Hidden degenerations in industrial time series often precede observable failures, they remain undetected by standard monitoring systems until anomalies become apparent. This gap between microscopic degradation and macroscopic observation renders conventional predictors inherently reactive, as they rely on correlations in sensor data rather than uncovering the underlying, physics‑consistent degradation states. Crucially, the microscopic mechanisms governing system evolution depend on macroscopic state variables—whose measurements are expectations over microscopic probability distributions—so purely data‑driven “top‑down” or purely physics‑guided “bottom‑up” approaches cannot forecast degeneration‑entangled industrial faults. To address these challenges, we propose a Physics-Guided Bidirectional Inference Framework that represents hidden microscopic states from macroscopic measurements. Our approach uniquely combines: (1) bottom-up physics-based simulation using Continuum Damage Mechanics to model micro-scale damage evolution under environmental stressors, and (2) top-down probabilistic inference via maximum entropy formalism to estimate latent microstate distributions from sparse sensor data. This bidirectional mechanism enables early failure prediction by bridging observable measurements with unobservable degeneration. Validation on real-world railway infrastruc datasets demonstrates significant improvements in early fault prediction compared to state-of-the-art baselines. Our method establishes a new paradigm for safety-critical industrial applications requiring reliable prediction of hidden degeneration processes.

Large language model (LLM) services increasingly rely on distributed inference across multiple GPU servers to sustain concurrent requests under limited compute, memory, and bandwidth resources. In such settings, a partitioned LLM can be represented as an inference chain (InFC), where the deployment decision determines both the sustainable concurrency ceiling (SCC) on the revenue side and the memory and communication overhead on the cost side. This paper studies the profit-aware inference chain deployment (InFCD) problem in heterogeneous data center networks. We show that increasing the InFC length does not monotonically improve profit: finer partitioning can relieve per-GPU resource bottlenecks and improve SCC, but may also increase deployment spread, inference path length, and internal traffic. To capture this tradeoff, we formulate profit-aware InFCD by jointly modeling static-weight vRAM occupation, per-user KV-cache occupation, user-side traffic, internal boundary traffic, and resource-coupled SCC, and prove its NP-hardness. We then propose the Maximum Sub-module Deployment Gain (MSDG) score and design an MSDG-based greedy algorithm. Theoretical analysis characterizes its online complexity and establishes a conditional positive-profit preservation property. Simulations show that MSDG improves total profit over SCC-oriented, cost-oriented, and local-profit-oriented baselines, characterize empirical optimality gaps and SLO sensitivity.

Pairwise learning underpins implicit collaborative filtering, yet its effectiveness is often hindered by sparse supervision, noisy interactions, and popularity-driven exposure bias. In this paper, we propose Variational Bayesian Personalized Ranking (VarBPR), a tractable variational framework for implicit-feedback pairwise learning that offers principled exposure controllability and theoretical interpretability. VarBPR reformulates pairwise learning as variational inference over discrete latent indexing variables, explicitly modeling noise and indexing uncertainty, and divides training into two stages: variational inference, which solve variational posteriors, and variational learning, which updates model parameters based on these posteriors. In the variational inference stage, we develop a variational formulation that integrates preference alignment, denoising, and popularity debiasing under a unified ELBO/regularization objective, deriving closed-form posteriors with clear control semantics: the prior encodes a target exposure pattern, while temperature/regularization strength controls posterior-prior adherence. As a result, exposure controllability becomes an endogenous and interpretable outcome of variational inference. In the variational learning stage, we propose a posterior-compression objective that reduces the ideal ELBO's computational complexity from polynomial to linear, with the approximation justified by an explicit Jensen-gap upper bound. Theoretically, we provide interpretable generalization guarantees by identifying a structural error component and revealing the opportunity cost of prioritizing certain exposure patterns (e.g., long-tail), offering a concrete analytical lens for designing controllable recommender systems. Empirically, We validate VarBPR across popular backbones; it demonstrates consistent gains in ranking accuracy, enables controlled long-tail exposure, and preserves the linear-time complexity of BPR.

Time series forecasting has become a critical task in data engineering, with the volume of time series data projected to reach 180 ZB by 2025. While traditional forecasting models are typically constrained to single domains, missing opportunities for transferring temporal patterns across different domains. Through analysis, we observe that time series from different domains, despite their distinct statistical characteristics, can be fundamentally understood through temporal dependency patterns, which manifest as either long-term dependencies ( like trends and cycles) or short-term dependencies ( like fluctuations and abrupt changes). This observation motivates us to rethink cross-domain modeling from the dependency preferences perspective. We propose LSTPO, a novel framework that captures cross-domain commonalities through temporal dependency preferences and leverages a meta-learning-based approach to prevent cross-domain training forgetting. LSTPO dynamically models changes in preference over time and swiftly adapts to preference variations across different domains, enabling robust cross-domain forecasting. Through extensive experimental evaluations, we have shown that LSTPO substantially outperforms state-of-the-art forecasting methods while enhancing model transferability under few-shot learning conditions. The source code will be made publicly available upon acceptance.

Text-Attributed Heterogeneous Graphs (TAHGs) integrate topological relationships with rich textual node attributes, offering expressive representations for complex multi-faceted data. While recent methods jointly leverage textual and structural information, they still face two critical limitations: (i) existing approaches are constrained to neighborhood modeling, failing to capture semantic dependencies in higher-order topologies; (ii) current techniques exhibit inadequate unified alignment strategies, limiting dynamic interaction between cross modalities. To address these challenges, we propose SATH, a self-supervised information aggregation model for TAHGs, designed to effectively leverage textual and structural information within TAHGs. SATH aggregates higher-order neighbor textual attributes through comparative learning, and dynamically aligns these attributes to higher-order topologies through a unified strategy. This approach integrates both types of information effectively, enhancing the expressiveness and discriminative capability of the learned node representations in downstream tasks. Extensive experiments on real-world datasets demonstrate that SATH significantly outperforms baseline models while eliminating the need for manual meta-path design or text feature concatenation. It also improves efficiency and scalability on large-scale TAHGs, achieving superior representation quality in TAHG-based tasks.

Out-of-distribution (OOD) detection in 3D point cloud data remains a challenge, particularly in applications where safe and robust perception is critical. While existing OOD detection methods have shown progress for 2D image data, extending these to 3D environments involves unique obstacles. This paper introduces a training-free framework that leverages Vision-Language Models (VLMs) for effective OOD detection in 3D point clouds. By constructing a graph based on class prototypes and testing data, we exploit the data manifold structure to enhancing the effectiveness of VLMs for 3D OOD detection. We propose a novel Graph Score Propagation (GSP) method that incorporates prompt clustering and self-training negative prompting to improve OOD scoring with VLM. Our method is also adaptable to few-shot scenarios, providing options for practical applications. We demonstrate that GSP consistently outperforms state-of-the-art methods across synthetic and real-world datasets 3D point cloud OOD detection.

Multivariate Time Series Forecasting (MTSF) has long been a key research focus. Traditionally, these studies assume a fixed number of variables, but in real-world applications, Cyber-Physical Systems often expand as new sensors are deployed, increasing variables in MTSF. In light of this, we introduce a novel task, Expanding-variate Time Series Forecasting (EVTSF). This task presents unique challenges, specifically (1) handling inconsistent data shapes caused by adding new variables, and (2) addressing imbalanced spatio-temporal learning, where expanding variables have limited observed data due to the necessity for timely operation. To address these challenges, we propose STEV, a flexible spatio-temporal forecasting framework. STEV includes a new Flat Scheme to tackle the inconsistent data shape issue, which extends the graph-based spatio-temporal modeling architecture into 1D space by flattening the 2D samples along the variable dimension, making the model variable-scale-agnostic while still preserving dynamic spatial correlations through a holistic graph. Additionally, we introduce a novel Spatio-temporal Focal Learning strategy that incorporates a negative filter to resolve potential conflicts between contrastive learning and graph representation, and a focal contrastive loss as its core to guide the framework to focus on optimizing the expanding variables. To evaluate the effectiveness of STEV, we benchmark EVTSF performance on three real-world datasets from various domains and compare it against three potential solutions employing state-of-the-art (SOTA) MTSF models tailored for EVSTF. Experimental results show that STEV significantly outperforms its competitors, especially in handling expanding variables. Notably, STEV, with only 5% of observations during the expanding period, is on par with SOTA MTSF models trained with complete data. Further exploration of various expanding scenarios underscores the generalizability of STEV in real-world applications.

Traffic flow forecasting task plays an essential role in intelligent transportation systems. Accurately capturing the intricate spatio-temporal dependencies in traffic network signals is the core of precise prediction. Recently, a paradigm that models spatio-temporal dependencies through graph neural networks and time series models has become one of the most promising methods to solve this problem. However, existing methods still have limitations due to ineffectively modeling dynamic spatial dependencies and high time and space complexity. To address these issues, we propose a simplifying and powerful general spatio-temporal traffic flow forecasting model called LightST. Specifically, LightST first embeds temporal covariates and spatial position information to enhance the spatio-temporal modeling capabilities. Then, stacked temporal linear layers are introduced to capture temporal dependencies efficiently. Finally,we propose a concise adaptive spatio-temporal embedding graph convolution method to extract implicit spatial dependencies over time via dynamic graph convolution with adaptive spatio-temporal embedding graph generation. Extensive experiment results on four public traffic flow datasets demonstrate the superiority of our LightST concerning computational efficiency and prediction performance.

The rapid expansion of Low Earth Orbit (LEO) satellite constellations presents immense potential for in-orbit services. However, the large-scale and dynamic nature of LEO constellations creates unstable communication environments, where traditional methods struggle to ensure the efficiency and stability of onboard inference services. This highlights the need for an advanced knowledge service framework capable of both inference and root cause analysis of service disruptions. To address this, we propose a novel knowledge service framework that integrates data-driven and knowledge-driven models through satellite-ground collaboration. The framework leverages lightweight onboard models for real-time data processing and ground-based knowledge graphs for advanced inference and cause analysis. To further enhance stability within complex interconnected onboard systems, we propose a prediction-based algorithm for LEO satellite networks that uses joint spatio-temporal modeling to achieve accurate link prediction. Additionally, we formulate an optimization problem aimed at minimizing path distance variance and maximizing path stability across LEO topologies, and we propose a heuristic path selection strategy to ensure efficient inter-satellite routing. Extensive in-orbit deployments and simulation experiments demonstrate the feasibility and effectiveness of the proposed framework. Satellite-ground verification on the BUPT-1 satellite shows its ability to provide real-time services, while inter-satellite simulations using real constellation data indicate significant improvements in response latency and path stability. Compared with baseline methods, our proposed method significantly reduces path jitter by up to 62.6% and improves path availability by up to 17.3% across various LEO constellations.

Spatio-temporal forecasting of future values of spatially correlated time series is important across many cyber-physical systems (CPS). Recent studies offer evidence that the use of graph neural networks to capture latent correlations between time series holds a potential for enhanced forecasting. However, most existing methods rely on predefined or self-learning graphs, which are either static or unintentionally dynamic, and thus cannot model the time-varying correlations that exhibit trends and periodicities caused by the regularity of the underlying processes in CPS. To tackle such limitation, we propose Time-aware Graph Structure Learning (TagSL), which extracts time-aware correlations among time series by measuring the interaction of node and time representations in high-dimensional spaces. Notably, we introduce time discrepancy learning that utilizes contrastive learning with distance-based regularization terms to constrain learned spatial correlations to a trend sequence. Additionally, we propose a periodic discriminant function to enable the capture of periodic changes from the state of nodes. Next, we present a Graph Convolution-based Gated Recurrent Unit (GCGRU) that jointly captures spatial and temporal dependencies while learning time-aware and node-specific patterns. Finally, we introduce a unified framework named Time-aware Graph Convolutional Recurrent Network (TGCRN), combining TagSL, and GCGRU in an encoder-decoder architecture for multi-step spatiotemporal forecasting. We report on experiments with TGCRN and popular existing approaches on five real-world datasets, thus providing evidence that TGCRN is capable of advancing the state-of-the-art. We also cover a detailed ablation study and visualization analysis, offering detailed insight into the effectiveness of time-aware structure learning.

Federated Learning (FL) has emerged as a promising collaborative learning paradigm that enables to train machine learning models across decentralized devices, while keeping the training data localized to preserve user privacy. However, the heterogeneity in both decentralized training data and distributed computing resources has posed significant challenges to the design of effective and efficient FL schemes. Most existing solutions either focus on tackling a single type of heterogeneity, or are unable to fully support model heterogeneity with low communication overhead, fast convergence, and good interpretability. In this paper, we present CloREF, a novel rule-based collaborative learning framework that allows devices in FL to use completely different local learning models to cater to both data and resource heterogeneity. In CloREF, each rule is represented as a linear model, which provides good interpretability. Each participating device chooses a local model and trains it using its local data. The decision boundary of each trained local model is then approximated using a set of rules, which effectively bridges the gap arising from model heterogeneity. All participating devices collaborate to select the optimal set of rules as the global model, employing evolutionary optimization to effectively fuse the knowledge acquired from all local models. Experimental results on both synthesized and real-world datasets demonstrate that the rules generated by our proposed method can mimic the behaviors of various learning models with high fidelity ($\gt $0.95 in most tests), and CloREF gives competitive performance in accuracy, AUC, and communication overhead, compared with both the best-performing model trained centrally and several state-of-the-art model-heterogeneous federated learning schemes.

With the digitization of modern cities, large data volumes and powerful computational resources facilitate the rapid update of intelligent models deployed in smart cities. Continual learning (CL) is a novel machine learning paradigm that constantly updates models to adapt to changing environments, where the learning tasks, data, and distributions can vary over time. Our survey provides a comprehensive review of continual learning methods that are widely used in smart city development. The content consists of three parts: 1) Methodology-wise. We categorize a large number of basic CL methods and advanced CL frameworks in combination with other learning paradigms including graph learning, spatial-temporal learning, multi-modal learning, and federated learning. 2) Application-wise. We present numerous CL applications covering transportation, environment, public health, safety, networks, and associated datasets related to urban computing. 3) Challenges. We discuss current problems and challenges and envision several promising research directions. We believe this survey can help relevant researchers quickly familiarize themselves with the current state of continual learning research used in smart city development and direct them to future research trends.

The rapid expansion of low-earth orbit satellite constellations poses a significant challenge for the operation and maintenance of thousands of satellites. In-orbit fault diagnosis helps minimize the cost of repairs, and ensure the overall reliability of the satellite constellation by identifying faults in their early stages. Compared to traditional fault detection methods, fault diagnosis requires knowledge to enhance very limited data and to infer cascading failures. In this paper, we propose a novel knowledge service framework that combines data-driven and knowledge-driven models to improve the efficiency and effectiveness of fault diagnosis. We implement a fault diagnosis service based on a constructed knowledge graph, which affords an assistant decision support function. The in-orbit deployment and simulation experiment verify the feasibility of the proposed framework, which shows great potential for fault diagnosis of low-earth orbit satellite constellation.

Abstract The dynamical performance of vehicles on railway tracks is significantly influenced by wheel‐rail interactions, which makes the wheel‐rail force be a safety indicator of vehicle systems. Owing to the high cost of direct measurement, inversion models are widely used to measure the wheel‐rail force. This study proposes a model called the Lightweight Wheel‐Rail Force Inversion Model (LFIM) to calculate the wheel‐rail force by using vibration signals collected from the vehicle system. The model can extract the relevant features, and outperforms prevalent models. It is also resource efficient and small in size, which makes it suitable for edge computing environment. The basic LFIM yielded a correlation coefficient of 0.99 in experiments, significantly higher than the value recorded by the traditional dynamic methods. The compressed LFIM yielded a 91% reduction in floating‐point operations (FLOPs) and had an R2 score of 90%, which satisfies the demands for vehicle monitoring. By balancing accuracy and size, LFIM is a feasible model to deploy on edge devices to monitor the wheel‐rail force in real‐time and assess the safety of railway vehicles.

Urban flow analysis is an essential research for smart city construction, in which urban flow pattern analysis focuses on the continuous state of urban flow. How to mine, store and reuse traffic patterns from urban multi-source heterogeneous big data is challenging. Therefore, this paper proposes a knowledge mining network for regional flow pattern to mine and store the urban flow pattern. The proposed model consists of two modules. In the first module, the features of the region and its flow pattern are extracted as the entity and relation, respectively. In the second module, POI features are modeled to enhance the embedding representation of relation and entity. Based on the translation distance method, the knowledge triplets of regional flow patterns are mined. Finally, the proposed model is compared with some benchmark methods using Chengdu Didi order and POI datasets. Experimental results show that the proposed model is effective. In addition, the knowledge triplets are visualized and some application examples are introduced.

The International Classification of Diseases (ICD) is a standard for categorizing physical conditions, which has been widely used for analyzing clinical data and monitoring health issues. Manual ICD coding takes a long time and is vulnerable to errors, so people pay more and more attention to the application of deep neural networks in ICD automatic coding. However, there is still no comprehensive review of these studies and prospects for further research. This paper is not limited to the study of deep neural networks, but gives a formal definition of ICD coding problems, and then systematically reviews the existing literature on how to design deep neural networks to address the four major challenges of ICD coding tasks. This paper also summarizes the public data sets and future research directions, to provide a guidance for the research of ICD coding in medical field.

Mobile edge computing (MEC) has been an effective paradigm for supporting computation-intensive applications by offloading resources at network edge. Especially in vehicular networks, the MEC server, is deployed as a small-scale computation server at the roadside and offloads computation-intensive task to its local server. However, due to the unique characteristics of vehicular networks, including high mobility of vehicles, dynamic distribution of vehicle densities and heterogeneous capacities of MEC servers, it is still challenging to implement efficient computation offloading mechanism in MEC-assisted vehicular networks. In this article, we investigate a novel scenario of computation offloading in MEC-assisted architecture, where task upload coordination between multiple vehicles, task migration between MEC/cloud servers and heterogeneous computation capabilities of MEC/cloud severs, are comprehensively investigated. On this basis, we formulate cooperative computation offloading (CCO) problem by modeling the procedure of task upload, migration and computation based on queuing theory, which aims at minimizing the delay of task completion. To tackle the CCO problem, we propose a probabilistic computation offloading (PCO) algorithm, which enables MEC server to independently make online scheduling based on the derived allocation probability. Specifically, the PCO transforms the objective function into augmented Lagrangian and achieves the optimal solution in an iterative way, based on a convex framework called Alternating Direction Method of Multipliers (ADMM). Last but not the least, we implement the simulation model. The comprehensive simulation results show the superiority of the proposed algorithm under a wide range of scenarios.

Neural semantic parsers usually fail to parse long and complicated utterances into nested SQL queries, due to the large search space. In this paper, we propose a novel recursive semantic parsing framework called RECPARSER to generate the nested SQL query layer-by-layer. It decomposes the complicated nested SQL query generation problem into several progressive non-nested SQL query generation problems. Furthermore, we propose a novel Question Decomposer module to explicitly encourage RECPARSER to focus on different components of an utterance when predicting SQL queries of different layers. Experiments on the Spider dataset show that our approach is more effective compared to the previous works at predicting the nested SQL queries. In addition, we achieve an overall accuracy that is comparable with state-of-the-art approaches.

Summary With the increase of data processing and Hadoop data center construction requirements, the performance of Hadoop data center is limited by inappropriate resources utilization. This paper introduces a new method to predict utilization for large‐scale Hadoop clusters. The new method adopts a two steps model, which includes Hadoop applications' performance simulation and resources utilization prediction. For performance simulation, a new simulator, which integrates baseline test and multilayered network model, is introduced and implemented. A resources utilization predictor is proposed in the second step. By analyzing the pattern of resources utilization, a single task model is proposed. A parallel‐batch‐task‐based (PBT) model, which represents the behavior of real Hadoop applications by integrating the single task model, is introduced. Two test scenarios are configured to verify the performance of our method. For the data center scenario, Terasort, Wordcount, and Hive are selected as benchmarks. In the virtual machines scenario, Terasort is used as benchmark. The experiments show that the error comparing between the simulator results and experimental environment results in most cases is less than 10%. The results confirm that we can locate the resource bottleneck for Hadoop clusters, meanwhile we can agilely configure clusters for applications with massive data.

With the development of healthcare 4.0, there has been an explosion in the amount of data such as image, medical text, physiological signals, lab tests, etc. Among them, medical records provide a complete picture of the associated clinical events. However, the processing of medical texts is difficult because they are structurally free, diverse in style, and have subjective factors. Assigning metadata codes from the International Classification of Diseases (ICD) presents a standardized way of indicating diagnoses and procedures, so it becomes a mandatory process for understanding medical records to make better clinical and financial decisions. Such a manual encoding task is time-consuming, error-prone and expensive. In this paper, we proposed a deep learning approach and a medical topic mining method to automatically predict ICD codes from text-free medical records. The result of the F1 score on Medical Information Mart for Intensive Care (MIMIC-III) dataset increases by 5% over the state of art. It also suitable for multiple ICD versions and languages. For the specific disease, atrial fibrillation, the F1 score is up to 96% and 93.3% using in-house ICD-10 datasets and MIMIC-III datasets, respectively. We developed an Artificial Intelligence based coding system, which can greatly improve the efficiency and accuracy of human coders, and meanwhile accelerate the secondary use for clinical informatics.

Automatic tongue image segmentation and tongue image classification are two crucial tongue characterization tasks in traditional Chinese medicine (TCM). Due to the complexity of tongue segmentation and fine-grained traits of tongue image classification, both tasks are challenging. Fortunately, from the perspective of computer vision, these two tasks are highly interrelated, making them compatible with the idea of Multi-Task Joint learning (MTL). By sharing the underlying parameters and adding two different task loss functions, an MTL method for segmenting and classifying tongue images is proposed in this paper. Moreover, two state-of-the-art deep neural network variants (UNET and Discriminative Filter Learning (DFL)) are fused into the MTL to perform these two tasks. To the best of our knowledge, our method is the first attempt to manage both tasks simultaneously with MTL. We conducted extensive experiments with the proposed method. The experimental results show that our joint method outperforms the existing tongue characterization methods. Besides, visualizations and ablation studies are provided to aid in understanding our approach, which suggest that our method is highly consistent with human perception.

Identifying relation from clinical texts is a complex and challenging task due to the specific biomedical knowledge. Existing methods for this work generally have the misclassification problem caused by sample class imbalance. In this paper, we propose a hierarchical attention-based convolutional long short-term memory (ConvLSTM) network model to solve this problem. We construct a sentence as multi-dimensional hierarchical sequence and directly learn local and global context information by a single-layer ConvLSTM network. Besides, a hierarchical attention-based pooling is built to capture the parts of a sentence that are relevant with the target semantic relation. Experiments on the 2010 i2b2/VA relation dataset show that our model outperforms several previous state-of-the-art models without relying on any external features.

Semi-supervised clustering ensemble has emerged as an important elaboration of classical clustering problem that improves quality and robustness in clustering by combining the results of different clustering components with user provided constraints. MapReduce is a parallel programming model for processing big data using large numbers of distributed computers (nodes). In this paper, we propose a novel semi-supervised multi-ant colonies consensus clustering algorithm and implement the parallelization of this algorithm using MapReduce on Hadoop platform. Our method incorporates pairwise constraints not only in each ant colony clustering process, but also in computing new similarity matrix during the process of the multi-ant colonies ensemble. In addition, it enhances the computational efficiency for big data by adopting a MapReduce Framework. Experimental results demonstrate the effectiveness of the proposed method.

Multi-core processors achieve a trade-off between the performance and the power consumption by using Dynamic Voltage Scaling (DVS) techniques. In this paper, we study the power efficient scheduling problem of real-time tasks in an identical multi-core system, and present Node Scaling model to achieve power-aware scheduling. We prove that there is a bound speed which results in the minimal power consumption for a given task set, and the maximal value of task utilization,$u_{max}$, in a task set is a key element to decide its minimal power consumption. Based on the value$u_{max}$, we classify task sets into two categories: the bounded task sets and the non-bounded task sets, and we prove the lower bound of power consumption for each type of task set. Simulations based on Intel Xeon X5550 and PXA270 processors show Node Scaling model can achieve power efficient scheduling by applying to existing algorithms such as EDF-FF and SPA2. The ratio of power reduction depends on the multi-core processor's property which is defined as the ratio of the bound speed to the maximal speed of the cores. When the ratio of speeds decreases, the ratio of power reduction increases for all the power efficient algorithms.

Clustering with pairwise constraints has received much attention in the clustering community recently. Particularly, must-link and cannot-link constraints between a given pair of instances in the data set are common prior knowledge incorporated in many clustering algorithms today. This approach has been shown to be successful in guiding a number of famous clustering algorithms towards more accurate results. However, recent work has also shown that the incorporation of must-link and cannot-link constraints makes clustering algorithms too much sensitive to “the assignment order of instances” and therefore results in consequent constraint violation. The major contributions of this paper are two folds. One is to address the issue of constraint violation in Cop-Kmeans by emphasizing a sequenced assignment of cannot-link instances after conducting a Breadth-First Search of the cannot-link set. The other is to reduce the computational complexity of Cop-Kmeans for massive data sets by adopting a MapReduce Framework. Experimental results show that our approach performs well on massive data sets while may overcome the problem of constraint violation.