Spectral clustering is traditionally formulated as a two-step procedure in which dimensionality reduction through Laplacian embedding is followed by a separate clustering stage. In this paper, we introduce a simultaneous spectral clustering framework for three-way data. The proposed approach jointly estimates a common Laplacian embedding and the corresponding cluster allocation within a unified optimization problem. Occasion-specific heterogeneity is incorporated through diagonal weighting matrices that modulate each occasion’s contribution to the shared latent representation, while preserving a common clustering structure across the third mode. An efficient alternating least squares (ALS) algorithm is derived for parameter estimation under orthogonality and clustering constraints.
This paper introduces the ellipsoidal confidence membership score machine (EC-MSM), an advanced improvement of the membership score machine (MSM) (Lee et al., 2023) designed for nonlinear classification of small, highly irregular datasets. The original MSM utilizes within-class clustering and principal component analysis (PCA) to capture the geometric features of the dataset, offering a robust classification through anisotropic distance measures. EC-MSM extends MSM by incorporating two novel enhancements: (1) an ellipsoidal discriminant adjustment to improve geometric representation within each class, and (2) a confidence absorption layer formulation to capture complex feature hierarchies effectively. These modifications aim to further reduce dimensionality while preserving the integrity of class-specific features, leading to improved performance in distinguishing non-globular data clusters. Numerical experiments demonstrate that EC-MSM achieves superior accuracy and generalization, particularly on highly nonlinear and challenging datasets, compared to the original MSM and other popular classifiers.
A complete Q-matrix is used to represent the cognitive model of a domain of interest. The Q-matrix is directly related to the identifiability of the latent attribute space, and the identifiability of item parameters of cognitive diagnostic models (CDMs). Polytomous responses and attributes can provide additional diagnostic information and are more common in practice. Recent research developed CDMs with polytomous attributes, such as the nonparametric polytomous attributes diagnostic classification method, and the polytomous generalized distance discriminating (GDD-P) method. However, the conditions of polytomous Q-matrix for the identifiability of latent space with polytomous attributes and responses have sparingly been taken into consideration. Theoretically, we establish a weaker condition for the identifiability of latent space and applied it to construct a family of complete Q-matrices, which include a set of singleton items covering various levels of the attributes. The singleton item can establish a one-to-one correspondence between collapsed attribute patterns and ideal item scores under a polytomous scoring rule. Moreover, we conduct simulation and empirical studies to investigate the performance of different designs of complete Q-matrix under the GDD-P method.
We propose a novel multivariate hidden Markov model (HMM) designed to analyze longitudinal mixed-type data comprising continuous and ordinal variables. Our model identifies and prioritizes discriminative dimensions, i.e., those useful for clustering, while separating them from noise dimensions. By modeling variables as linear combinations of two independent latent factor sets, we achieve both parsimony and interpretability: one latent factor set represents cluster structures and evolves according to an HMM, while the other captures noise through a time-invariant multivariate normal distribution. To overcome the computational complexity of high-dimensional integrals required to compute the likelihood function, we adopt a composite likelihood approach for efficient parameter estimation. This framework enables simultaneous clustering and dimensionality reduction, offering a robust tool for analyzing complex mixed-type longitudinal datasets. The proposal is tested on simulated data by considering a large-scale simulation study and further applied to the study of lifestyle and health in the Chinese elderly population.
This paper introduces augmented functional random forests, a supervised classification framework for functional data that combines tree-based ensembles with leakage-free functional representation. The method augments smoothed curves with their first and second derivatives, applies blockwise functional principal component analysis separately to each functional representation, and tunes the number of retained components and ensemble parameters using training-based out-of-bag criteria. This construction allows level, slope, and curvature information to be incorporated into functional classification while controlling representation complexity. The paper also develops structured conditional permutation diagnostics for augmented functional principal component scores and combines them with a stability-based ranking criterion to mitigate correlation-induced distortions in feature importance. The resulting scores are interpreted as structured approximations to conditional relevance, rather than as pure conditional importance measures. Simulated scenarios and benchmark datasets show that derivative-based augmentation can improve accuracy when local dynamics are discriminative, while providing stability-aware feature relevance diagnostics.
