Dictionary learning is traditionally formulated as an $L_1$-regularized signal reconstruction problem. While recent developments have incorporated discriminative, hierarchical, or generative structures, most approaches rely on encouraging representation sparsity over individual samples that overlook how atoms are shared across samples, resulting in redundant and sub-optimal dictionaries. We introduce a parsimony promoting regularizer based on the row-wise $L_\infty$ norm of the coefficient matrix. This additional penalty encourages entire rows of the coefficient matrix to vanish, thereby reducing the number of dictionary atoms activated across the dataset. We derive the formulation from a probabilistic model with Beta-Bernoulli priors, which provides a Bayesian interpretation linking the regularization parameters to prior distributions. We further establish theoretical calculation for optimal hyperparameter selection and connect our formulation to both Minimum Description Length, Bayesian model selection and pathlet learning. Extensive experiments on benchmark datasets demonstrate that our method achieves substantially improved reconstruction quality (with a 20\% reduction in RMSE) and enhanced representation sparsity, utilizing fewer than one-tenth of the available dictionary atoms, while empirically validating our theoretical analysis.

The increasing availability of user data on music streaming platforms opens up new possibilities for analyzing music consumption. However, understanding the evolution of user preferences remains a complex challenge, particularly as their musical tastes change over time. This paper uses the dictionary learning paradigm to model user trajectories across different musical genres. We define a new framework that captures recurring patterns in genre trajectories, called pathlets, enabling the creation of comprehensible trajectory embeddings. We show that pathlet learning reveals relevant listening patterns that can be analyzed both qualitatively and quantitatively. This work improves our understanding of users' interactions with music and opens up avenues of research into user behavior and fostering diversity in recommender systems. A dataset of 2000 user histories tagged by genre over 17 months, supplied by Deezer (a leading music streaming company), is also released with the code.

This paper addresses the challenge of multi-agent path planning for efficient data collection in dynamic, uncertain environments, exemplified by autonomous underwater vehicles (AUVs) navigating the Gulf of Mexico. Traditional greedy algorithms, though computationally efficient, often fall short in long-term planning due to their short-sighted nature, missing crucial data collection opportunities and increasing exposure to hazards. To address these limitations, we introduce WAITR (Weighted Aggregate Inter-Temporal Reward), a novel path-planning framework that integrates a knowledge graph with pathlet-based planning, segmenting the environment into dynamic, speed-adjusted sub-regions (pathlets). This structure enables coordinated, adaptive planning, as agents can operate within time-bound regions while dynamically responding to environmental changes. WAITR's cumulative scoring mechanism balances immediate data collection with long-term optimization of Points of Interest (POIs), ensuring safer navigation and comprehensive data coverage. Experimental results show that WAITR substantially improves POI coverage and reduces exposure to hazards, achieving up to 27.1\% greater event coverage than traditional greedy methods.

Advances in tracking technologies have spurred the rapid growth of large-scale trajectory data. Building a compact collection of pathlets, referred to as a trajectory pathlet dictionary, is essential for supporting mobility-related applications. Existing methods typically adopt a top-down approach, generating numerous candidate pathlets and selecting a subset, leading to high memory usage and redundant storage from overlapping pathlets. To overcome these limitations, we propose a bottom-up strategy that incrementally merges basic pathlets to build the dictionary, reducing memory requirements by up to 24,000 times compared to baseline methods. The approach begins with unit-length pathlets and iteratively merges them while optimizing utility, which is defined using newly introduced metrics of trajectory loss and representability. We develop a deep reinforcement learning framework, PathletRL, which utilizes Deep Q-Networks (DQN) to approximate the utility function, resulting in a compact and efficient pathlet dictionary. Experiments on both synthetic and real-world datasets demonstrate that our method outperforms state-of-the-art techniques, reducing the size of the constructed dictionary by up to 65.8%. Additionally, our results show that only half of the dictionary pathlets are needed to reconstruct 85% of the original trajectory data. Building on PathletRL, we introduce PathletRL++, which extends the original model by incorporating a richer state representation and an improved reward function to optimize decision-making during pathlet merging. These enhancements enable the agent to gain a more nuanced understanding of the environment, leading to higher-quality pathlet dictionaries. PathletRL++ achieves even greater dictionary size reduction, surpassing the performance of PathletRL, while maintaining high trajectory representability.

Trajectory representation learning on a network enhances our understanding of vehicular traffic patterns and benefits numerous downstream applications. Existing approaches using classic machine learning or deep learning embed trajectories as dense vectors, which lack interpretability and are inefficient to store and analyze in downstream tasks. In this paper, an explainable trajectory representation learning framework through dictionary learning is proposed. Given a collection of trajectories on a network, it extracts a compact dictionary of commonly used subpaths called "pathlets", which optimally reconstruct each trajectory by simple concatenations. The resulting representation is naturally sparse and encodes strong spatial semantics. Theoretical analysis of our proposed algorithm is conducted to provide a probabilistic bound on the estimation error of the optimal dictionary. A hierarchical dictionary learning scheme is also proposed to ensure the algorithm's scalability on large networks, leading to a multi-scale trajectory representation. Our framework is evaluated on two large-scale real-world taxi datasets. Compared to previous work, the dictionary learned by our method is more compact and has better reconstruction rate for new trajectories. We also demonstrate the promising performance of this method in downstream tasks including trip time prediction task and data compression.