An Lightweight  Anchor-Based Incremental Framework to Multi-view Clustering

Venue: acmmm_org_ACMMM_2024_Conference
Published: 2024-03-18 09:10:12

Abstract: The rapid development of multi-media techniques boosts the emergence of multi-view data, and how to uncover its intrinsic structure and utilize it to conduct the subsequent downstream tasks is crucial in data analysis. Multi-view clustering is a representative to handle multi-view data. The anchor-based method has received widespread attention for excellent performance and low time complexity. However, existing methods encounter two drawbacks, cutting down their performance, i.e., the assumption of the availability of all views and limited interaction of anchor generation among views. In some scenes, views arrive sequentially, and storing them is challenging owing to the limited space/ privacy considerations, and the existing anchor-based MVC is unsuitable for this. Additionally, recent works fail to generate anchors with the guidance of other views, and it is tough to align the anchor graphs. To this end, we propose A Lightweight Anchor-Based Incremental Framework for Multi-view Clustering. Specifically, we first initialize an anchor graph with the assistance of $k$-means when a new view arrives. Then, the consensus one of the anchor graphs is updated by the newly collected view with a permutation matrix. Our proposed method is more capable of anchor alignment because, in incremental MVC, the anchor graphs of previous views could be listed as a reference to guide the generation of anchor graphs of the coming view. Furthermore, we design a three-step iterative and convergent strategy to solve the resultant problem. Notably, the proposed algorithm shows outstanding effectiveness and time/space efficiency in extensive experiments.

Main paper: 
 related work: 
 In this section, we will introduce some related researches, including continual multi-view clustering and multi-view anchor graph clustering.Continual Multi-view Clustering (CMVC), proposed by Wan et al. [21] , combines continual learning with the late fusion method. CMVC maintains a consensus partition matrix and further enhances it by accumulating new views. The base partition matrix utilizes a permutation matrix to align old and new information appropriately. Additionally, it introduces a regularization parameter to balance the weights of two sets of information effectively.When the 𝑡-view arrives, with H 𝑡 as the base partition and the consensus partition matrix H * 𝑡 -1 maintained, the optimal permutation matrix can be computed by maximizing the objective formulation in Eq. (1) . maxEQUATIONAs indicated in Eq.( 1), the update process only requires two matrices, making it more adaptable and time-saving. Maintaining the consensus partition matrix instead of individual base partition matrices reduces the storage space needed for previous views. Overall, the CMVC approach is more flexible and cost-effective in terms of both time and space.Multi-view anchor graph clustering has been proposed to make multi-view clustering methods suitable for large-scale data. Usually, traditional graph clustering approaches attach O (𝑣𝑛 2 ) space and O (𝑛 3 ) time complexity to instance numbers [18] , while multiview anchor graph clustering can effectively reduce the time and space consumption to O (𝑣𝑛𝑚) and O (𝑛𝑚 2 ) by constructing anchor graphs on 𝑣 views and 𝑚 anchors instead of the all 𝑛 instances.Constructing the anchor graph of each view is the first step in the multi-view anchor graph clustering. The following equation can implement this process, minEQUATIONThe matrix A 𝑖 ∈ R 𝑚×𝑑 𝑖 serves as the anchor matrix for the 𝑖-th view. The matrix Z 𝑖 ∈ R 𝑛×𝑚 represents the anchor graph for the 𝑖-th view, and the equation Z 𝑖 1 𝑚 = 1 𝑛 ensures that the similarity of each instance to all anchors is standardized. It should be noted that the quality of anchors significantly impacts clustering effectiveness, along with some literature on anchor sampling methods.After constructing the view-specific anchor graphs {Z 𝑖 } 𝑣 𝑖=1 , the final anchor graph G ∈ R 𝑛×𝑚 can be fused as follows, min𝜶 ,G 𝑣 ∑︁ 𝑖=1 𝛼 𝑖 Z 𝑖 -G 2 F , s.t. G1 𝑚 = 1 𝑛 , 𝜶 ⊤ 1 𝑣 = 1, 𝜶 ≥ 0. (3)The weight coefficient 𝜶 ∈ R 𝑣 measures the different impact of each view, and the constraint 𝜶 ⊤ 1 𝑣 = 1 ensures that G1 𝑚 = 1 𝑛 . The optimization process alternates between the weight coefficient 𝜶 and fused graph G within a unified framework. In a follow-up study, the assumptions of equal weights for all views and the rank constraints on the fusion anchor graph are proposed to ensure a non-trivial solution [6, 8] . After obtaining the fusion graph, k-means clustering is applied to its left singular vectors for final clustering. 
method: 
 In this section, we present the formulation of LAIMVC and then propose a three-step alternate optimization approach to address the issue. Following that, we provide its convergence, complexity, and potential expansion.In light of challenges faced by prevailing anchor-based multi-view clustering (MVC) methods when dealing with sequentially arriving or storage-restricted views, we propose LAIMVC to creatively extend anchor-based MVC into an incremental framework. Unlike prior works that struggle with generating anchors without cross-view guidance and encounter difficulties in aligning a unified anchor graph, LAIMVC addresses these limitations effectively.Given a multi-view data matrix X 𝑡 of the 𝑡-th view with 𝑛 samples, 𝑑 𝑡 denotes its feature dimension. Considering that the inconsistent of dimensions among views might lead to the difficulty in anchor graph integration, we first conduct PCA on the feature matrix to a unified dimension 𝑑 as X 𝑡 when the 𝑡-th view is collected. And the consensus anchor graph Z 𝑡 ∈ R 𝑛×𝑚 of previous views has already been attained, under its guidance, we update the consistent anchor graph in an incremental framework to avoid the alignment of anchor graphs among views in the literature. Ω is a regularization term. We formulate it as follows, minEQUATIONA small trick is that a permutation matrix H 𝑡 ∈ R 𝑚×𝑚 is imposed to allow the change of the anchor graph from a certain degree. As shown in Eq.( 5), the permutation matrix ensures the sustainability of data decomposition while performing data alignment. When H 𝑡 H ⊤ 𝑡 = I 𝑚 is satisfied, we haveEQUATIONBy imposing the square of the Frobenius norm as regularization with the trick in Eq.( 5), we can achieve the optimal anchor graph by minimizing the specific objective formulation as, minEQUATION) As shown in Eq.( 6), LAIMVC merely retains the consensus anchor matrix and associated anchor graph pertaining to all prior views, eschewing the save of base matrices or anchor graphs specific to each view. Besides, upon acquisition of a new view, the consensus anchors and graph are jointly refined with a permutation matrix, which fosters interaction in graph generation across views. It iteratively integrates views individually until all views are attained, we ultimately derive the final clustering results through 𝑘-means on the last consensus graph Z 𝑣 .Eq.( 6) comprises three distinct variables requiring optimization, a task that can prove arduous when performed concurrently. So we develop a three-step alternate optimization, optimizing one variable while the rest remain fixed. The formula detailed derivation is given in the appendix.Updating Z 𝑡 . Fixing B 𝑡 and H 𝑡 , the optimization in Eq.( 6) w.r.t Z 𝑡 can be reduced to maxEQUATIONwhereA = X 𝑡 B ⊤ 𝑡 + Z 𝑡 -1 H 𝑡 .The optimum of Z 𝑡 can be analytically obtained with rank 𝑚 truncated the singular value decomposition (SVD) by [24] . Specifically, if the SVD form is A = SΣV ⊤ , the closedform solution in Eq.( 7) is as followsEQUATION)Updating B 𝑡 . Fixing Z 𝑡 and H 𝑡 , the optimization w.r.t B 𝑡 can be reduced to maxEQUATIONwhereC = Z ⊤ 𝑡 X 𝑡 + H ⊤ 𝑡 B 𝑡 -1. Similar to Eq.( 7) and suppose the SVD form is C = S ′ ΣV ′ ⊤ , the closed-form solution in 9 is as followsEQUATIONUpdating H 𝑡 . Fixing Z 𝑡 and B 𝑡 , the optimization w.r.t H 𝑡 can be reduced to maxEQUATIONwhere D = Z ⊤ 𝑡 -1 Z 𝑡 + B 𝑡 -1 B 𝑡 . Similar to Eq.( 7) and suppose the SVD form is D = S ′′ ΣV ′′ ⊤ , the closed-form solution in 11 is as followsEQUATION)The optimization process of the LAIMVC is outlined in Algorithm 1. It can be seen that the views arrive sequentially so the X 𝑡 and Z 𝑡 𝑡 are generated when 𝑡-th view is obtained. The convergence of LAIMVC in theory and its time/space complexity and potential expansion will be argued in the following part.In this section, we give the theoretical proof of the convergence of the proposed LAIMVC, which is the important support for the solvability of the optimization algorithm. In Eq.( 6), every square term is not less than 0. Therefore, the objective function has a lower bound. We will verify in the following part the objective value of Eq.( 6) monotonically decreases along with iterations. For ease of expression, we simplify the objective formula as, minEQUATIONAs demonstrated in Algorithm 1, the optimization process consists of three iterative parts every iteration, i.e. Preprocessing: X 𝑡 to X 𝑡 by PCA. while not converged do 8:Update Z 𝑡 by solving Eq.( 7).9:Update B 𝑡 by solving Eq.( 9).10:Update H 𝑡 by solving Eq.( 11).11:𝑖 ← 𝑖 + 1 12:end while 𝑜𝑏 𝑗 can be updated via Eq.( 7), soEQUATION2)EQUATION𝑡 can be updated via Eq.( 9), soEQUATION3) H 𝑡 -subproblem: Given Z can be updated via Eq.( 11), soEQUATIONCombining Eq.( 14), Eq.( 15) and Eq.( 16), we know,EQUATIONwhich illustrates that the objective value monotonically decreases with iterations. Together with the objective function existing in a lower bound, the algorithm is theoretically convergent. Furthermore, we will verify the convergence of it in the experiment.In this part, we will analyze the space and time complexity of our algorithm. Space Complexity: In our paper, the major memory costs of LAIMVC are matrices Z 𝑡 and B 𝑡 . Thus the space complexity of our LAIMVC is O (𝑛𝑚 + 𝑚𝑑). In our algorithm, 𝑚 ≪ 𝑛 and 𝑑 ≪ 𝑛. Therefore, the space complexity is O (𝑛).Time Complexity: The computational complexity of LAIMVC is composed of three steps as mentioned before. Preprocessing costs O (𝑛𝑑2 + 𝑑3 ). When updating Z 𝑡 , B 𝑡 and H 𝑡 for one iteration, it costs O (𝑛𝑚 2 + 𝑚𝑘 2 + 𝑚 3 ). Let 𝑇 denote the maximum number of iterations and 𝑉 represent the number of views, the time complexity of LAIMVC is O (𝑛𝑑 2 + 𝑑 3 + 𝑇𝑉 (𝑛𝑚 2 + 𝑚𝑘 2 + 𝑚 3 )), which is linear complexity with respect to 𝑛.In conclusion, LAIMVC achieves MVC with both linear space and time complexity, which demonstrates efficiency.To the best of our knowledge, LAIMVC combines incremental learning and anchor graph clustering for the first time, which expands application to sequential scenarios and will provide inspiration for future research. Furthermore, the proposed LAIMVC is more flexible and efficient by incremental learning of anchor points and graphs than the traditional anchorbased methods. The proposed framework has the potential to be used in more complicated data scenarios or extended to other MVC paradigms due to its simple operation and scalability.  
experiments: 
 In this section, we conduct experiments to compare LAIMVC with several state-of-the-art multi-view clustering methods, including three incremental, three anchor-based, and two other methods on several representative datasets. After that, intrinsic structure, running time and complexity comparison, view-fusion performance, parameter sensitivity, and convergence are discussed.4.1.1 Datasets. Seven benchmark datasets of different categories are tested to prove the effectiveness of LAIMVC, including Dermatology1 , Flower17 2 , Cora 3 , AWA104 , ALOI5 , YouTubuFace106 , YouTubeFace100 7 . The brief information on each dataset is summarized in Table 1 and the details are given in the appendix. The first four datasets are regular datasets and the last three are large-scale datasets.(1) OPLFMVC [14] is a pattern of late fusion multi-view clustering using the one-pass method to attain a discrete partition matrix. (2) OPMC [12] is a one-pass algorithm that successfully unifies the multi-view matrix factorization with partition generation. (3) LMVSC [6] implements spectral clustering on the final anchor graph learned by the anchor graph for each view, which handles large-scale data with linear complexity. (4) FPMVS-CAG [26] proposes a subspace clustering method that jointly conducts anchor selection and subspace graph construction without any extra hyper-parameters. ( 5) SMVSC[20] proposes a scalable multi-view subspace clustering with unified anchor points, which combines anchor learning and graph construction into a unified framework. ( 6) IMSC [33] implements multi-view spectral clustering by storing several consensus graphs of previous views and updating them when a new view is collected. ( 7) SCGL [28] proposes an efficient incremental multi-view clustering method by seeking a consensus sparse and connected graph. ( 8) CMVC [21] combines continual learning and late fusion into a unified framework, whose time complexity is linear concerning sample number.We obtained the public code for all the algorithms mentioned above from their original websites. The parameters for the comparison methods were set based on recommendations from the relevant literature. In the experiment, the number of anchor points in LAIMVC is chosen within [𝑘, 5𝑘]. It is assumed that for all datasets, the true number of clusters is known and set to be equal to the true number of classes.The clustering performance is evaluated using commonly used metrics including clustering accuracy (ACC), normalized mutual information (NMI), and Purity. To mitigate the impact of randomness caused by 𝑘-means, each experiment is repeated 20 times with random initialization, and the average result is reported for all algorithms. Our experiments are conducted on a PC with Intel(R) Core(TM)-i7-6800K 3.4GHz CPU and 96G RAM environment. Moreover, the code of LAIMVC will be available on GitHub after acceptance. Table 2 compares the ACC, NMI, and Purity of the aforementioned clustering methods. The notation "OM" signifies that certain algorithms could not produce results due to memory constraints. For instance, when applied to datasets containing over 30,000 samples, SCGL consumes tens of thousands of computational units per parameter tuning and subsequently encounters the issue. And we can illustrate the following conclusions:(1) On four small-scale datasets with fewer than 10,000 samples, LAIMVC achieves top scores on three evaluation metrics in the majority of cases. Taking the results on Cora as an instance and comparing to the algorithm with the secondbest results, LAIMVC outperforms the SMVSC by 14.8% in ACC and exceeds the SCGL by 1.56% for NMI and 6.73% for Purity.(2) For the remaining three large-scale datasets exceeding 10,000 samples, LAIMVC displays a remarkable edge. During the experiments, the regular incremental MVC algorithms, except for the CMVC that solves large-scale data, suffer directly from the "out-of-memory" problem. Our proposed LAIMVC even performs better on these large datasets, more than the second method by 11.31%, 4.24%, and 11.22% on ACC, NMI, and Purity, respectively on ALOI.In summary, as an incremental multi-view clustering technique, LAIMVC can handle scenarios where the number of views is variable, significantly enhancing the performance over anchor-based counterparts. overall, the proposed method can nearly achieve the best clustering performance on listed metrics among the compared algorithms. Since the anchor graph Z 𝑡 of each view in LAIMVC is learned with the new view coming, we construct the corresponding complete graphs by Z 𝑡 Z ⊤ 𝑡 . The complete graphs can be used to show the relationships between pairs of samples and the existing intrinsic structure on a certain dataset.In LAIMVC, the anchor graph for previous views is continuously updated upon introducing new views, we accordingly reconstruct the associated complete graphs. For instance, we plot complete graphs of YouTubuFace10 in Fig. 2 . As the number of views increases, the complete graph shows a clearer block structure with an improved clustering result, demonstrating the incremental learning capability of our proposed method in capturing the intrinsic structure and illustrating it as suitable for sequential-view scenarios and a good blend of integrating knowledge among different views.We conduct experiments to assess the time effectiveness of LAIMVC, whose results are displayed in Table 3 . It should be noted that the execution time of LAIMVC is from initialization to the final fusion of views, while other incremental algorithms exhibit similar calculations. Non-incremental algorithms record the time from the start of processing to obtaining the final characteristic representation of the data. We also plot the log-processed running time in Fig. 3 to make it intuitive. It can be concluded that LAIMVC, since it combines the time advantages of anchor graph decomposition and incremental method, has a much faster running time than other algorithms in processing multi-view data, surpassing the current mainstream rapid clustering One-Pass method.The time complexity can be corresponded to the running time written above. As for the space complexity, we compare the time complexity and storage space required by our method with the other methods, as detailed in the appendix. To summarise, LAIMVC has the lowest time and space complexity, together with CMVC. Especially when the number of views 𝑣 increases sharply, LAIMVC will show significant advantages.In conclusion, our LAIMVC algorithm has a lower computing complexity handling data, realizes superior clustering performance on most datasets, and can be used in situations where the number of views can increase over time. We hope that the effectiveness and excellent efficiency of LAIMVC make it a not-bad consideration for applications in practical clustering scenarios and boost improvement in clustering theory.Over time, previous views may not be available due to privacy concerns or memory restrictions. Most existing methods may be disturbed which makes it difficult to utilize the consistent and complementary information during view fusion, affecting the clustering performance. To solve the problem of dynamic collection of data views, the proposed incremental framework preserves a consensus representation of all previously acquired data and uses it to guide the view-fusion. To show the view-fusion performance, we carry out experiments where the views are sequentially accumulated over time. We plot the results of views integrated one by one in Fig. 4 and Fig. 5 across three distinct datasets, which are Dermatology, AWA10, and YouTubeFace arranged in ascending order of sample number.In Fig. 4 , 'Each' denotes the clustering performance on each view without any other process. Generally speaking, all three metrics are appreciably improved proving that the attempt to utilize previous information to guide the clustering process is vital. And, our proposed method can reduce the influence of view quality on clustering results to some extent.In Fig. 5 , we compare the view-fusion performance of our method with existing incremental multi-view clustering methods. The results of the other two metrics are similar and given in the appendix. With the increase in the number of views, our proposed method maintains satisfactory clustering effects and shows excellent sustainable learning ability. For instance, on AWA10 and YouTube-Face10, the clustering performances of the compared methods show downward trends when dealing with the last obtained views, while LAIMVC still shows a gain effect. Meanwhile, our proposed method remains a promising performance even though a view arrives with poor clustering quality, such as on AWA10.Through these visual representations, we demonstrate how our method progressively improves the clustering performance as more views are combined. The detailed experiments on the effect of the preprocessing of LAIMVC on low-quality views are presented in the appendix, which is omitted here due to space limitations.In our method, we tune the number of anchor points according to the true number of classes 𝑘. So we conduct a sensitivity experiment about the anchor number to illustrate the impact of which on performance. As shown in Fig. 6 , when the anchor number varies from 𝑘 to 5𝑘, it is observed that the values of representative metrics generally remain within a stable range. This indicates that the clustering performance can remain stable when the number of anchor points varies within a wide range, which also illustrates the superior robustness of our proposed method.According to [1] , our algorithm is theoretically guaranteed to converge to a local minimum. The examples of the objective values with iteration are shown in Fig. 7 on Dermatology and YouTube-Face10 datasets (one regular dataset and one large-scale dataset). The results on other datasets or other views are similar and omitted due to space limits. It can be clearly verified that its objective value decreases monotonically and the algorithm converges in less than 15 iterations.  
conclusion: 
 In this paper, we propose a method to solve the clustering problem for sequential-view data efficiently termed a lightweight anchorbased incremental framework for multi-view clustering (LAIMVC). On the one hand, the theoretical analysis of LAIMVC with incremental learning and anchor graph theory is provided, including the convergence and linear space and time complexity. On the other hand, extensive experiments exhibit the superiority of our proposed method, including the intrinsic structure, running time and complexity comparison, view-fusion performance, parameter sensitivity, and convergence. In the future, we intend to explore the framework for the scenario of incremental sample numbers or incomplete data, etc.  
: 
 proper clusters. The core of MVC is to integrate and reconcile the information from different views to reveal more comprehensive insights than a single view alone [2, 7, 15, 16, 27] .As MVC approaches achieving great success in clustering theory, existing research in MVC can be roughly classified into four categories, i.e., multi-view subspace clustering (MVSC), multiple kernel clustering (MKC), multi-view graph clustering (MVGC), and multiview clustering based on matrix factorization (MVCMF). Specifically, MVSC generates the inherent consistency and complementarity of the data into consistent low-dimensional subspace and performs eigen-decomposition on the corresponding subspace [4, 25, [29] [30] [31] . MKC learns a consensus kernel by following a multi-kernel learning framework in which the individual kernels of each view are combined and conduct clustering on the consensus kernel [11, 13, 23, 34] . Most MVGC algorithms construct the similarity graph for each view and perform graph fusion and spectral clustering to obtain optimal unified graph and clustering results [10, 22] . As described in [5] , MVCMF transforms multi-view data into data matrices and reveals their underlying consensus structure through matrix techniques such as feature decomposition of the data matrices, getting the final result on the consensus matrix subsequently [3, 9, 32] .Nevertheless, the prominent drawback of the above methods is the high time complexity consumption, such as cubic complexity in subspace/graph construction and the spectral clustering process, which hinders their application to large-scale scenarios. To handle this handicap, anchor-based MVC has been proposed to alleviate the high complexity of traditional methods [6, 17, 19] . Specifically, it builds a consensus graph by sampling anchors to capture consistent spatial structure across multiple views. The time complexity of it is reduced to linear concerning sample number per iteration. However, existing anchor-based methods encounter two drawbacks, which are the assumption of the availability of all views and the limited interaction of anchor generation among views, leading to their performance decreasing. In some scenes, views arrive sequentially, and storing them is challenging owing to privacy considerations/the limited space, such as the multi-angle videos allowed to be obtained within a specific time range, thus the existing anchor-based MVC is unsuitable. Additionally, recent works fail to generate anchors with the guidance of other views, causing difficulty in the alignment of the unified anchor graph.To address aforementioned issues, we propose a novel algorithm termed A Lightweight Anchor-Based Incremental Framework to Multi-view Clustering (LAIMVC). It combines incremental learning and the anchor-based method into a unified framework. The illustration of our framework is shown in Fig. 1 . Specifically, LAIMVC effectively harmonizes distinct views by reducing dimensions via Principal Component Analysis (PCA) to facilitate the subsequent anchor graph fusion. We generate the anchor graph of the first view by conducting 𝑘-means on it. Then, the consensus one of the anchor graphs is updated by the newly collected view with a permutation matrix, which not only avoids the repetitive computation of sampling anchors but enhances the interaction of anchor generation among views. Especially, the algorithm not only has linear time complexity for large-scale multi-view data, but it can cope well with view-sequential data costing only linear space complexity. What's more, our proposed method is more capable of anchor alignment because, in incremental MVC, the anchor graphs of previous views could be listed as a reference to guide the generation of anchor graphs of the coming view. Admittedly, a three-step alternative strategy is proposed to solve the optimization problem and the convergence can be guaranteed. Experimental results on seven multiple datasets show that the method can obtain comparable or better performance.The main contributions of our proposed framework can be listed as follows,(1) LAIMVC is a creative attempt to extend anchor-based MVC to an incremental framework. By merely retaining the consensus anchor matrix and graph pertaining to all prior views, it iteratively integrates views individually until no further novel views come, making it applicable to sequential-view data scenarios. (2) Different from existing methods that align anchor graphs trickly, LAIMVC alleviates this problem owing to the guidance of the previous consensus anchor graph. Thus it increases the clustering performance and efficiency of the learned anchor graph structure. (3) An alternate optimization method with proven convergence is developed to address the resulting issue. LAIMVC shows clearly superior clustering performance and significantly less running time/storing space compared with state-of-the-art methods, so it is critical for large-scale and sequential-view datasets, especially with limited computing sources. 
 
 Appendix: https://www.kaggle.com/datasets/syslogg/dermatology-dataset/datahttps://www.robots.ox.ac.uk/Ëoevgg/data/flowers/17/https://relational.fit.cvut.cz/dataset/CORAhttps://cvml.ista.ac.at/AwA2/https://www.kaggle.com/alvations/aloi-datasethttps://www.cs.tau.ac.il/Ëoewolf/ytfaces/https://www.cs.tau.ac.il/Ëoewolf/ytfaces/ 


Decision: This paper works lightweight anchor-based incremental framework for multi-view clustering with one-pass learning. The authors consider the anchor interaction across different views and alignment with graphs. They initialize an anchor graph with 𝑘-means for new views. The consensus anchor graph is updated with a permutation matrix. A three-step iterative learning algorithm is conceived for optimization. Experimental results show the effectiveness of the proposed method.

Four reviewers checked this paper, and one reviewer insisted on his/her opinion with a clear negative recommendation. The reviewer has concerns about the technical parts, like weak comparison and discussion with one-pass learning, anchor learning, anchor graph integration, and other detailed experimental settings. The overall idea of this paper is incremental to this research field. We have to reject this paper and its current form is not ready for ACM MM 2024.

***TPC Addendum ***
The paper has a clear split in opinions. Given the variation, and strong positive ratings, we would like to give the authors a chance to share their perspective at the conference.

Reviews: review: paper_summary: paper_summary: This submission proposed a Lightweight Anchor-Based Incremental framework (LAIMVC) to address several issues in practical multi-view clustering such as the one-pass problem. The authors designed k-means-based initialization and permutation-matrix-based update for the anchor graph. Optimization and algorithm were presented in detail together with extensive experimental results.
strength_weakness: strength_weakness: This manuscript presents an anchor-based approach that deviates from conventional methods by employing anchor graphs to multi-view data in an ingenious way not explored before in this one-pass multi-view problem. The work is grounded in a mathematically elucidated problem formulation. The optimization and algorithm are sound, with detailed derivations and steps. The evaluation is comprehensive, benchmarking the approach against multiple baselines across diverse datasets.
limitations: limitations: 1) Some one-pass multi-view works are missing. The authors are encouraged to clarify where the difference lies between one-pass multi-view clustering and continual multi-view clustering since they are facing the same problem of new views arriving sequentially over time.

[Ref.1] "One-pass multi-view learning." Asian conference on machine learning. PMLR, 2016.

[Ref. 2] "Online multi-view clustering with incomplete views." 2016 IEEE International conference on big data (Big Data). IEEE, 2016.

[Ref. 3] "One-pass incomplete multi-view clustering." Proceedings of the AAAI conference on artificial intelligence. Vol. 33. No. 01. 2019.

[Ref. 4] "Efficient one-pass multi-view subspace clustering with consensus anchors." Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 36. No. 7. 2022.

[Ref. 5] "One-pass View-unaligned Clustering." IEEE Transactions on Multimedia (2024).

2) Some anchor-based multi-view works are missing. The authors are encouraged to clarify any novel contributions to the usage of anchor graphs in this submission. It seems your contribution only lies in applying to a new multi-view sub-scenario.

[Ref. 6] "Anchors bring ease: An embarrassingly simple approach to partial multi-view clustering." Proceedings of the AAAI conference on artificial intelligence. Vol. 33. No. 01. 2019.

[Ref. 7] "Adaptive anchor-based partial multiview clustering." IEEE Access 8 (2020): 175150-175159.

[Ref. 8] "Anchor-based incomplete multi-view spectral clustering." Neurocomputing 514 (2022): 526-538.

[Ref. 9] "Multi-View Fuzzy Clustering Based on Anchor Graph." IEEE Transactions on Fuzzy Systems (2023).

3) In the formulation step, the authors claimed to use PCA to deduct the feature dimensions of all views to a unified dimension because the inconsistent dimensions among views might lead to difficulty in anchor graph integration. The reviewer is confused as anchor graphs are a set of relationships between all samples and anchors. There is no original feature in the anchor graph, so how could it influence the anchor graph integration? Additionally, why do you use PCA rather than other more effective unsupervised algorithms? Also, there are too many missing details, for example, what does $B_t$ stand for? If it is for anchors, then why are there orthogonal constraints on anchor graph $Z_t$ and also $B_t$? 

4) The details of features in each view of used datasets are missing. Additionally, the reviewer is curious if there are any GNN-based features used here that outperform hand-crafted features since the sample-to-sample relations can be incorporated before the anchor graph integration.

5) The proposed method has some randomness such as the initialization of means. Hence, all the results should be in the form of mean+/-standard deviation. It is not convincing based on the current results. Besides, it is recommended to do a significant test.

6) Did the baseline methods declare the parameters on all your datasets used here? Obviously not, but why do you directly use the recommendations on parameters rather than fine-tuning them? The reviewer is not convinced by your results from the baseline methods as they were not achieved with optimal parameters. Furthermore, could you explain how you fine-tuned the parameters in the experiments including using your unsupervised method?

7) Is there any difference if we re-arrange the orders of all views' sequences? Are there any results that reveal any insight?

8) Your convergence analysis and figures only show a local convergence. Is there any theoretical support for a global convergence?
paper_summary: paper_summary: The advantages of this paper lie in its proposal of a lightweight anchor-based incremental framework capable of handling incremental multi-view data. By improving anchor generation and alignment methods and designing an efficient iterative convergence algorithm, it addresses the limitations of existing methods regarding the assumption of availability of all views and insufficient interaction in anchor generation among views. The proposed method demonstrates significant advantages in terms of time and space complexity and exhibits superior performance in extensive experiments.
strength_weakness: strength_weakness: The paper introduces a lightweight anchor-based incremental framework for multi-view clustering (LAIMVC) that effectively handles incremental multi-view data. This method improves anchor generation and alignment methods and designs an efficient iterative convergence algorithm, addressing the limitations of existing methods related to the assumption of all views being available and insufficient interaction in anchor generation among views. Specifically, LAIMVC demonstrates significant advantages in terms of time and space complexity, making it capable of handling sequentially arriving view data under limited storage and privacy constraints. It also shows outstanding performance on large-scale datasets. Extensive experiments have validated its effectiveness and practicality, showcasing excellent clustering performance, running time, and space efficiency.
limitations: limitations: Despite LAIMVC's excellent performance in handling incremental multi-view data, it has some limitations. First, the method relies on the initial selection and generation of anchors, and poor initial anchor selection might affect the final clustering results. Second, in certain complex data scenarios, LAIMVC's performance may be limited, requiring further optimization and parameter adjustment. Additionally, while the method has demonstrated superior performance in experiments, its real-world application needs more validation to ensure robustness and applicability across different datasets and application scenarios. Lastly, LAIMVC primarily addresses scenarios with incremental views, and further research and extension are needed to handle incremental samples or incomplete data effectively. Details as follows:

1、The introduction gives a good overview of multi-view clustering and mentions various methods. However, it lacks a specific problem statement that clearly outlines the unique challenge that this paper addresses.

2、Some technical terms and components of the proposed framework are introduced without sufficient explanation (e.g., the role of the permutation matrix in the algorithm).

3、The methodology section is densely packed with technical descriptions that might be challenging for readers to follow.

4、The experiments section includes extensive results but lacks detailed discussion on why certain datasets were chosen and the implications of the results.

5、The paper presents performance metrics but does not discuss the statistical significance of the results.

6、The conclusion summarizes the work done but does not adequately highlight the main findings or their implications.
paper_summary: paper_summary: This paper presents a novel algorithm, LAIMVC, designed to address the challenges of multi-view clustering in scenarios where data views are sequentially arriving or storage is restricted. LAIMVC is an incremental learning approach that integrates anchor-based methods, using a permutation matrix to enhance anchor alignment and interaction across views. This paper provides not only theoretical analysis but also extensive experiment results of the algorithm's effectiveness.
strength_weakness: strength_weakness: 1. Innovative Motivation: LAIMVC combines incremental learning with anchor-based clustering, offering a new perspective for handling sequential-view data, which is a significant contribution to the relevant field.
2. Comprehensive Experiments: Experimental results show that LAIMVC outperforms the performance of state-of-the-art methods, which demonstrates the effectiveness of the proposed method. 
3. Scalability: LAIMVC can handle sequentially arriving views without storing all views, making it highly scalable and applicable to real-world data streams.
limitations: limitations: 1. Necessary Question: How does LAIMVC algorithm perform better than other incremental multi-view clustering methods in terms of time and space complexity? In which cases are its advantages more obvious?
2. Clarity and Conciseness of Expression: The expression might not be clear or accurate enough.        The last paragraph of the introduction section appears to be somewhat verbose, which should be tightened to enhance. There may be misinterpretation or confusion about accurately conveying complex ideas in English. Please pay attention to polish.
3. Reference Format: There are some questions in the format of references. For example, references 29 and 30 are repeated, and the title format of references 32 and 33 is not standardized. Please pay attention to modification.
paper_summary: paper_summary: Existing multi-view anchor-based clustering methods never consider incremental scenarios, resulting in limited application. The paper extends anchor-based MVC to an incremental framework, while handling the difficulty of the alignment for anchor graphs. Extensive experiments on different datasets demonstrate the effectiveness and efficiency of the proposed method.
strength_weakness: strength_weakness: 1. The paper is well-motivated. The existing anchor-based methods ignore the dynamic learning scenario, it is the first attempt to extend anchor-based MVC to an incremental framework.
2. The experiments demonstrate its effectiveness well.
3. The authors provide the code and enhance its reproducibility.
4. The complexity analysis of the method is given, and the authors compare it with existing methods in appendix to show its superiority.
limitations: limitations: 1. In the algorithm, the reason for choosing PCA as the preprocessing method could be explained. Also, other dimension-conduction methods should be compared to demonstrate its superiority.
2. The view order might have a significant effect on the performance. The authors should investigate this in experiments. 
3. The novelty of Eq.(6) should be claimed. It seems that the equation is widespread in the literature.
4. Pay more attention to the layout details. For example, both Figure 4 and Figure 5 are three parallel discount graphs, taking care to keep their figure and font size consistent.
5. There is no notation table in the main body, the authors could provide it for readability.
6. In Table 2, the bold fonts should be clarified.