, and the target structure matrix V is updated using momentum. It is important to emphasize that this structure update is performed as a dynamic target generation process during the training phase and does not directly participate in backpropagation as an explicitly differentiable term in the overall target. Therefore, the soft assignment matrix S during the training phase is functionally distinct from the final predicted labels.

[0021] like Figure 1 As shown, the overall framework of MSPOT-DKC is presented. During the training phase, the input data X undergoes multi-layer representation learning, layer-by-layer deep kernel construction, and adaptive weighted fusion to obtain a fusion kernel K. This fusion kernel is simultaneously used for kernel consistency constraints, periodic OT-Sinkhorn structure updates, kernel row reconstruction, and multi-scale structure preservation regularization. During the inference phase, based on the final fusion kernel... Perform independent post-processing to obtain the final cluster labels. .

[0022] Given an unlabeled dataset (1) Where N represents the number of samples and d represents the input dimension, the goal of this application is to divide the samples into C clusters under unsupervised conditions and learn a symmetric kernel matrix that can characterize the nonlinear similarity relationship between samples.

[0023] (2) To describe the soft clustering structure during the training phase, a soft assignment matrix is ​​introduced. (3) The instantaneous structure matrix induced by S is denoted as

[0024] Let the centered matrix be

[0025] Throughout the text, Indicates the first Layer hidden representation, It is only used for dual-centering operations on the kernel matrix and distance matrix.

[0026] To unify the numerical scale of the layer kernel, fusion kernel, and target structure matrix, a unified kernel normalization operator is defined: (4) in This is the numerical stability constant. The operator sequentially performs symmetry, bicentering, and trace normalization, thereby mitigating instability caused by scale drift during training. When the trace value is too small or a non-finite value appears, a stability backoff strategy can be employed to avoid numerical degradation.

[0027] This paper employs a full-batch transductive clustering configuration. Both training and inference construct the kernel matrix and its row representations based on the entire current dataset. During training, the soft assignment matrix S is used to generate and update the target structure matrix V; the final cluster labels are determined by the final fusion kernel. It is obtained through independent post-processing, rather than by direct hardening of S during the training period.

[0028] Multilayer deep core structure and cross-layer fusion: Indicating a multi-layer encoder, the input sample is at the th The hidden representation of a layer is written as: (5) in, This paper employs a two-stage mapping method to construct and display deep kernel features. First, through the projection head... Map this layer representation to the projection space: (6) In implementation Normalization is performed to reduce the impact of differences in sample scales on subsequent kernel construction. Then, the kernel feature head is used... Map the projected representation to the explicit kernel feature space: (7) In implementation, It can be further combined with feature centering, optional nonnegativity constraints, row normalization and temperature scaling to improve the stability and comparability of explicit kernel features.

[0029] Based on explicit kernel features, the first kernel is defined. The Gram core of the layer is: (8) In large-sample scenarios, direct calculation This may result in high memory overhead; therefore, in practical implementations, a block-based dot product strategy can be used to construct the kernel matrix. Subsequently, a unified kernel normalization operator is applied to the layer kernels, resulting in: (9) After obtaining all layer kernels, cross-layer learnable weights are introduced for adaptive fusion, let: (10) The final fusion core is defined as: (11) Equation (11) corresponds to the two-stage kernel normalization strategy.

[0030] First, apply the following to each sub-nucleus: To alleviate the scale differences caused by different depth representations; secondly, the same operator is applied to the kernel matrix after cross-layer weighted fusion to maintain the comparability of the fused kernel in terms of centralization, consistent scale and numerical stability. Thus, Equations (8) to (11) give the complete definition of intra-layer deep kernel construction and cross-layer adaptive fusion.

[0031] In the structure update step, the model generates a soft assignment matrix S based on the current fusion kernel K, and updates the target structure matrix V accordingly. Upon first entering the structure update, if no available soft assignment matrix exists, a kernel-means algorithm is first performed on the current fusion kernel K to obtain an initial hard assignment, which is then one-hot encoded as the initial value of S; correspondingly, the initial target structure matrix is ​​set to... The initial cluster size is a priori set as .

[0032] First, define the sample. The k-means distance to the soft kernel of cluster j is (12) in, Let S represent the soft size of cluster j. When S degenerates into one-hot assignment, equation (12) degenerates into the standard kernel k-means distance.

[0033] Based on distance matrix Define the unnormalized similarity matrix:

[0034] in Let be the temperature parameter. Then, an entropy-normalized target column edge constraint is applied to P, and a non-negative coupling matrix that approximately satisfies the constraint is obtained through finite-step Sinkhorn alternating scaling. Let the target column edge be... ,satisfy Its idealized counterpart, the entropy-normal optimal transport subproblem, is: (13) The feasible region is defined as follows:

[0035] It should be noted that in actual implementation, it is not required that the double edge constraint be strictly satisfied after a finite number of iterations. Equation (13) is mainly used as an idealized reference form for structural updates, and the finite-step Sinkhorn alternating scaling is used to obtain the approximate coupling matrix Q. Since Q obtained by the finite-step Sinkhorn only approximately satisfies the double edge constraint, we further perform row normalization on Q to obtain the standard row random soft assignment matrix:

[0036] To control cluster size and mitigate drastic fluctuations in soft assignments during training, the target cluster size is updated using an exponential sliding method. Let the prior cluster size for the previous round be... Record the current unnormalized column sum as Then the target edge is updated to

[0037] This article adopts Instead Alternatively, the column sum of S can be used to update the target edge. The reason is that... This more directly reflects the original cluster occupancy tendency induced by the current kernel distance, without the secondary corrections brought about by column edge constraints and row normalization. This allows for the preservation of current structural information while reducing the strong coupling between the target edge and the constrained coupling matrix, thereby improving the empirical stability of edge updates. Before the first structural update, the currently initially assigned columns and the initial cluster size can be used as a priori parameters. After each target edge update, let This is used as a priori cluster size for the next outer loop or the next round of structure update. In the actual algorithm, t changes dynamically with the training process and the current soft assignment state, and its role is to provide a controlled priori cluster size, rather than a fixed and strict constraint.

[0038] After obtaining the new soft assignment matrix, construct the instantaneous structure matrix. The self-trained target structure matrix V is updated using an exponential moving average:

[0039] in, Let be the momentum coefficient. In this paper, the fundamental momentum is taken as . And adaptively update based on the average confidence of the current soft assignment:

[0040] in This represents the average confidence level of the current sample. The strategy enhances time smoothing in the low-confidence stage to suppress violent oscillations of the target structure; and weakens smoothing in the high-confidence stage to improve the responsiveness of structural updates.

[0041] Therefore, the structure update step is performed in the following order: first, the distance matrix D is calculated using equation (12), and then... An unnormalized similarity matrix P is constructed, and the target column edges t are updated according to Equation (15). Then, a finite-step Sinkhorn scaling is performed with Equation (13) as the idealized reference to obtain the approximate coupling matrix Q. The soft assignment matrix S is then generated by Equation (14), and finally, the target structure matrix V is updated by Equation (16). In this process, OT-Sinkhorn is mainly used for structure generation and cluster size adjustment during the training phase, while the updated V serves as dynamic structure supervision in the parameter update step. Therefore, the goal of this process is not to directly provide the final cluster label, but to continuously provide controlled structure teacher signals during the training process to guide the fusion kernel to evolve towards a more stable cluster structure.

[0042] In summary, equations (12) to (16) together constitute the constrained structure update sub-process during the training phase. To facilitate its subsequent use in the overall training process, this process is now summarized as Algorithm 1.

[0043] Multi-scale structure preservation regularization: To constrain the structural consistency between the input space and the kernel space, this paper constructs multi-scale structure preservation regularization from two levels: local neighborhood preservation and global geometric correlation. Here, structure preservation is a soft constraint, which does not require the kernel space to mechanically replicate the geometry of the input space, but is used to suppress excessive geometric distortions that are detrimental to clustering, while preserving the degrees of freedom for favorable rearrangements around the potential cluster structure.

[0044] Given a symmetric kernel matrix K, the RKHS pairwise distance induced by it is defined by the kernel trick as:

[0045] in This is the numerical stability term. The kernel distance matrix obtained from equation (17) is denoted as... .

[0046] Local structure preservation, within the input space, for multiple neighborhood scales Construct a symmetric k-nearest neighbor graph and obtain the target neighborhood distribution using RBF weights based on Euclidean distance. In kernel space, kernel distances are mapped to soft neighborhood distributions.

[0047] Where T is the temperature parameter. Let represent the distance matrix after masking the diagonal elements before softmax. Therefore, the local structure preservation loss at the k-th scale is defined as...

[0048] This term is used to constrain local nearest neighbor relationships in the input space to be well preserved in the kernel space.

[0049] Global structure preservation. In addition to local neighborhoods, this paper also requires that the overall geometry of the kernel space remain consistent with the input space. (Note: The original text contains a typo and can be omitted.) Given the Euclidean distance matrix in the input space, scale normalization is performed by dividing by the maximum value. For any distance matrix D, its bicentering result is denoted as...

[0050] in , and These represent the row mean, column mean, and overall mean, respectively. Furthermore, the correlation of the centered distance matrix is ​​used to measure... and Overall geometric consistency:

[0051] This quantity essentially corresponds to the normalized correlation between the bi-centered distance matrices, used to characterize the consistency of the overall geometric relationship between the input space and the kernel space. Based on this, the global structure preservation loss is defined as:

[0052] Multi-scale fusion. Integrating both local and global constraints, the overall structure preservation loss is obtained: (20) in, and The contributions of local and global terms are controlled separately. In implementation, the input spatial distance matrix... Pre-compile and reuse k-nearest neighbor graphs at various scales; simultaneously Set it as a learnable scalar and constrain T within the stability interval.

[0053] As can be seen from equations (17) to (20), the calculation of the multi-scale structure preservation term mainly includes three steps: kernel distance construction, local neighborhood distribution alignment, and global geometric consistency evaluation. To facilitate repeated use in subsequent training phases, the calculation process of this loss is now summarized as Algorithm 2.

[0054] Learning Objectives and Optimization Process: Optimization of MSPOT-DKC involves network parameters. Structure-related state variables ;in It is only used for recursive updates of the target column edges and does not participate in backpropagation optimization. In each epoch, the model alternates between parameter update and structure update steps. The parameter update step optimizes the network parameters and learns the kernel matrix K while keeping v constant; the structure update step updates S, V, and [other parameters] using the OT-Sinkhorn soft-kernel k-means algorithm described in Section 3.3 while keeping K constant. .

[0055] Reconstruction constraints. This paper defines reconstruction branches based on kernel row relation representation. For the sample , the i-th row of the kernel matrix This is viewed as a relational representation of the sample relative to all samples in the current dataset, and is processed through a decoder with shared parameters. Map this relation back to the original feature space:

[0056] Therefore, the reconstruction loss is defined as follows: (twenty two) It should be noted that this term is not equivalent to the sample-by-sample reconstruction of the input from the single-sample local latent representation in a conventional autoencoder. The goal here is to ensure that the relational representation encoded by the fusion kernel still retains recoverable sample content information, thereby reducing excessive deviation from the original feature semantics during kernel learning.

[0057] Kernel consistency loss. To align the current fused kernel with the target structure matrix, a kernel consistency loss is defined. Let the off-diagonal mask be...

[0058] If a soft assignment matrix S exists, then the sample confidence level is defined using normalized entropy. , And construct the weight matrix

[0059] If there is no S, then let Simultaneously, the centralized kernel matrix and the target structure matrix are respectively...

[0060] Based on this, define the kernel alignment term:

[0061] This term is essentially a confidence-weighted CKA-type alignment loss on the centered kernel matrix.

[0062] Furthermore, to constrain the consistency between the multilayer representation and the relational structure induced by the fusion kernel, a kernel-induced representation consistency term is defined: (twenty four) This term does not require K to act as an explicit graph diffusion operator or a random walk operator, but rather constrains the representations of each layer to remain consistent under the sample relationships induced by the fusion kernel, thereby reducing the deviation between representation learning and kernel structure learning. Therefore, the kernel consistency loss is written as... (25) Overall goals and scheduling strategy. It is important to emphasize that the parameter update objective is defined only under the condition that the current target structure matrix V is fixed. The soft assignment matrix S, the target structure matrix V, and the cluster size prior are also considered. The update is performed by the periodic structural update process given in Section 3.3, and does not directly participate in backpropagation as an explicit differentiable loss term in the following equation.

[0063] Considering all the losses involved in the comprehensive parameter learning phase, the parameter update objective of the model in the t-th epoch is written as: (26) Therefore, the overall training process consists of alternating parameter update steps driven by explicit loss and periodic structure update steps based on OT-Sinkhorn, rather than a one-time joint optimization of all variables under a single objective function. It should be noted that although the warm-up phase retains the v constructed from the initial hard assignment as a static structure reference, no new periodic structure updates are performed at this time; only when... And S, V, and ... are only recalculated when the update interval condition is met. .

[0064] in, and These represent the dynamic weights of the kernel consistency term and the structure preservation term, respectively. For the kernel consistency term, the following segmented scheduling strategy is adopted:

[0065] That is, after the preheating is completed, Depend on Gradually decrease to .

[0066] Sinkhorn temperature With the number of iterations Linear scheduling is employed. Structure preservation terms are only used when... Enabled at that time, and subsequently Within one epoch from Linear scheduling to When both take the same value, this term degenerates into a constant weight.

[0067] In terms of optimization, this paper adopts the AdamW optimizer in conjunction with cosine annealing learning rate scheduling. During training, mixed precision is used to reduce memory overhead, and non-finite value cleaning and norm pruning are performed on gradients; block inner product is used for kernel matrix calculation to reduce memory overhead.

[0068] Based on the above loss definition, dynamic weight scheduling, and periodic structure update mechanism, the overall training process of MSPOT-DKC can be summarized as Algorithm 3. The calculation of the multi-scale structure preservation term corresponds to Algorithm 2, while the periodic structure update sub-process corresponds to Algorithm 1.

[0069] Computational complexity and inner layer update properties: Let the number of samples be N, the input dimension be d, the number of clusters be C, the kernel feature dimension be r, and the number of encoder layers be L. The layer represents the dimension as Multiscale sets are (its base is) The outer loop iteration count is R, the Sinkhorn iteration count is I, and the target structure update interval is [missing value]. The training of MSPOT-DKC includes two parts: parameter optimization and structure update, which is consistent with the definitions in Section 3.3 to the above.

[0070] Time complexity and space complexity Let the total computational cost of a single epoch be...

[0071] Here, each term represents the computational cost of encoding mapping, kernel construction, reconstruction branch, structure preservation term, and periodic target update, respectively.

[0072] The encoder and kernel feature network propagate forward point by point according to the samples, and its complexity is approximately

[0073] For each layer of explicit kernel features The Gram kernel has a construction complexity of 1. Therefore, the overall kernel construction complexity is

[0074] The kernel-induced representation of the consistency term in kernel consistency loss mainly involves The computational complexity is approximately:

[0075] If the width of the first layer of the decoder is The complexity of refactoring the branch is approximately: .

[0076] For the multi-scale structure preservation term, input distance matrix The construction complexity is Kernel induced distance matrix The construction complexity is ; at each scale Below, both local neighborhood distribution alignment and KL matching are... Therefore, the total cost of the partial terms is The global item is also Therefore, there is

[0077] when When the above costs are pre-calculated and reused with k-nearest neighbor graphs at various scales, they can be partially amortized.

[0078] The structural update process occurs every The calculation is performed once per epoch. As shown in Equation (12), the dominant cost of distance matrix computation comes from... and The complexity of Sinkhorn scaling with I inner iterations and R outer loops is... Therefore, the complexity of a complete target update can be written as:

[0079] In summary, the dominant computational cost of MSPOT-DKC under large sample conditions is due to Item control, namely

[0080] In terms of space complexity, the kernel matrix Occupy Space; the input distance matrix, kernel distance matrix, and multi-scale structural intermediates also belong to Soft assignment matrix Only Space. Therefore, the overall dominant storage overhead is (32) Convergence and uniqueness of subprocesses: This proposition describes the properties of inner processes under fixed margins, strict positive initialization, and infinite alternating scaling conditions, serving to clarify the theoretical motivation behind the structure update mechanism in this paper; it does not constitute a rigorous convergence proof for Algorithm 1 or the overall training process. Since the overall training of MSPOT-DKC involves alternating optimization and dynamic structure updates, the overall problem is non-convex and does not guarantee global optimal convergence.

[0081] The part that this paper can rigorously characterize is the idealized inner Sinkhorn subprocess in Section 3.3, that is, the process under the conditions of fixed target column edges, strict positive initialization, and infinite alternating scaling.

[0082] Among them, the properties of idealized Sinkhorn scaling under fixed target column edges. Let the initial matrix be satisfy Given the target column edge vector ,satisfy and Define alternating scaling iteration:

[0083] Then when hour, Converging to the unique limit and satisfy

[0084] and It is the unique solution to the following KL projection problem:

[0085] prove.

[0086] Depend on Given the strict positivity of , the strict positivity of t, and the consistency of the total edge quality, it can be deduced that a diagonal scaling matrix exists. , making Simultaneously satisfying the specified row and column edges, and the scaling is unique under strictly positive conditions. The row normalization and column normalization in equation (33) correspond to the scaling of the set under KL geometry.

[0087] and

[0088] Alternating Bregman projections. Due to the feasible set The sequence is non-empty and has a unique scaling solution, therefore... The unique solution converges to the KL projection problem. Q.E.D.

[0089] The theorem described above describes an idealized inner scaling process with a fixed target column edge t. In the actual algorithm, t is dynamically updated based on the prior cluster size from the previous round and the current column sum, and scaling only performs a finite number of iterations, followed by row normalization to obtain the standard soft assignment matrix. Therefore, the theorem does not correspond to a strict convergence guarantee for the entire process of Algorithm 1, but rather provides a theoretical reference for its inner scaling mechanism.

[0090] The feasibility of soft assignment under the idealized limit is inferred.

[0091] make To define the limit of the theorem, soft assignment is defined.

[0092] Then we have: ; That is, S is a row random matrix; because In the idealized limit, the total mass of the column is explicitly controlled by the target edge t; when each component of t has a positive lower bound, extreme cluster occupancy degradation can be avoided.

[0093] This conclusion provides a theoretical motivation for adjusting the cluster size through the target edge in practical algorithms, but it does not mean that the actual soft assignment after a finite number of steps and dynamic edge updates must strictly satisfy the same edge properties.

[0094] prove.

[0095] Depend on achievable And again by ,right Even after normalization, there are still In addition, by It can be seen that the total mass of the train is controlled by t; if Therefore, the total mass of each cluster has a positive lower bound, thus avoiding extreme imbalance or collapse. Q.E.D.

[0096] Therefore, the theorem and corollary only characterize the idealized inner Sinkhorn mechanism under the conditions of fixed target column edges, strict positive initialization, and infinite step alternating scaling.

[0097] The results demonstrate that, under the aforementioned ideal conditions, the constrained scaling process exhibits good feasibility, uniqueness, and row-random soft assignment induced properties, thus providing a theoretical motivation for the aforementioned structural update design. For the actual Algorithm 1 and the overall training process of MSPOT-DKC, the target edge is dynamically updated during training, scaling is performed in only a finite number of steps, and the outer layer still includes kernel learning, momentum target evolution, and non-convex alternating optimization. Therefore, the above results should not be interpreted as a strict guarantee of convergence for the overall algorithm, but rather as a theoretical reference for the inner-layer constrained scaling mechanism.

[0098] In actual training, the evolution of the target structure is achieved through the following momentum update:

[0099] This update smooths the temporal evolution of the target structure to suppress oscillations caused by self-training noise. Simultaneously, the kernel matrix undergoes symmetry, bicentering, and trace normalization after each construction to maintain scale comparability and numerical stability. Thus, the boundary between the idealized inner-layer conclusions and the actual implementation is clearly distinguished: the former provides the design basis, while the latter is mainly characterized through empirical training dynamics and overall experimental results.

[0100] Experimental Results and Discussion Experimental setup This section introduces the datasets used in the experiments, the comparison methods, the evaluation metrics, and the training configuration of MSPOT-DKC. Except for the input dimension d and the number of clusters C, which are determined by the dataset itself, MSPOT-DKC uses a uniform default configuration and training process on all datasets, without additional parameter tuning for any individual dataset. This is to ensure the reproducibility of the comparison process as much as possible and to reduce the impact of dataset-specific parameter tuning on the interpretation of results. The experiments were conducted in an Anaconda isolated environment, implemented using Python 3.11, PyTorch, and scikit-learn, and ran on a workstation equipped with an Intel Core i7 processor, 16GB of host memory, and an NVIDIA GeForce RTX 4060 GPU.

[0101] Comparison Methods and Experimental Protocol: To systematically evaluate the effectiveness and reproducibility of MSPOT-DKC, the experiment compared 12 representative baseline methods under unified sample attribute feature input, unified preprocessing, and unified evaluation criteria. For graph methods that additionally rely on graph topology in the standard settings, the required structural input was supplemented while maintaining consistent attribute features. The baselines cover three categories: traditional clustering methods KMeans++ and Spectral(RBF); kernel and multi-kernel clustering methods (KernelKM, MKKM-MR, RMKKM, SimpleMKKM, DPMKKM, AMKC-LRR, MPS); and deep clustering methods (DEC, IDEC, CVGAE). Among them, KMeans++ is initialized with k-means++; Spectral(RBF) constructs a graph with RBF similarity and performs K-means after spectral embedding; KernelKM and multi-kernel series methods are used to characterize nonlinear cluster structures and multi-kernel fusion capabilities; DEC / IDEC models follow the technical paradigm of combining representation learning and cluster fine-tuning; CVGAE relies on variational graph autoencoders to learn node latent variables and performs K-means clustering operations in the latent space.

[0102] All methods are based on consistent data partitioning and sample attribute feature input, with the number of clusters uniformly set to the number of true classes, C. Input feature matrix. Unified sample level Normalization:

[0103] For high-dimensional sparse data such as text, original features such as TF-IDF are directly used, and only the above normalization is performed without additional dimensionality reduction or feature selection. For multi-kernel methods that require kernel functions, the same basic kernel set is used uniformly: one linear kernel and seven RBF kernels. RBF kernel parameters. Determined adaptively by medianheuristic and further multiplied by the scale set.

[0104] A multi-scale RBF kernel candidate set is formed to ensure the comparability of multi-kernel methods in a consistent candidate kernel space.

[0105] For baselines that depend on graph structures (such as CVGAE), standard graph topology information is provided while keeping the sample attribute feature input unchanged: datasets with original graphs use the original graphs directly; datasets without original graphs uniformly use KNN graph construction. The input model is undirected. This setting ensures the consistency of attribute feature inputs while satisfying the standard operating conditions of graph methods. Therefore, the focus of this paper is to examine the empirical performance of each method under unified data, unified preprocessing, and standard protocols, rather than stripping away the input forms necessary for different method families. In other words, the results in this paper reflect the empirical performance of each method under its standard applicable settings, and do not constitute an absolutely fair comparison after completely stripping away different input priors. For Cora and CiteSeer, MSPOT-DKC uses only the node attribute matrix as a single-view input and does not use graph edge information; the graph topology is only used to satisfy the standard operating conditions of the graph baseline.

[0106] The deep baseline uses a uniform capacity setting. Both DEC and IDEC use symmetric fully connected autoencoders. The encoder maps the input dimension d sequentially to 500, 500, and 2000, outputting a 128-dimensional latent representation; the decoder symmetrically reconstructs the 128-dimensional representation back to d dimensions. Pre-training uses Adam (learning rate...). The training phase lasts 50 epochs, with a fine-tuning phase using a uniform 400 epochs. All other parameters remain publicly available at their default configurations. CVGAE uses a variational graph autoencoder to learn the latent variable representations before executing K-means; when the dataset lacks the original graph structure, the aforementioned KNN is used. The graph is constructed, and the remaining training parameters use the default settings of the publicly available implementation.

[0107] MSPOT-DKC uses a uniform default configuration across all datasets, keeping all hyperparameters fixed except for the input dimension d and the number of clusters C. This indicates that the learning backbone is consistent with DEC and IDEC, and the encoder is... The decoder's hidden layer is Unless otherwise specified, all results are based on the same execution configuration: training for 400 epochs, with an initial learning rate of... The optimizer uses AdamW (learning rate). Weight decay This is combined with cosine annealing learning rate scheduling and a gradient pruning threshold of 5.0. The kernel module uses a composable kernel module based on the NKN style, with a default projection dimension of 384 and a hidden layer... dropout=0.15, rank parameter This is combined with feature centering and row normalization; the kernel correlation loss weights are taken as follows: Consistent with Section 3.5, the target structure matrix for each Update once every epoch, warm-up rounds set to... The fundamental momentum coefficient is set to During the structural update phase, Adaptively adjust based on the current average confidence level of soft assignments: , in, This represents the average confidence level of the current sample. Soft assignment is implemented using OT-relaxed soft kernel k-means combined with Sinkhorn normalization; the termination temperature is set to... The number of iterations to terminate is set to And within the first 100 epochs The linear annealing strength was reduced from 0.8 to 0.5, while the number of iterations was linearly increased from 20 to 50. Multi-scale structure preservation constraints are enabled by default, with nearest-neighbor scale... The weights for local and global terms are 1.0 and 0.5 respectively, and the initial structural temperature is 0.1 (learnable); the structure maintains the total weight. Scheduling parameters , Furthermore, in the experimental setup of this paper... This means that the structural term is activated after preheating, but its amplitude remains constant.

[0108] To reduce the fluctuations caused by random initialization, all methods were performed 10 independent replicate experiments on each dataset (random seed 0–9), and the mean and standard deviation of each indicator were reported uniformly.

[0109] This paper uses four metrics—ACC, NMI, ARI, and F1—to evaluate clustering quality. Let the true labels be... Predicted cluster labels are The number of samples is N, and the number of categories and clusters is denoted as C.

[0110] ClusteringAccuracy (ACC) Cluster labels exhibit non-uniqueness of permutations; ACC is calculated under optimal label matching. Let the set of all permutations be denoted as . ,but

[0111] NMI measures the consistency between the true partition and the cluster partition:

[0112] Adjusted RandIndex (ARI) Let the contingency table be... ,in Represents the number of intersection samples between the true i-th class and the predicted j-th cluster; the row edges and column edges are respectively... , ARI is defined as

[0113] F1 score (F1) F1 is calculated after the same optimal label match as ACC. Define category c.

[0114] The final approach used is macro averaging:

[0115] To verify the contribution of each component of MSPOT-DKC to clustering performance, this paper conducts ablation experiments on 12 datasets, with evaluation metrics including ACC, NMI, ARI, and F1. Comparative variants include: w / oSP (removing multi-scale structure-preserving constraints), w / oOT (removing optimal transport soft assignment updates), AEonly (retaining only the reconstruction target), and Latent+k-means (directly performing K-means on the learned latent space representation). All settings were repeated under the same training and evaluation protocol as the full model. Here, w / oSP means setting the weight of the structure preservation term in equation (20) to 0, while keeping the rest of the training process unchanged; w / oOT means removing the OT-Sinkhorn constraint update from equations (13)–(15) and using a soft assignment mechanism without target column edge constraints to generate S, while keeping the rest of the process unchanged; AEonly means training only with the reconstruction loss of equation (22); Latent+k-means means directly performing K-means on the last latent representation of the encoder without introducing kernel construction and structure update processes, with the results as follows: Figure 3 As shown.

[0116] Further comparison reveals that AEonly and Latent+k-means exhibit more significant performance degradation, indicating that relying solely on reconstruction learning or directly performing clustering on the latent space is insufficient to obtain stable clustering results. This phenomenon suggests that the performance of MSPOT-DKC does not stem from a single module, but rather from the synergistic effect between fusion kernel learning, structure preservation, and dynamic structure updating.

[0117] To more intuitively compare the degree of degradation of each variant relative to the complete model, Figure 4 The performance difference distribution is given, where , when When the value is less than the full model, it indicates that the performance of the corresponding variant is lower. It can be seen that the difference for w / oOT is generally close to 0, while the distributions of w / oSP, AEonly, and Latent+k-means are generally more biased towards the negative region, with the latter two showing greater dispersion. This is consistent with... Figure 3 The overall trend is consistent with this, further illustrating that the structure preservation mechanism is the main source of performance gain for the complete model, while performance degrades more significantly after removing key structures from the model.

[0118] It should be noted that on individual datasets, w / oSP or w / oOT performs close to, or even slightly better than, the full model on a few metrics. Such local fluctuations are common in multi-dataset clustering experiments and are insufficient to negate the overall average performance advantage of the full model. A more reasonable interpretation is that the OT module is not the decisive source of main gain, but its introduction into the structure update during training does indeed bring relatively consistent marginal benefits.

[0119] Parameter sensitivity analysis To evaluate the sensitivity of MSPOT-DKC to key hyperparameters, this paper conducts parameter scanning experiments on three representative datasets: MF, Cora, and COIL20. The experiments employ a single-factor control strategy, fixing the remaining hyperparameters at their default settings and adjusting only one parameter. The means and standard deviations of ACC, ARI, NMI, and F1 are then calculated. The parameter examined includes the kernel consistency weight. Structure maintains weight The rank parameter r of NKN, the number of Sinkhorn iterations I, and the Sinkhorn temperature. And the structural temperature T. The candidate values ​​for each parameter are as follows:

[0120]

[0121] Figure 5 Sensitivity curves for each parameter on three datasets are presented. Overall, the degree of influence of different parameters on model performance varies, but the trends are relatively consistent. Specifically, , The structural temperature T is a relatively more sensitive parameter. For example, it shows a more obvious gain trend on COIL20, exhibits an initial increase followed by stabilization on MF, and is more sensitive to larger values ​​on Cora; when At that time, many indicators showed varying degrees of decline. For All three datasets showed some sensitivity, with the changes on Cora being the most pronounced. The model achieves optimal results in the vicinity of the optimal value; however, when the value is too small or too large, the performance falls below the optimal point. The structural temperature T also shows a strong influence: the model performance is relatively stable in the small to medium range, but when T increases to 0.5, the performance on MF and Cora decreases more significantly, and a certain decline also occurs on COIL20.

[0122] In comparison, the rank parameter r of NKN, the number of Sinkhorn iterations I, and the Sinkhorn temperature The overall impact on model performance is relatively weak. For r, MF and COIL20 achieve relatively stable results within a moderate range, while Cora shows a slight benefit at larger r values. For I and The performance curves on the three sets of data are generally flat, indicating that MSPOT-DKC has good adaptability to OT solution parameters over a wide range.

[0123] Overall, MSPOT-DKC does not exhibit excessive sensitivity to capacity parameters and OT solution parameters, but is more sensitive to loss weights and structural temperature, although the latter still shows a relatively clear stability range. This indicates that although this method requires reasonable setting of structure-related hyperparameters, its usable parameter range is not narrow. Figure 5 The results will be used in subsequent experiments. The scale is set to a medium magnitude, and the structural temperature T is controlled in a small to medium range to achieve a good balance between discriminability and structural stability.

[0124] This section evaluates the empirical computational overhead of MSPOT-DKC and its scaling behavior under controlled load conditions. Section 3.6 has already presented the dominant time and space complexity analysis; therefore, we further validate this empirically through scaling experiments. The experiments are conducted on the Basehock dataset, with a target size set as follows: . in, and This represents the actual subsample size; since the original Basehock sample size was 1993, and By constructing a test with replacement that maintains the class proportions, a stress test scenario under higher loads is created. Each scale point is run three times, trained for 200 epochs, with a fixed learning rate. Furthermore, the first 5 warm-up epochs were removed when calculating the average training time per epoch to reduce fluctuations caused by the initialization phase.

[0125] Figure 6 (a) and Figure 6 (c) shows that as the sample size N increases, both training time and peak GPU memory usage continue to rise. The average training time per epoch increases from... The time increased from 0.0390s to The peak GPU memory usage increased from 0.4465GB to 3.3359GB, approximately 7.47 times the initial size, at 0.3727s. Figure 6 The log-log fit slope in (a) is 1.24, indicating that the empirical time cost under the current implementation shows a significant superlinear trend with the increase of scale.

[0126] In terms of performance, Figure 6 (b) shows that ACC, NMI and ARI generally increase with size, and tend to level off in the larger size range.

[0127] Overall, Figure 7 The results show that the training process of MSPOT-DKC on the BBC dataset is stable and reproducible: the overall objective continuously decreases, no significant conflicts appear among the loss components, and the discriminativeness of the kernel representation gradually increases with training. Therefore, the results in this section support the empirical stability of the method and complement the discussion above regarding the properties of the idealized inner layer update. It is important to emphasize that the results obtained here are empirical evidence of training stability, rather than a rigorous theoretical guarantee of the overall nonconvex optimization process.

Claims

1. A multi-scale structure-preserving optimal transmission depth kernel clustering method, characterized in that, Includes the following steps: S1: Perform multi-layer encoding on the input unlabeled single-view data to obtain hierarchical hidden representations. Based on each layer of hidden representations, perform projection mapping and kernel feature mapping in sequence to construct multi-layer explicit kernel features. Then, calculate the Gram kernel within the layer based on the explicit kernel features and apply unified kernel normalization to obtain the normalized kernel matrix of each layer. S2: Based on the normalized kernel matrices of each layer obtained in step S1, learnable weights are introduced to complete adaptive cross-layer fusion. After applying unified kernel normalization again, the data adaptive fusion kernel matrix is ​​obtained, which provides the basic kernel representation for subsequent structural constraints and clustering updates. S3: Based on the fusion kernel matrix obtained in step S2, construct a multi-scale structure-preserving regularization term that couples the consistency of local neighborhood distribution and global geometric correlation, constrain the geometric offset of the kernel space relative to the input space, and suppress the structural distortion in the kernel learning process; S4: Based on the fusion kernel matrix obtained in step S2, a soft kernel k-means structure update mechanism inspired by the optimal transmission margin constraint is designed. A controlled soft assignment matrix that satisfies the margin constraint is generated by Sinkhorn normalization, and the target structure matrix is ​​smoothly updated in an adaptive momentum manner to provide dynamic structure supervision for kernel learning. S5: Using the multi-scale structure preservation regularization term in step S3 as the core constraint, and combining the reconstruction loss and kernel consistency loss based on the fusion kernel matrix to construct the overall learning objective, the model training is completed using the optimization framework of alternating parameter updates and periodic structure updates supported by steps S1-S4. S6: After the model training converges and the final fusion kernel matrix is ​​obtained, perform independent post-processing based on the final fusion kernel matrix to obtain the final clustering label and complete the single-view unsupervised deep kernel clustering.

2. The multi-scale structure-preserving optimal transmission depth kernel clustering method according to claim 1, characterized in that: The unified kernel normalization described in steps S1 and S2 involves performing symmetry normalization, dual centering, and trace normalization operations sequentially to unify the numerical scale of the layer kernel, fusion kernel, and target structure matrix, thereby reducing instability caused by scale drift during training.

3. The multi-scale structure-preserving optimal transmission depth kernel clustering method according to claim 2, characterized in that: The adaptive cross-layer fusion described in step S2 calculates the learnable weights of the normalized kernel matrix of each layer using the softmax function, and performs unified kernel normalization again after weighted summation of the multi-layer kernel matrices to achieve adaptive weighted integration of kernel representations at different levels.

4. The multi-scale structure-preserving optimal transmission depth kernel clustering method according to claim 1, characterized in that: The multi-scale structure preservation regularization term in step S3 depends on the fusion kernel matrix in step S2 and the original input data. Specifically, it includes local structure preservation loss: constructing a multi-scale k-nearest neighbor graph in the input space to obtain the target neighborhood distribution; converting the fusion kernel matrix into a soft neighborhood distribution in the kernel space; and constraining the consistency of the multi-scale neighborhood distribution using KL divergence; global structure preservation loss: Calculate the bicentering correlation between the Euclidean distance matrix of the input space and the induced distance matrix of the fusion kernel, and use 1 minus this correlation as a global geometric consistency constraint.

5. The multi-scale structure-preserving optimal transmission depth kernel clustering method according to claim 1, characterized in that: The soft-kernel k-means structure update mechanism described in step S4 directly relies on the fusion kernel matrix output in step S2 to calculate the soft-kernel k-means distance from the sample to the cluster. Specifically, it includes: constructing an unnormalized similarity matrix based on the distance matrix and dynamically updating the target cluster size edge constraints using an exponential sliding method. An approximate coupling matrix is ​​obtained by performing a finite number of Sinkhorn alternating scaling steps, and the soft assignment matrix is ​​obtained after row normalization. An instantaneous structure matrix is ​​constructed based on the soft assignment matrix, and the target structure matrix is ​​updated by an exponential moving average of the adaptive momentum coefficient.

6. The multi-scale structure-preserving optimal transmission depth kernel clustering method according to claim 1, characterized in that: The adaptive momentum coefficient is correlated with the sample average confidence level of the soft assignment matrix. In the low confidence stage, the momentum is increased to suppress structural oscillations, while in the high confidence stage, the momentum is decreased to improve the structural update responsiveness.

7. The multi-scale structure-preserving optimal transmission depth kernel clustering method according to claim 1, characterized in that: The overall learning objective mentioned in step S5 is to integrate the multi-scale structure preservation regularization term of step S3, the target structure matrix of step S4, and the fusion kernel matrix of step S2. Specifically, the total loss is: total loss = reconstruction loss + kernel consistency weight × kernel consistency loss + structure preservation weight × multi-scale structure preservation loss. Among them, the reconstruction loss is the input data reconstruction error based on the row relation representation of the fusion kernel matrix, and the kernel consistency loss includes the confidence-weighted alignment loss between the centralized fusion kernel matrix and the target structure matrix, and the representation consistency loss between the multi-layer encoding representation and the fusion kernel.

8. The multi-scale structure-preserving optimal transmission depth kernel clustering method according to claim 1, characterized in that: The alternating optimization framework described in step S5, with the fusion kernel matrix of step S2 and the target structure matrix of step S4 as the interaction core, is divided into: Parameter update step: With the target structure matrix fixed, optimize the parameters of the encoder, projector head, kernel feature head and decoder through backpropagation, and update the fusion kernel matrix synchronously; Periodic structure update step: Fix the fusion kernel matrix, execute the soft kernel k-means structure update in step S4 at set intervals, and refresh the soft assignment matrix and the target structure matrix.

9. The multi-scale structure-preserving optimal transmission depth kernel clustering method according to claim 1, characterized in that: In step S5, a dynamic segmented scheduling strategy is adopted for the core consistency weight and the structure preservation weight. The weights are fixed during the warm-up phase and gradually decay or are linearly adjusted according to preset rules after the warm-up is completed, which is coordinated and adapted with the structure update cycle in step S4.

10. The multi-scale structure-preserving optimal transmission depth kernel clustering method according to claim 1, characterized in that: The independent post-processing described in step S6 uses a spectral rounding algorithm to discretize the final fusion kernel matrix obtained in step S5. The soft assignment matrix in the training phase is only used as dynamic structure supervision in step S5 and does not directly participate in the final clustering label generation.

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