Representation Learning for Trustworthy AI

Kernel-based subspace clustering, which addresses the nonlinear structures in data, is an evolving area of research. Despite noteworthy progressions, prevailing methodologies predominantly grapple with limitations relating to (i) the influence of predefined kernels on model performance; (ii) the difficulty of preserving the original manifold structures in the nonlinear space; (iii) the dependency of spectral-type strategies on the ideal block diagonal structure of the affinity matrix. This paper presents DKLM, a novel paradigm for kernel-induced nonlinear subspace clustering. DKLM provides a data-driven approach that directly learns the kernel from the data’s self-representation, ensuring adaptive weighting and satisfying the multiplicative triangle inequality constraint, which enhances the robustness of the learned kernel. By leveraging this learned kernel, DKLM preserves the local manifold structure of data in a nonlinear space while promoting the formation of an optimal block-diagonal affinity matrix. A thorough theoretical examination of DKLM reveals its relationship with existing clustering paradigms. Comprehensive experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed method.

We investigate the problem of discovering and forecasting regular regime switches in a financial ecosystem comprising multiple time series. Such regime switches, indicative of varying market behaviors across distinct time intervals, are pivotal for a nuanced understanding of market dynamics, which in turn allows informed model selection for forecasting and enhanced interpretability of predictive outcomes. Despite strides in this domain, prevailing methodologies often falter due to: (1) an inability to effectively model the temporal behaviors inherent in financial series; and (2) neglecting the interdependencies among series when discovering regimes. In this paper, we propose RHINE, a Regime-switcHIng model with Nonlinear rEpresentation. RHINE stands out with its kernel-based representation, adept at capturing the dynamic shifts in market regimes. This representation encapsulates the nonlinear interplay across multiple financial time series. By leveraging the kernel representation, we introduce an eigengap thresholding measure, designed to automatically discern the optimal number of financial market regimes, enhancing the model’s adaptability to market fluctuations. Empirical assessments on both synthetic and real-world stock market datasets underscore RHINE’s prowess. The findings illuminate that the inherent structures governing financial market behaviors are dynamic, and harnessing these dynamics via RHINE leads to a regime-based model that outperforms both conventional and state-of-the-art neural network models in predictive capabilities.

Correlations between variables in complex ecosystems such as weather and financial markets lead to a great amount of dynamic and co-evolving time series data, posing a significant challenge to the current forecast methods. Discovering dynamic patterns (aka regimes) is crucial to an accurate forecast, especially for the interpretability of the outcome. In this paper, we develop a kernel-based method to learn effective representations for capturing dynamically changing regimes. Each such representation accounts for the non-linear interactions among multiple time series, thereby facilitating more effective regime discovery. On the basis of regime information, we build a regression model to forecast all the variables simultaneously for the next multiple time points. The results on six real-life datasets demonstrate that our method can yield the most accurate forecast (with the lowest root mean square error) in comparison with seven predictive models.

Kernel-based subspace clustering methods that can reveal the nonlinear structure of data are an emerging research topic. While advances have been made, existing methods suffer from one or both of the following shortcomings: (1) the predefined kernel determines their performance; (2) they may be vulnerable in arbitrary manifold subspace. In this paper, we propose a novel data-driven kernel subspace clustering model with local manifold preservation, named DKLM. Specifically, DKLM provides an explicit data-driven kernel learning strategy for learning kernel directly from the self-representation of data while satisfying the adaptive-weighting. Based on the kernel, DKLM allows preserving the local manifold structure of data through a kernel local manifold term in nonlinear space and encourages acquiring an affinity matrix with the optimal block diagonal. Various experiments on both synthetic data and real-world data demonstrate the effectiveness of our method.

Multi-view clustering, which optimally integrates complementary information from different views to improve clustering performance, has drawn considerable attention in recent years. Despite recent advances, issues remain when dealing with data of high dimensionality and heterogeneity, especially in categorical sequences. These unique challenges and properties have motivated us to develop a novel Multi-view Kernel Clustering framework for Categorical sequences (MKCC), where views are expressed in terms of kernel matrices and a weighted combination of the instances is learned in parallel to the partitioning. Concretely, MKCC adaptively constructs the kernel matrix without the need of defining the kernel function. Nonetheless, the computational cost of storing the kernel matrix is O(N^2). To address this issue, we integrate a simple and efficient method for approximating the kernel matrix. A new multi-view clustering algorithm and a cluster validity index for categorical sequences are also proposed based on the framework. An empirical analysis on synthetic data sets and several commonly used real-world data sets demonstrates the appropriateness of the proposal, with the results showing the method’s outstanding performance.