Consensus Matrix Research Articles

Multi-kernel clustering with tensor fusion on Grassmann manifold for high-dimensional genomic data

The high dimensionality and noise challenges in genomic data make it difficult for traditional clustering methods. Existing multi-kernel clustering methods aim to improve the quality of the affinity matrix by learning a set of base kernels, thereby enhancing clustering performance. However, directly learning from the original base kernels presents challenges in handling errors and redundancies when dealing with high-dimensional data, and there is still a lack of feasible multi-kernel fusion strategies. To address these issues, we propose a Multi-Kernel Clustering method with Tensor fusion on Grassmann manifolds, called MKCTM. Specifically, we maximize the clustering consensus among base kernels by imposing tensor low-rank constraints to eliminate noise and redundancy. Unlike traditional kernel fusion approaches, our method fuses learned base kernels on the Grassmann manifold, resulting in a final consensus matrix for clustering. We integrate tensor learning and fusion processes into a unified optimization model and propose an effective iterative optimization algorithm for solving it. Experimental results on ten datasets, comparing against 12 popular baseline clustering methods, confirm the superiority of our approach. Our code is available at https://github.com/foureverfei/MKCTM.git.

Selective multiple kernel fuzzy clustering with locality preserved ensemble

Multiple kernel fuzzy clustering (MKFC) has demonstrated promising performance in capturing the non-linear relationships within data. However, its effectiveness relies heavily on the appropriate selection of the fuzzification coefficient and kernel functions. To address this challenge, this paper proposes a novel clustering ensemble approach for improving the robustness and accuracy of the MKFC algorithm. The proposed method employs a multi-objective evolutionary optimization approach to heuristically select the optimal fuzzification and kernel coefficients. By employing the selected coefficients, the MKFC algorithm generates a diverse set of accurate candidate clustering results. Subsequently, a locality preserved ensemble mechanism is introduced to derive the final partition matrix, ensuring that all candidate clusterings within the Pareto non-dominated set contribute to the final consensus matrix. Moreover, this mechanism incorporates the knowledge about the locality of the dataset via a graph regularization term, thereby further enhancing the clustering performance. Comprehensive experiments conducted on widely adopted benchmark datasets demonstrate the superiority of the proposed method over the state-of-the-art approaches.

The identification of heterogeneous reactive oxygen subtypes in esophageal squamous cell carcinoma to aid patient prognosis and immunotherapy

IntroductionEsophageal cancer is increasingly recognized as a significant global malignancy. The main pathological subtype of this cancer is esophageal squamous cell carcinoma (ESCC), which displays a higher degree of malignancy and a poorer prognosis. Reactive oxygen species (ROS) play a critical role in modulating the immune response to tumors, and understanding the regulation of ROS in ESCC could lead to novel and improved therapeutic strategies for ESCC patients. MethodsA consensus matrix derived from genes involved in the ROS pathway revealed two subtypes of ROS. These subtypes were categorized as ROS-active or ROS-suppressive based on their level of ROS activity. The heterogeneity among the different ROS subtypes was then explored from various perspectives, including gene function, immune response, genomic stability, and immunotherapy. In order to assess the prognosis and the potential benefits of immunotherapy, a ROS activity score (RAS) was developed using the identified ROS subtypes. In vitro experiments were performed to confirm the impact of core RAS genes on the proliferative activity of esophageal cancer cell lines. ResultsTwo distinctive subtypes of ROS were identified. The first subtype, referred to as ROS-active, exhibited elevated ROS activity, enhanced involvement in cancer-associated immune pathways, and increased infiltration of effector immune cells. The second subtype, named ROS-suppressive, demonstrated weaker ROS activity but displayed more pronounced dysregulation in the cell cycle and a denser extracellular matrix, indicating malignant characteristics. Genomic stability, particularly in terms of copy number variation (CNV) events, differed between the two ROS subtypes. By developing a RAS model, reliable risk assessment for overall survival (OS) in patients with ESCC was achieved, and the model demonstrated strong predictive capabilities in real-world immunotherapy cohorts. Moreover, the core gene LDLRAD1 within the RAS model was found to enhance proliferative activity in esophageal cancer cell lines. ConclusionBased on the ROS pathway, we successfully identified two distinct subtypes in ESCC: the ROS-active subtype and the ROS-suppressive subtype. These subtypes were utilized to evaluate prognosis and the sensitivity to immunotherapy.

Consensus and discriminative non-negative matrix factorization for multi-view unsupervised feature selection

Multi-view unsupervised feature selection (MUFS) has been proven to be an efficient dimensionality reduction technique for multi-view data. Existing methods have two main challenges: (1) The consistency information from different views is not fully exploited. (2) The cluster structure of the original data is not well utilized. To settle these problems, we propose a novel consensus and discriminative non-negative matrix factorization (CDNMF) for multi-view unsupervised feature selection. Specifically, CDNMF obtains a robust low-dimensional latent space by NMF with an ℓ2,1-norm constraint. To select more discriminative features, we further impose a sparsity constraint on the learned latent features. Moreover, CDNMF performs k-means clustering on all views separately to obtain the pseudo-labels of each view, which are used to guide the learning of consensus information among views. To solve our model, we develop an efficient iterative optimization algorithm. Extensive experimental results on ten benchmark datasets demonstrate that the proposed significantly outperforms several existing feature selection methods in clustering tasks.

Optimizing Uterine Synchronization Analysis in Pregnancy and Labor Through Window Selection and Node Optimization

1) Introduction: Preterm labor (PL) has globally become the leading cause of death in children under the age of 5 years. One of the most significant keys to preventing preterm labor is its early detection. 2) Objectives: The primary objectives of this study are to address the problem of PL by providing a new approach by analyzing the electrohysterographic (EHG) signals, which are recorded on the mother's abdomen during labor and pregnancy. 3) Methods: The EHG signal reflects the electrical activity that induces the mechanical contraction of the myometrium. Because EHGs are known to be non-stationary signals, and because we anticipate connectivity to alter during contraction (due to electrical diffusion and the mechanotransduction process), we applied the windowing approach on real signals to identify the best windows and the best nodes with the most significant data to be used for classification. The suggested pipeline includes: i) dividing the 16 EHG signals that are recorded from the abdomen of pregnant women in N windows; ii) apply the connectivity matrices on each window; iii) apply the Graph theory-based measures on the connectivity matrices on each window; iv) apply the consensus Matrix on each window in order to retrieve the best windows and the best nodes. Following that, several neural network and machine learning methods are applied to the best windows and best nodes to categorize pregnancy and labor contractions, based on the different input parameters (connectivity method alone, connectivity method plus graph parameters, best nodes, all nodes, best windows, all windows). 4) Results: Results showed that the best nodes are nodes 8, 9, 10, 11, and 12; while the best windows are 2, 4, and 5. The classification results obtained by using only these best nodes are better than when using the whole nodes. The results are always better when using the full burst, whatever the chosen nodes. 5) Conclusion: The windowing approach proved to be an innovative technique that can improve the differentiation between labor and pregnancy EHG signals.

A novel game-based belief rule base

Establishing an initial belief rule base (BRB) expert system typically relies on expert knowledge. However, the heterogeneity in knowledge arising from variations in expert cognition directly impacts the accuracy and robustness of BRB. Furthermore, the existing research lacks a discussion on building the initial BRB under multi-expert knowledge. In response to this challenge, a novel game-based belief rule base (GBRB) is proposed in this paper. First, a consensus matrix is introduced to formalize the interaction among expert knowledge, which is the foundation for constructing a multi-expert evolutionary game. Subsequently, the replicator equation for population dynamics is employed to simulate the dynamic process of the multi-expert evolutionary game. Finally, optimal expert knowledge, which refers to referential values and belief degrees, is determined based on the evolution results to participate in establishing GBRB. Case studies are conducted to illustrate the construction process and effectiveness of the GBRB. The experimental results are compared with machine learning-related methodologies. The comparative results demonstrate the good performance of GBRB in modeling effectiveness and prediction accuracy.

ScEWE: high-order element-wise weighted ensemble clustering for heterogeneity analysis of single-cell RNA-sequencing data.

With the emergence of large amount of single-cell RNA sequencing (scRNA-seq) data, the exploration of computational methods has become critical in revealing biological mechanisms. Clustering is a representative for deciphering cellular heterogeneity embedded in scRNA-seq data. However, due to the diversity of datasets, none of the existing single-cell clustering methods shows overwhelming performance on all datasets. Weighted ensemble methods are proposed to integrate multiple results to improve heterogeneity analysis performance. These methods are usually weighted by considering the reliability of the base clustering results, ignoring the performance difference of the same base clustering on different cells. In this paper, we propose a high-order element-wise weighting strategy based self-representative ensemble learning framework: scEWE. By assigning different base clustering weights to individual cells, we construct and optimize the consensus matrix in a careful and exquisite way. In addition, we extracted the high-order information between cells, which enhanced the ability to represent the similarity relationship between cells. scEWE is experimentally shown to significantly outperform the state-of-the-art methods, which strongly demonstrates the effectiveness of the method and supports the potential applications in complex single-cell data analytical problems.

Community detection based on nonnegative matrix tri-factorization for multiplex social networks

Abstract Nowadays, community detection is one of the important fields for understanding network topology and has many applications in information diffusion, interaction mining and migration behaviour analysis. Therefore, community detection in social networks can help to understand user behaviour and network characteristics. There are many community detection methods, which are often designed for single-layer social networks. However, real-world networks use several types of relationships to establish connections between users, each of which has different characteristics. Hence, real-world networks can be modelled as multiplex networks. In general, multiplex networks are an example of multilayer networks in which the relationships between users in different networks can be considered simultaneously. In these networks, each layer represents the connections between users in a social network. Meanwhile, communities in multiplex networks are identified based on the structure and connections between overlapping users in different layers of the network. In this article, the nonnegative matrix tri-factorization (NMTF) strategy is used to model multiplex social networks, and a solution for community detection is developed based on it. According to this strategy, a common consensus matrix and then an alignment matrix are extracted based on similarity metrics and network structure. The use of these matrices as a flexible modelling framework enables the detection of coherent community between overlapping users in multiplex social networks. We evaluate the proposed NMTF method through various metrics on a multiplex social network. The results of this evaluation show the better performance of NMTF in terms of community quality compared to equivalent methods.

ScEM: A New Ensemble Framework for Predicting Cell Type Composition Based on scRNA-Seq Data.

With the advent of single-cell RNA sequencing (scRNA-seq) technology, many scRNA-seq data have become available, providing an unprecedented opportunity to explore cellular composition and heterogeneity. Recently, many computational algorithms for predicting cell type composition have been developed, and these methods are typically evaluated on different datasets and performance metrics using diverse techniques. Consequently, the lack of comprehensive and standardized comparative analysis makes it difficult to gain a clear understanding of the strengths and weaknesses of these methods. To address this gap, we reviewed 20 cutting-edge unsupervised cell type identification methods and evaluated these methods comprehensively using 24 real scRNA-seq datasets of varying scales. In addition, we proposed a new ensemble cell-type identification method, named scEM, which learns the consensus similarity matrix by applying the entropy weight method to the four representative methods are selected. The Louvain algorithm is adopted to obtain the final classification of individual cells based on the consensus matrix. Extensive evaluation and comparison with 11 other similarity-based methods under real scRNA-seq datasets demonstrate that the newly developed ensemble algorithm scEM is effective in predicting cellular type composition.

Fuzzy similarity based hierarchical clustering for communities in twitter social networks

The complexity of the Internet has significantly increased along with its expansions. In particular, social networking has resulted in user clusters pertaining to many communities at different levels. Studies of online communities are a growing area of research user preferences can be categorized including dangerous groups. This work uses pre-processing techniques including stemming, stop words removals, and tokenizations of data using unigram, bigram, and 1–3 g representations. TF-IDFs (Term Frequency-Inverse Document Frequencies) and Word Embeds are used in feature Extractions. Perspectives generate hierarchical data structures which are then combined using consensus matrices followed by computations of dissimilarities between observed sets. This work employs FS-HC (fuzzy similarity based Hierarchical Clustering) to generate dendrograms for views. Finally, consensus matrices are generated by integrating several hierarchical agglomerations using transitive consensus matrix generations. They contain representative data of generated dendrograms. Performance metrics including precisions, recalls, f-measures, accuracies, clustering coefficients, conductance, and contractions are used to evaluate outcomes of benchmarked clustering algorithms. The proposed approach attains higher accuracy value of about 92 % when compared to other existing algorithms. The required data for community discoveries in social media were gathered from Twitter.

Ensemble Prototype Network For Weakly Supervised Temporal Action Localization.

Weakly supervised temporal action localization (TAL) aims to localize the action instances in untrimmed videos using only video-level action labels. Without snippet-level labels, this task should be hard to distinguish all snippets with accurate action/background categories. The main difficulties are the large variations brought by the unconstraint background snippets and multiple subactions in action snippets. The existing prototype model focuses on describing snippets by covering them with clusters (defined as prototypes). In this work, we argue that the clustered prototype covering snippets with simple variations still suffers from the misclassification of the snippets with large variations. We propose an ensemble prototype network (EPNet), which ensembles prototypes learned with consensus-aware clustering. The network stacks a consensus prototype learning (CPL) module and an ensemble snippet weight learning (ESWL) module as one stage and extends one stage to multiple stages in an ensemble learning way. The CPL module learns the consensus matrix by estimating the similarity of clustering labels between two successive clustering generations. The consensus matrix optimizes the clustering to learn consensus prototypes, which can predict the snippets with consensus labels. The ESWL module estimates the weights of the misclassified snippets using the snippet-level loss. The weights update the posterior probabilities of the snippets in the clustering to learn prototypes in the next stage. We use multiple stages to learn multiple prototypes, which can cover the snippets with large variations for accurate snippet classification. Extensive experiments show that our method achieves the state-of-the-art weakly supervised TAL methods on two benchmark datasets, that is, THUMOS'14, ActivityNet v1.2, and ActivityNet v1.3 datasets.

HCTMFS: A multi-modal feature selection framework with higher-order correlated topological manifold for ESRDaMCI

Background and ObjectiveThe diagnosis of end-stage renal disease associated with mild cognitive impairment (ESRDaMCI) mainly relies on objective cognitive assessment, clinical observation, and neuro-psychological evaluation, while only adopting clinical tools often limits the diagnosis accuracy. MethodsWe proposed a multi-modal feature selection framework with higher-order correlated topological manifold (HCTMFS) to classify ESRDaMCI patients and identify the discriminative brain regions. It constructed brain structural and functional networks with diffuse kurtosis imaging (DKI) and functional magnetic resonance imaging (fMRI) data, and extracted node efficiency and clustering coefficient from the brain networks to construct multi-modal feature matrices. The topological relationship matrices were constructed to measure the lower-order topological correlation between features. Then the consensus matrices were learned to approximate the topological relationship matrices at different confidence levels and eliminate the noise influence of individual matrices. ResultsThe higher-order topological correlation between features was explored by the Laplacian matrix of the hypergraph, which was calculated through the consensus matrix. The new framework achieved an accuracy rate of 93.56 % for classifying ESRDaMCI patients, and outperformed the existing state-of-the-art methods in terms of sensitivity, specificity, and area under the curve. ConclusionsThis study contributes to effectively reflect the functional neural degradation of ESRDaMCI and provide a reference for the diagnosis of ESRDaMCI by selecting discriminative brain regions.

DAC-HPP: deep attributed clustering with high-order proximity preserve

Attributed graph clustering, the task of grouping nodes into communities using both graph structure and node attributes, is a fundamental problem in graph analysis. Recent approaches have utilized deep learning for node embedding followed by conventional clustering methods. However, these methods often suffer from the limitations of relying on the original network structure, which may be inadequate for clustering due to sparsity and noise, and using separate approaches that yield suboptimal embeddings for clustering. To address these limitations, we propose a novel method called Deep Attributed Clustering with High-order Proximity Preserve (DAC-HPP) for attributed graph clustering. DAC-HPP leverages an end-to-end deep clustering framework that integrates high-order proximities and fosters structural cohesiveness and attribute homogeneity. We introduce a modified Random Walk with Restart that captures k-order structural and attribute information, enabling the modelling of interactions between network structure and high-order proximities. A consensus matrix representation is constructed by combining diverse proximity measures, and a deep joint clustering approach is employed to leverage the complementary strengths of embedding and clustering. In summary, DAC-HPP offers a unique solution for attributed graph clustering by incorporating high-order proximities and employing an end-to-end deep clustering framework. Extensive experiments demonstrate its effectiveness, showcasing its superiority over existing methods. Evaluation on synthetic and real networks demonstrates that DAC-HPP outperforms seven state-of-the-art approaches, confirming its potential for advancing attributed graph clustering research.

Latent information-guided one-step multi-view fuzzy clustering based on cross-view anchor graph

Although graph-inspired clustering methods have achieved impressive success in the area of multi-view data analysis, current methods still face several challenges. First, classical graph construction approaches are computationally expensive in terms of both time and space for large-scale data. Second, fusing graphs from different views remains a challenge. Third, most existing methods require additional post-processing steps to generate the label assignment matrix. To address the above challenges, this paper proposes a novel multi-view clustering algorithm, called latent information-guided one-step multi-view fuzzy clustering based on cross-view anchor graph. Specifically, we introduce an efficient cross-view anchor graph learning approach to construct the similarity matrix of multi-view data and extract latent information from the graph, which reduces the computational complexity of graph learning and inspires the optimization of the consensus membership matrix. Following that, our one-step multi-view fuzzy clustering algorithm can directly generate the final clustering result in an effective and straightforward manner. Furthermore, during the optimization process, the proposed method balances consensus matrix learning and view-specified membership exploration via a self-tuned weighting mechanism. The comprehensive experimental analysis demonstrates the superiority of our approach over the state-of-the-art approaches.

Identification of distinct clinical phenotypes of cardiogenic shock using machine learning consensus clustering approach

BackgroundCardiogenic shock (CS) is a complex state with many underlying causes and associated outcomes. It is still difficult to differentiate between various CS phenotypes. We investigated if the CS phenotypes with distinctive clinical profiles and prognoses might be found using the machine learning (ML) consensus clustering approach.MethodsThe current study included patients who were diagnosed with CS at the time of admission from the electronic ICU (eICU) Collaborative Research Database. Among 21,925 patients with CS, an unsupervised ML consensus clustering analysis was conducted. The optimal number of clusters was identified by means of the consensus matrix (CM) heat map, cumulative distribution function (CDF), cluster-consensus plots, and the proportion of ambiguously clustered pairs (PAC) analysis. We calculated the standardized mean difference (SMD) of each variable and used the cutoff of ± 0.3 to identify each cluster’s key features. We examined the relationship between the phenotypes and several clinical endpoints utilizing logistic regression (LR) analysis.ResultsThe consensus cluster analysis identified two clusters (Cluster 1: n = 9,848; Cluster 2: n = 12,077). The key features of patients in Cluster 1, compared with Cluster 2, included: lower blood pressure, lower eGFR (estimated glomerular filtration rate), higher BUN (blood urea nitrogen), higher creatinine, lower albumin, higher potassium, lower bicarbonate, lower red blood cell (RBC), higher red blood cell distribution width (RDW), higher SOFA score, higher APS III score, and higher APACHE IV score on admission. The results of LR analysis showed that the Cluster 2 was associated with lower in-hospital mortality (odds ratio [OR]: 0.374; 95% confidence interval [CI]: 0.347–0.402; P < 0.001), ICU mortality (OR: 0.349; 95% CI: 0.318–0.382; P < 0.001), and the incidence of acute kidney injury (AKI) after admission (OR: 0.478; 95% CI: 0.452–0.505; P < 0.001).ConclusionsML consensus clustering analysis synthesized the pattern of clinical and laboratory data to reveal distinct CS phenotypes with different clinical outcomes.

Incomplete Multiview Clustering Using Normalizing Alignment Strategy With Graph Regularization

Matrix factorization has demonstrated promising performance in the incomplete multiview clustering (IMC) tasks. However, many algorithms require feature normalization operations to ensure the stability of model results, so either the convergence is unstable, or the objective function cannot fit the data well. Addressing these issues, we propose a novel IMC algorithm using a normalizing alignment strategy (IMCNAS) based on nonnegative matrix factorization. Specifically, the columns of the basis matrices are constrained into unit vector space, which integrates the feature normalization and the optimizing process, and makes the model converge fast and stable. On the other hand, this enables the model to fit the data better and produce more reasonable factorization results. Further, we develop a novel pairwise co-regularization to align incomplete multiple views more directly, without introducing a common consensus matrix like traditional centroid-based co-regularization. Graph regularization is also incorporated in the proposed model to utilize the geometrical information of data. We implement IMCNAS with a centroid-based regularization and a pairwise co-regularization respectively, and leads to two variants, i.e., IMCNAS-1 and IMCNAS-2. Both variants are optimized with multiplicative updating rules. Extensive experiments conducted on various real-world datasets comparing several state-of-the-art IMC methods verified the effectiveness of the proposed methods. The source code is available at: <uri>https://github.com/GuoshengCui/IMCNAS</uri>.

A multi-view clustering algorithm based on deep semi-NMF

Multi-view clustering (MVC) aims to fuse the information among multiple views to achieve effective clustering. Many MVC algorithms based on semi-nonnegative matrix factorization (SNMF) typically have two issues: (1) their optimization schemes are not flexible enough; and (2) the variables are updated only rely on the data but not guided by learning rate. These problems can result in very poor clusters generated. In this paper, we present a multi-view clustering algorithm based on deep SNMF (MCDS) to resolve these issues. Specifically, we first design two types of activation functions to restrict the value domain of the element in the low-dimensional matrix to eliminate the constraint. Then, the SGD algorithm is used to implement element update guided by the learning rate. After obtaining the corresponding weight matrix and bias matrix, we combine them with the activation functions to construct a deep SNMF (DSNMF) network. This network is to update the element in the corresponding low-dimensional matrix for each view and obtain the consensus matrix. To validate the proposed algorithm, numerous experiments are performed on six multi-view datasets including both normal and large-scale datasets. The results demonstrate that MCDS can achieve excellent clustering results and outperform other competitive methods.

Decision of the Optimal Rank of a Nonnegative Matrix Factorization Model for Gene Expression Data Sets Utilizing the Unit Invariant Knee Method: Development and Evaluation of the Elbow Method for Rank Selection

Background There is a great need to develop a computational approach to analyze and exploit the information contained in gene expression data. The recent utilization of nonnegative matrix factorization (NMF) in computational biology has demonstrated the capability to derive essential details from a high amount of data in particular gene expression microarrays. A common problem in NMF is finding the proper number rank (r) of factors of the degraded demonstration, but no agreement exists on which technique is most appropriate to utilize for this purpose. Thus, various techniques have been suggested to select the optimal value of rank factorization (r). Objective In this work, a new metric for rank selection is proposed based on the elbow method, which was methodically compared against the cophenetic metric. Methods To decide the optimum number rank (r), this study focused on the unit invariant knee (UIK) method of the NMF on gene expression data sets. Since the UIK method requires an extremum distance estimator that is eventually employed for inflection and identification of a knee point, the proposed method finds the first inflection point of the curvature of the residual sum of squares of the proposed algorithms using the UIK method on gene expression data sets as a target matrix. Results Computation was conducted for the UIK task using gene expression data of acute lymphoblastic leukemia and acute myeloid leukemia samples. Consequently, the distinct results of NMF were subjected to comparison on different algorithms. The proposed UIK method is easy to perform, fast, free of a priori rank value input, and does not require initial parameters that significantly influence the model’s functionality. Conclusions This study demonstrates that the elbow method provides a credible prediction for both gene expression data and for precisely estimating simulated mutational processes data with known dimensions. The proposed UIK method is faster than conventional methods, including metrics utilizing the consensus matrix as a criterion for rank selection, while achieving significantly better computational efficiency without visual inspection on the curvatives. Finally, the suggested rank tuning method based on the elbow method for gene expression data is arguably theoretically superior to the cophenetic measure.

Reducing incompatibility in a local AHP-group decision making context

In the context of local analytic hierarchy process-group decision making (AHP-GDM), this paper presents a theoretical framework and a semi-automatic procedure for reducing incompatibility between the actors involved in the decision making process and the collective position. The row geometric mean is employed as the prioritisation procedure and the geometric compatibility index (textrm{GCOMPI}) as the incompatibility measure; individual pairwise comparison matrices are considered as the input of the reduction process, whilst the collective vector is the output. The reduction is attained by slightly modifying, in relative terms, the judgements of the collective pairwise comparison matrix, irrespective of the method used to obtain it, that further improve the textrm{GCOMPI}. The resulting judgements of the collective matrix and the associated collective priorities are close to the initial collective values. The procedure does not modify the judgements of the initial individual matrices and this simplifies the process of reaching consensus. A simulation analysis is utilised to study the performance of the algorithm along with an illustrative numerical example. The analysis proves that the proposed algorithm is easy to implement and efficient, it provides mathematically closed results and significantly reduces the textrm{GCOMPI} associated with the precise consistency consensus matrix which is one of the AHP-GDM tools. The framework allows the procedure to be adapted to specific interests.

Assessing long-term rainfall trends and changes in a tropical watershed Brantas, Indonesia: an approach for quantifying the agreement among satellite-based rainfall data, ground rainfall data, and small-scale farmers questionnaires.

The agreement between meteorological data and societal perception is essential in supporting a robust policy making and its implementation. In humid tropic watersheds like Brantas, such consensus is important for water resources management and policies. This study exemplifies an effort to understand the long-term rainfall characteristics within the watershed and to build a common link among the differing data sources: CHIRPS rainfall satellite data, rain gauge data, and farmers perceptions. Six rainfall characteristics were derived using statistical measures from the scientific data and then were translated to a series of structured questionnaires given to small-scale farmers. A consensus matrix was built to examine the level of agreement among three data sources, supporting the spatial pattern of the meteorological data and farmers perception. Two rainfall attributes were classified with high agreement, four with moderate and one with low agreement. The agreements and discrepancies of rainfall characteristics were found in the study area. The discrepancies originated from the accuracy in translating scientific measurements to practical meanings for farmers, complexity of the farming system, the nature of phenomena in questions, and farmers' ability to record long-term climatic events. This study shows an implication that a combined approach to link scientific data and societal data is needed to support powerful climate policy making.