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DTSFormer: Decoupled temporal-spatial diffusion transformer for enhanced long-term time series forecasting

KNOWLEDGE-BASED SYSTEMS 2025年 309卷

作者： Zhu, Jiaming Liu, Dezhi Chen, Huayou Liu, Jinpei Tao, Zhifu Anhui Univ Sch Internet Hefei 230039 Anhui Peoples R China Natl Engn Res Ctr Agroecol Big Data Anal & Applica Hefei 230601 Anhui Peoples R China Anhui Univ Sch Big Data & Stat Hefei 230601 Anhui Peoples R China Anhui Univ Sch Business Hefei 230601 Anhui Peoples R China

Transformer-based models have significantly advanced long-term time series forecasting by leveraging self- attention mechanisms to capture long-term dependencies. However, these models face high computational costs, slow inference speeds, and limitations in utilizing information from longer lookback windows. Additionally, existing methods often neglect implicit spatial dependencies between variables, and struggle with semantic misalignment and insufficient diffusion of spatial information. To address these challenges, we propose DTSFormer, a D ecoupled T emporal-Spatial Diffusion Transformer designed specifically for long-term time series forecasting: (1) DTSFormer effectively integrates temporal features with implicit spatial attributes, ensuring comprehensive utilization of both temporal and spatial information. (2) DTSFormer introduce a Mix- hop Diffusion layer to effectively propagate and aggregate spatial information while preserving the original graph structure, significantly improving the accuracy of spatial information dissemination. (3) we develop a cross-diffusion attention mechanism based on the expectation-maximization algorithm, which integrates graph structure information with varying semantics under a seasonal trend decomposition framework. This approach enhances the fusion of semantic information from different graph structures and reduces computational complexity. Our extensive experiments on multiple benchmark datasets across different domains demonstrate that DTSFormer consistently achieves state-of-the-art performance in both accuracy and efficiency. These results validate DTSFormer as a robust and scalable solution for advanced long-term time series forecasting tasks.

关键词： Long-term series forecasting Transformer-based model expectation-maximization algorithm Diffusion Temporal-Spatial features

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Censored trajectory data clustering using mixture of semi-Markov models with application to targeted marketing

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2025年 1-27页

作者： Lahoti, Geet Ranjan, Chitta Chen, Jialei Ebrahimi, Samaneh Zhang, Chuck Georgia Tech H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA ProcessMiner Atlanta GA USA Pandora Oakland CA 94611 USA

A trajectory is a spatio-temporal data instance in which a customer or user moves between a set of discrete states while spending a certain amount of time in each state. Using trajectory data as a proxy for customers' behavior and performing clustering can help to devise targeted marketing strategies. However, the censoring is often encountered due to the inability to observe the complete trajectories. In addition, the exact number of clusters is often unknown. In this work, we propose a novel mixture model-based clustering methodology to analyze the trajectory data and decipher different user segments based on their behavior. Each cluster is profiled using a semi-Markov model while considering the effect of censoring. Each entity is assigned to a cluster based on its similarity to the cluster's profile. Entity assignments and cluster profiles are simultaneously inferred using a robust expectation maximization algorithm. In the simulation study, our methodology demonstrates better performance than existing methods. The effectiveness of our methodology is further corroborated using a real data set obtained from an internet music provider, where the obtained clustering results are found to be helpful in devising better marketing strategies to target users in different segments.

关键词： Trajectory clustering Semi-Markov models Censored data Model-based clustering expectation-maximization algorithm Customer segmentation

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Efficient and Effective Variational Bayesian Inference Method for Log-Linear Cognitive Diagnostic Model

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Psychometrika 2025年第1期90卷 74-107页

In this paper, we propose a novel and highly effective variational Bayesian expectation maximization-maximization (VBEM-M) inference method for log-linear cognitive diagnostic model (CDM). In the implementation of the variational Bayesian approach for the saturated log-linear CDM, the conditional variational posteriors of the parameters that need to be derived are in the same distributional family as the priors, the VBEM-M algorithm overcomes this problem. Our algorithm can directly estimate the item parameters and the latent attribute-mastery pattern simultaneously. In contrast, Yamaguchi and Okada’s (2020a) variational Bayesian algorithm requires a transformation step to obtain the item parameters for the log-linear cognitive diagnostic model (LCDM). We conducted multiple simulation studies to assess the performance of the VBEM-M algorithm in terms of parameter recovery, execution time, and convergence rate. Furthermore, we conducted a series of comparative studies on the accuracy of parameter estimation for the DINA model and the saturated LCDM, focusing on the VBEM-M, VB, expectation-maximization, and Markov chain Monte Carlo algorithms. The results indicated that our method can obtain more stable and accurate estimates, especially for the small sample sizes. Finally, we demonstrated the utility of the proposed algorithm using two real datasets.

关键词： cognitive diagnostic assessments expectation-maximization algorithm log-linear cognitive diagnostic model Markov chain Monte Carlo variational Bayesian algorithm

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An improved EM algorithm for variable selection with missing data in spatial error models

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2025年第6期95卷 1141-1164页

作者： Wang, Yuanfeng Song, Yunquan China Univ Petr Coll Sci Qingdao 266580 Peoples R China

In the field of spatial economics, choosing the right variables for spatial error models (SEM) with missing data is of utmost importance. Many excellent approaches are proposed to select variables for regression models with missing data. However, little literature addresses this problem in the SEM model. To address this issue, we have developed an observed-data penalized quasi-maximum likelihood estimation method called OPQMLE, which simultaneously performs variable selection and parameter estimation in the presence of a missing response. This method employs the Smoothly Clipped Absolute Deviation (SCAD) penalty to select variables for SEM models. Under certain assumptions, we have established the method's theoretical properties, including consistency and asymptotic normality. Furthermore, we have provided an improved expectation-maximization algorithm for optimizing the penalized quasi-likelihood function. We have conducted a simulation and real data analysis to evaluate the proposed method's performance.

关键词： Spatial error models observed penalized quasi-likelihood function expectation-maximization algorithm missing data variable selection

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Estimating the Coefficients of a Mixture of Two Linear Regressions by expectation maximization

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IEEE TRANSACTIONS ON INFORMATION THEORY 2019年第6期65卷 3515-3524页

作者： Klusowski, Jason M. Yang, Dana Brinda, W. D. Rutgers Univ New Brunswick Dept Stat Piscataway NJ 08854 USA Yale Univ Dept Stat & Data Sci New Haven CT 06511 USA

We give convergence guarantees for estimating the coefficients of a symmetric mixture of two linear regressions by expectation maximization (EM). In particular, we show that the empirical EM iterates converge to the target parameter vector at the parametric rate, provided the algorithm is initialized in an unbounded cone. In particular, if the initial guess has a sufficiently large cosine angle with the target parameter vector, a sample-splitting version of the EM algorithm converges to the true coefficient vector with high probability. Interestingly, our analysis borrows from tools used in the problem of estimating the centers of a symmetric mixture of two Gaussians by EM. We also show that the population of EM operator for mixtures of two regressions is anti-contractive from the target parameter vector if the cosine angle between the input vector and the target parameter vector is too small, thereby establishing the necessity of our conic condition. Finally, we give empirical evidence supporting this theoretical observation, which suggests that the sample-based EM algorithm may not converge to the target vector when initial guesses are drawn accordingly. Our simulation study also suggests that the EM algorithm performs well even under model misspecification (i.e., when the covariate and error distributions violate the model assumptions).

关键词： Mixture models expectation-maximization algorithm iterative algorithms clustering algorithms regression analysis

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Structured Covariance Matrix Estimation With Missing-(Complex) Data for Radar Applications via expectation-maximization

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2021年 69卷 5920-5934页

作者： Aubry, Augusto De Maio, Antonio Marano, Stefano Rosamilia, Massimo Univ Napoli Federico II Dept Elect Engn & Informat Technol DIETI I-80125 Naples Italy Natl Interuniv Consortium Telecommun I-43124 Parma Italy Univ Salerno Dipartimento Ingn Informaz Elettr & Matemat Appli I-84084 Fisciano SA Italy

Structured covariance matrix estimation in the presence of missing-(complex) data is addressed in this paper with emphasis on radar signal processing applications. After a motivation of the study, the array model is specified and the problem of computing the maximum likelihood estimate of a structured covariance matrix is formulated. A general procedure to optimize the observed-data likelihood function is developed resorting to the expectation-maximization algorithm. The corresponding convergence properties are thoroughly established and the rate of convergence is analyzed. The estimation technique is contextualized for two practically relevant radar problems: beamforming and detection of the number of sources. In the former case an adaptive beamformer leveraging the EM-based estimator is presented;in the latter, detection techniques generalizing the classic Akaike information criterion, minimum description length, and Hannan-Quinn information criterion, are introduced. Numerical results are finally presented to corroborate the theoretical study.

关键词： Covariance matrices Estimation Radar Array signal processing Convergence Radar antennas Radar signal processing Missing data expectation-maximization algorithm adaptive array signal processing beamforming source number detection

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expectation-maximization-based joint data detection and channel estimation for a cellular multi-carrier code division multiple access network using single-hop relaying

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INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS 2013年第4期26卷 449-464页

作者： Kabaoglu, Nihat Maltepe Univ Dept Elect & Elect Engn Istanbul Turkey

This paper is concerned with channel estimation and data detection for a cellular multi-carrier code division multiple access network using single-hop relaying in the presence of frequency selective fading channels. The proposed expectationmaximization (EM) algorithm was used to jointly estimate both the coefficients of the channel between a relay and a base station and the data. EM algorithm is particularly suited to multi-carrier code division multiple access systems because they have multi-carrier signal format. The considered network uses single-hop relaying technique to provide a higher quality transmission to the users with low quality channels. The base station (managing mechanism) gives them an opportunity to send their messages via the users with high quality channels in a time sharing mode. The performance of the proposed EM algorithm, with and without hopping and with cooperative communication technique, was analyzed by a computer simulation, and the results are presented. Copyright (c) 2011 John Wiley & Sons, Ltd.

关键词： opportunistic communication MC-CDMA expectation-maximization algorithm data detection and channel estimation

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Dental radiography segmentation using expectation-maximization clustering and grasshopper optimizer

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MULTIMEDIA TOOLS AND APPLICATIONS 2020年第29-30期79卷 22027-22045页

作者： Qaddoura, Raneem Al Manaseer, Waref Abushariah, Mohammad A. M. Alshraideh, Mohammad Aref Philadelphia Univ Informat Technol Amman Jordan Univ Jordan King Abdullah II Sch Informat Technol Dept Comp Sci Amman Jordan Univ Jordan King Abdullah II Sch Informat Technol Dept Comp Informat Syst Amman Jordan

Image segmentation is a popular technique that is used for extracting information from images, which has also gained a lot of interest lately due to its importance in different scientific fields such as the medical field. This paper proposes a novel image segmentation technique using expectation-maximization (EM) clustering algorithm and Grasshopper Optimizer algorithm (GOA). The proposed technique and the concept of image segmentation are effectively applied on dental radiography datasets that are collected from 120 patients with an age between 6 to 60 years old. To validate the proposed technique, a comparison in terms of purity and entropy measures is conducted against K-means, X-means, EM, and Farthest First algorithms. Based on our experimental results, the proposed technique using EM and GOA achieved the best results compared to other algorithms for all three datasets in terms of entropy and purity. The best results were obtained using the second dataset, which achieved purity value of 0.7126 and entropy value of 0.3083. Further, the proposed technique also outperforms U-net and Random Forest algorithms for the selected datasets.

关键词： Image segmentation expectation-maximization algorithm Grasshopper optimization algorithm Dental radiography Anatomical segmentation and classification

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A COPULA APPROACH TO JOINT MODELING OF LONGITUDINAL MEASUREMENTS AND SURVIVAL TIMES USING MONTE CARLO expectation-maximization WITH APPLICATION TO AIDS STUDIES

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JOURNAL OF BIOPHARMACEUTICAL STATISTICS 2015年第5期25卷 1077-1099页

作者： Ganjali, M. Baghfalaki, T. Shahid Beheshti Univ Dept Stat Tehran Iran Tarbiat Modares Univ Dept Stat Tehran Iran Inst Res Fundamental Sci IPM Sch Biol Sci Tehran Iran

Joint modeling of longitudinal measurements and time to event data is often performed by fitting a shared parameter model. Another method for joint modeling that may be used is a marginal model. As a marginal model, we use a Gaussian model for joint modeling of longitudinal measurements and time to event data. We consider a regression model for longitudinal data modeling and a Weibull proportional hazard model for event time data modeling. A Gaussian copula is used to consider the association between these two models. A Monte Carlo expectation-maximization approach is used for parameter estimation. Some simulation studies are conducted in order to illustrate the proposed method. Also, the proposed method is used for analyzing a clinical trial dataset.

关键词： Copula models expectation-maximization algorithm Longitudinal model Non-ignorability Shared parameter model Time to event model

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MUSIC-Expected maximization gaussian mixture methodology for clustering and detection of task-related neuronal firing rates

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BEHAVIOURAL BRAIN RESEARCH 2017年第0期317卷 226-236页

作者： Ortiz-Rosario, Alexis Adeli, Hojjat Buford, John A. Ohio State Univ Dept Biomed Engn Columbus OH 43210 USA Ohio State Univ Dept Biomed Engn Dept Biomed Informat Dept Civil & Environm Engn 470 Hitchcock Hall2070 Neil Ave Columbus OH 43210 USA Ohio State Univ Dept Geodet Sci Dept Elect & Comp Engn Dept Neurol 470 Hitchcock Hall2070 Neil Ave Columbus OH 43210 USA Ohio State Univ Dept Neurosci 470 Hitchcock Hall2070 Neil Ave Columbus OH 43210 USA Ohio State Univ Sch Hlth & Rehabil Sci Div Phys Therapy 453 W 10th AveRm 516E Columbus OH 43210 USA

Researchers often rely on simple methods to identify involvement of neurons in a particular motor task. The historical approach has been to inspect large groups of neurons and subjectively separate neurons into groups based on the expertise of the investigator. In cases where neuron populations are small it is reasonable to inspect these neuronal recordings and their firing rates carefully to avoid data omissions. In this paper, a new methodology is presented for automatic objective classification of neurons recorded in association with behavioral tasks into groups. By identifying characteristics of neurons in a particular group, the investigator can then identify functional classes of neurons based on their relationship to the task. The methodology is based on integration of a multiple signal classification (MUSIC) algorithm to extract relevant features from the firing rate and an expectation-maximization Gaussian mixture algorithm (EM-GMM) to cluster the extracted features. The methodology is capable of identifying and clustering similar firing rate profiles automatically based on specific signal features. An empirical wavelet transform (EWT) was used to validate the features found in the MUSIC pseudospectrum and the resulting signal features captured by the methodology. Additionally, this methodology was used to inspect behavioral elements of neurons to physiologically validate the model. This methodology was tested using a set of data collected from awake behaving non-human primates. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Multiple signal classification Gaussian mixture model expectation-maximization algorithm Firing rate Neurons Signal processing Empirical wavelet transform

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