Convolutional sparse coding (CSC) is a useful tool in many image and audio applications. Maximizing the performance of CSC requires that the dictionary used to store the features of signals can be learned from real data. The so-called convolutional dictionary learning (CDL) problem is formulated within a nonconvex, nonsmooth optimization framework. Most existing CDL solvers alternately update the coefficients and dictionary in an iterative manner. However, these approaches are prone to running redundant iterations, and their convergence properties are difficult to analyze. Moreover, most of those methods approximate the original nonconvex sparse inducing function using a convex regularizer to promote computational efficiency. This approach to approximation may result in nonsparse representations and, thereby, hinder the performance of the applications. In this paper, we deal with the nonconvex, nonsmooth constraints of the original CDL directly using the modified forward-backward splitting approach, in which the coefficients and dictionary are simultaneously updated in each iteration. We also propose a novel parameter adaption scheme to increase the speed of the algorithm used to obtain a usable dictionary and in so doing prove convergence. We also show that the proposed approach is applicable to parallel processing to reduce the computing time required by the algorithm to achieve convergence. The experimental results demonstrate that our method requires less time than the existing methods to achieve the convergence point while using a smaller final functional value. We also applied the dictionaries learned using the proposed and existing methods to an application involving signal separation. The dictionary learned using the proposed approach provides performance superior to that of comparable methods.

In this work, we formulated the optimal bitallocation problem for a scalable codec for images/videos as a graph-based constrained vector-valued optimization problem with many optimal solutions, which are referred to as Pareto points. Pareto points are generally derived using weighted sum scalarization; however, it has yet to be determined whether all Pareto points can be derived using this approach. This paper addresses this issue. When presented as a theorem, our results indicate that as long as the rate-distortion function of each resolution is strictly decreasing and convex and the Pareto points form a continuous curve, then all Pareto points can be derived using scalarization. The theorem is verified using the state-of-theart scalable coding method H.264/SVC and a scalability extension of HEVC (SHVC). We highlight a number of easily interpretable Pareto points that represent a good trade-off between candidate resolutions. The proximity point is defined as the Pareto point closest to the ideal performance for each resolution. We also model the Pareto points as a function of bit-rate and demonstrate that the Pareto points at other bit-rates can be predicted.

Recent advancements in Artificial Intelligence (AI) and Machine Learning (ML) have achieved remarkable success in natural language processing, computer vision, and reinforcement learning. However, when applied to human behavior understanding and motion prediction, most deep learning architectures remain black-box models—lacking interpretability in how perceptual cues and motor actions interact to form human decision-making patterns. To address this limitation, this study proposes an Explainable Multimodal Event Knowledge Graph (E²-KG) framework that integrates eye-tracking data and OpenPose-based joint angles to construct a semantic representation of cognitive–motor coupling in dynamic tasks. Instead of treating perception and motion as separate streams, E²-KG embeds them within a unified perception–action manifold, where local energy gradients automatically detect event transitions (fixation, preparation, release, follow-through). These events are organized into a knowledge graph structure, enabling interpretable reasoning about causal links between visual attention, body movement, and task outcomes. A perception–action manifold model capturing the joint evolution of gaze and motion through local energy variations. A multimodal event extraction pipeline for synchronized eye–pose data. An event knowledge graph that supports cause–effect reasoning. Validation through a throwing-distance prediction task, demonstrating higher interpretability and transparency than data-driven baselines. E²-KG thus bridges manifold learning and knowledge-graph reasoning, offering a transparent, cognitively grounded approach for explainable human performance modeling—applicable to domains such as human factors, adaptive training, and human–robot collaboration.

This study presents an explainable knowledge graph (KG) framework that transforms continuous spindle monitoring time-series data into transparent, reasoning-ready diagnostic structures. Existing data-driven approaches, while accurate, often lack the interpretability required for high-stakes industrial decision-making and are sensitive to operating condition drifts. To address these limitations, we propose a two-level temporal segmentation method combining label transition detection and statistical drift analysis to identify meaningful state boundaries. Furthermore, a percentile-based discretization mechanism converts statistical features into interpretable semantic tags. A Neo4j-based state–event–feature schema captures lifecycle evolution and evidence relations, enabling attribution path reasoning that links failure events to salient precursor features. Experiments on real industrial spindle data demonstrate a fault detection accuracy of 84.97% and a false alarm rate of 3.43%, effectively capturing stable baselines and intermittent abnormal bursts. The proposed framework provides a distinct novelty in bridging the gap between numerical time-series and symbolic reasoning, offering a practical pathway for deploying explainable and maintainable spindle health analytics.