Kaijie Xu

Kaijie Xu

The identification of co-regulated genes and their transcription-factor binding sites (TFBS) are the key steps toward understanding transcription regulation. In addition to effective laboratory assays, various bi-clustering algorithms for detection of the co-expressed genes have been developed. Bi-clustering methods are used to discover subgroups of genes with similar expression patterns under to-be-identified subsets of experimental conditions when applied to gene expression data. By building two fuzzy partition matrices of the gene expression data with the Axiomatic Fuzzy Set (AFS) theory, this paper proposes a novel fuzzy bi-clustering algorithm for identification of co-regulated genes. Specifically, the gene expression data is transformed into two fuzzy partition matrices via sub-preference relations theory of AFS at first. One of the matrices is considering the genes as the universe and the conditions as the concept, the other one is considering the genes as the concept and the conditions as the universe. The identification of the co-regulated genes (bi-clusters) is carried out on the two partition matrices at the same time. Then, a novel fuzzy-based similarity criterion is defined based on the partition matrixes, and a cyclic optimization algorithm is designed to discover the significant bi-clusters at expression level. The above procedures guarantee that the generated bi-clusters have more significant expression values than that of extracted by the traditional bi-clustering methods. Finally, the performance of the proposed method is evaluated with the performance of the three well-known bi-clustering algorithms on publicly available real microarray datasets. The experimental results are in agreement with the theoretical analysis and show that the proposed algorithm can effectively detect the co-regulated genes without any prior knowledge of the gene expression data.

Kaijie Xu, Mustafa Bugti, Clark Verbrugge

Modern 3D game levels rely heavily on visual guidance, yet the navigability of level layouts remains difficult to quantify. Prior work either simulates play in simplified environments or analyzes static screenshots for visual affordances, but neither setting faithfully captures how players explore complex, real-world game levels. In this paper, we build on an existing open-source visual affordance detector and instantiate a screen-only exploration and navigation agent that operates purely from visual affordances. Our agent consumes live game frames, identifies salient interest points, and drives a simple finite-state controller over a minimal action space to explore Dark Souls-style linear levels and attempt to reach expected goal regions. Pilot experiments show that the agent can traverse most required segments and exhibits meaningful visual navigation behavior, but also highlight that limitations of the underlying visual model prevent truly comprehensive and reliable auto-navigation. We argue that this system provides a concrete, shared baseline and evaluation protocol for visual navigation in complex games, and we call for more attention to this necessary task. Our results suggest that purely vision-based sense-making models, with discrete single-modality inputs and without explicit reasoning, can effectively support navigation and environment understanding in idealized settings, but are unlikely to be a general solution on their own.

Kaijie Xu, Yiwei Zhang, Brian Yang et al.

Open-world missions often rely on repeated formulas, yet designers lack systematic ways to examine pacing, variation, and experiential balance across large portfolios. We introduce the Mission Action Quality Vector (MAQV), a six-dimensional framework-covering combat, exploration, narrative, emotion, problem-solving, and uniqueness-paired with an action block grammar representing missions as gameplay sequences. Using about 2200 missions from 20 AAA titles, we apply LLM-assisted parsing to convert community walkthroughs into structured action sequences and score them with MAQV. An interactive dashboard enables designers to reveal underlying mission formulas. In a mixed-methods study with experienced players and designers, we validate the pipeline's fidelity and the tool's usability, and use thematic analysis to identify recurring design trade-offs, pacing grammars, and systematic differences by quest type and franchise evolution. Our work offers a reproducible analytical workflow, a data-driven visualization tool, and reflective insights to support more balanced, varied mission design at scale.

Kaijie Xu, Fandi Meng, Clark Verbrugge et al.

In Social Deduction Games (SDGs) such as Avalon, Mafia, and Werewolf, players conceal their identities and deliberately mislead others, making hidden-role inference a central and demanding task. Accurate role identification, which forms the basis of an agent's belief state, is therefore the keystone for both human and AI performance. We introduce CSP4SDG, a probabilistic, constraint-satisfaction framework that analyses gameplay objectively. Game events and dialogue are mapped to four linguistically-agnostic constraint classes-evidence, phenomena, assertions, and hypotheses. Hard constraints prune impossible role assignments, while weighted soft constraints score the remainder; information-gain weighting links each hypothesis to its expected value under entropy reduction, and a simple closed-form scoring rule guarantees that truthful assertions converge to classical hard logic with minimum error. The resulting posterior over roles is fully interpretable and updates in real time. Experiments on three public datasets show that CSP4SDG (i) outperforms LLM-based baselines in every inference scenario, and (ii) boosts LLMs when supplied as an auxiliary "reasoning tool." Our study validates that principled probabilistic reasoning with information theory is a scalable alternative-or complement-to heavy-weight neural models for SDGs.

Kaijie Xu, Clark Verbrugge

Procedural content generation (PCG) has made substantial progress in shaping static 2D/3D geometry, while most methods treat gameplay mechanics as auxiliary and optimize only over space. We argue that this limits controllability and expressivity, and formally introduce High-Dimensional PCG (HDPCG): a framework that elevates non-geometric gameplay dimensions to first-class coordinates of a joint state space. We instantiate HDPCG along two concrete directions. Direction-Space augments geometry with a discrete layer dimension and validates reachability in 4D (x,y,z,l), enabling unified treatment of 2.5D/3.5D mechanics such as gravity inversion and parallel-world switching. Direction-Time augments geometry with temporal dynamics via time-expanded graphs, capturing action semantics and conflict rules. For each direction, we present three general, practicable algorithms with a shared pipeline of abstract skeleton generation, controlled grounding, high-dimensional validation, and multi-metric evaluation. Large-scale experiments across diverse settings validate the integrity of our problem formulation and the effectiveness of our methods on playability, structure, style, robustness, and efficiency. Beyond quantitative results, Unity-based case studies recreate playable scenarios that accord with our metrics. We hope HDPCG encourages a shift in PCG toward general representations and the generation of gameplay-relevant dimensions beyond geometry, paving the way for controllable, verifiable, and extensible level generation.

Kaijie Xu, Clark Verbrugge

Large scale control of nonplayer agents is central to modern games, while production systems still struggle to balance several competing goals: locally smooth, natural behavior, and globally coordinated variety across space and time. Prior approaches rely on handcrafted rules or purely stochastic triggers, which either converge to mechanical synchrony or devolve into uncorrelated noise that is hard to tune. Continuous noise signals such as Perlin noise are well suited to this gap because they provide spatially and temporally coherent randomness, and they are already widely used for terrain, biomes, and other procedural assets. We adapt these signals for the first time to large scale AI control and present a general framework that treats continuous noise fields as an AI coordinator. The framework combines three layers of control: behavior parameterization for movement at the agent level, action time scheduling for when behaviors start and stop, and spawn or event type and feature generation for what appears and where. We instantiate the framework reproducibly and evaluate Perlin noise as a representative coordinator across multiple maps, scales, and seeds against random, filtered, deterministic, neighborhood constrained, and physics inspired baselines. Experiments show that coordinated noise fields provide stable activation statistics without lockstep, strong spatial coverage and regional balance, better diversity with controllable polarization, and competitive runtime. We hope this work motivates a broader exploration of coordinated noise in game AI as a practical path to combine efficiency, controllability, and quality.

Kaijie Xu, Clark Verbrugge

In complex 3D game environments, players rely on visual affordances to spot map transition points. Efficient identification of such points is important to client-side auto-mapping, and provides an objective basis for evaluating map cue presentation. In this work, we formalize the task of detecting traversable Spatial Transition Points (STPs)-connectors between two sub regions-and selecting the singular Main STP (MSTP), the unique STP that lies on the designer-intended critical path toward the player's current macro-objective, from a single game frame, proposing this as a new research focus. We introduce a two-stage deep-learning pipeline that first detects potential STPs using Faster R-CNN and then ranks them with a lightweight MSTP selector that fuses local and global visual features. Both stages benefit from parameter-efficient adapters, and we further introduce an optional retrieval-augmented fusion step. Our primary goal is to establish the feasibility of this problem and set baseline performance metrics. We validate our approach on a custom-built, diverse dataset collected from five Action RPG titles. Our experiments reveal a key trade-off: while full-network fine-tuning produces superior STP detection with sufficient data, adapter-only transfer is significantly more robust and effective in low-data scenarios and for the MSTP selection task. By defining this novel problem, providing a baseline pipeline and dataset, and offering initial insights into efficient model adaptation, we aim to contribute to future AI-driven navigation aids and data-informed level-design tools.

Kaijie Xu, Clark Verbrugge

Procedural Content Generation for 3D game levels faces challenges in balancing spatial coherence, navigational functionality, and adaptable gameplay progression across multi-floor environments. This paper introduces a novel framework for generating such levels, centered on the offline, LLM-assisted construction of reusable databases for architectural components (facilities and room templates) and gameplay mechanic elements. Our multi-phase pipeline assembles levels by: (1) selecting and arranging instances from the Room Database to form a multi-floor global structure with an inherent topological order; (2) optimizing the internal layout of facilities for each room based on predefined constraints from the Facility Database; and (3) integrating progression-based gameplay mechanics by placing components from a Mechanics Database according to their topological and spatial rules. A subsequent two-phase repair system ensures navigability. This approach combines modular, database-driven design with constraint-based optimization, allowing for systematic control over level structure and the adaptable pacing of gameplay elements. Initial experiments validate the framework's ability in generating diverse, navigable 3D environments and its capability to simulate distinct gameplay pacing strategies through simple parameterization. This research advances PCG by presenting a scalable, database-centric foundation for the automated generation of complex 3D levels with configurable gameplay progression.

Kaijie Xu, Clark Verbrugge

Guard patrol behavior is central to the immersion and strategic depth of stealth games, while most existing systems rely on hand-crafted routes or specialized logic that struggle to balance coverage efficiency and responsive pursuit with believable naturalness. We propose a generic, fully explainable, training-free framework that integrates global knowledge and local information via Composite Potential Fields, combining three interpretable maps-Information, Confidence, and Connectivity-into a single kernel-filtered decision criterion. Our parametric, designer-driven approach requires only a handful of decay and weight parameters-no retraining-to smoothly adapt across both occupancy-grid and NavMesh-partition abstractions. We evaluate on five representative game maps, two player-control policies, and five guard modes, confirming that our method outperforms classical baseline methods in both capture efficiency and patrol naturalness. Finally, we show how common stealth mechanics-distractions and environmental elements-integrate naturally into our framework as sub modules, enabling rapid prototyping of rich, dynamic, and responsive guard behaviors.

Kaijie Xu

Bi-clustering refers to the task of finding sub-matrices (indexed by a group of columns and a group of rows) within a matrix of data such that the elements of each sub-matrix (data and features) are related in a particular way, for instance, that they are similar with respect to some metric. In this paper, after analyzing the well-known Cheng and Church (CC) bi-clustering algorithm which has been proved to be an effective tool for mining co-expressed genes. However, Cheng and Church bi-clustering algorithm and summarizing its limitations (such as interference of random numbers in the greedy strategy; ignoring overlapping bi-clusters), we propose a novel enhancement of the adaptive bi-clustering algorithm, where a shielding complex sub-matrix is constructed to shield the bi-clusters that have been obtained and to discover the overlapping bi-clusters. In the shielding complex sub-matrix, the imaginary and the real parts are used to shield and extend the new bi-clusters, respectively, and to form a series of optimal bi-clusters. To assure that the obtained bi-clusters have no effect on the bi-clusters already produced, a unit impulse signal is introduced to adaptively detect and shield the constructed bi-clusters. Meanwhile, to effectively shield the null data (zero-size data), another unit impulse signal is set for adaptive detecting and shielding. In addition, we add a shielding factor to adjust the mean squared residue score of the rows (or columns), which contains the shielded data of the sub-matrix, to decide whether to retain them or not. We offer a thorough analysis of the developed scheme. The experimental results are in agreement with the theoretical analysis. The results obtained on a publicly available real microarray dataset show the enhancement of the bi-clusters performance thanks to the proposed method.

Kaijie Xu, Witold Pedrycz, Zhiwu Li et al.

Traditional clustering methods are limited when dealing with huge and heterogeneous groups of gene expression data, which motivates the development of bi-clustering methods. Bi-clustering methods are used to mine bi-clusters whose subsets of samples (genes) are co-regulated under their test conditions. Studies show that mining bi-clusters of consistent trends and trends with similar degrees of fluctuations from the gene expression data is essential in bioinformatics research. Unfortunately, traditional bi-clustering methods are not fully effective in discovering such bi-clusters. Therefore, we propose a novel bi-clustering method by involving here the theory of Granular Computing. In the proposed scheme, the gene data matrix, considered as a group of time series, is transformed into a series of ordered information granules. With the information granules we build a characteristic matrix of the gene data to capture the fluctuation trend of the expression value between consecutive conditions to mine the ideal bi-clusters. The experimental results are in agreement with the theoretical analysis, and show the excellent performance of the proposed method.

Kaijie Xu, Witold Pedrycz, Zhiwu Li

Information granules have been considered to be the fundamental constructs of Granular Computing (GrC). As a useful unsupervised learning technique, Fuzzy C-Means (FCM) is one of the most frequently used methods to construct information granules. The FCM-based granulation-degranulation mechanism plays a pivotal role in GrC. In this paper, to enhance the quality of the degranulation (reconstruction) process, we augment the FCM-based degranulation mechanism by introducing a vector of fuzzification factors (fuzzification factor vector) and setting up an adjustment mechanism to modify the prototypes and the partition matrix. The design is regarded as an optimization problem, which is guided by a reconstruction criterion. In the proposed scheme, the initial partition matrix and prototypes are generated by the FCM. Then a fuzzification factor vector is introduced to form an appropriate fuzzification factor for each cluster to build up an adjustment scheme of modifying the prototypes and the partition matrix. With the supervised learning mode of the granulation-degranulation process, we construct a composite objective function of the fuzzification factor vector, the prototypes and the partition matrix. Subsequently, the particle swarm optimization (PSO) is employed to optimize the fuzzification factor vector to refine the prototypes and develop the optimal partition matrix. Finally, the reconstruction performance of the FCM algorithm is enhanced. We offer a thorough analysis of the developed scheme. In particular, we show that the classical FCM algorithm forms a special case of the proposed scheme. Experiments completed for both synthetic and publicly available datasets show that the proposed approach outperforms the generic data reconstruction approach.

Kaijie Xu, Witold Pedrycz, Zhiwu Li et al.

As an important technology in artificial intelligence Granular Computing (GrC) has emerged as a new multi-disciplinary paradigm and received much attention in recent years. Information granules forming an abstract and efficient characterization of large volumes of numeric data have been considered as the fundamental constructs of GrC. By generating prototypes and partition matrix, fuzzy clustering is a commonly encountered way of information granulation. Degranulation involves data reconstruction completed on a basis of the granular representatives. Previous studies have shown that there is a relationship between the reconstruction error and the performance of the granulation process. Typically, the lower the degranulation error is, the better performance of granulation is. However, the existing methods of degranulation usually cannot restore the original numeric data, which is one of the important reasons behind the occurrence of the reconstruction error. To enhance the quality of degranulation, in this study, we develop an augmented scheme through modifying the partition matrix. By proposing the augmented scheme, we dwell on a novel collection of granulation-degranulation mechanisms. In the constructed approach, the prototypes can be expressed as the product of the dataset matrix and the partition matrix. Then, in the degranulation process, the reconstructed numeric data can be decomposed into the product of the partition matrix and the matrix of prototypes. Both the granulation and degranulation are regarded as generalized rotation between the data subspace and the prototype subspace with the partition matrix and the fuzzification factor. By modifying the partition matrix, the new partition matrix is constructed through a series of matrix operations. We offer a thorough analysis of the developed scheme. The experimental results are in agreement with the underlying conceptual framework