Real-Time Three-Way Classification

• Real-time three-way classification is defined as systems that rapidly assign streaming data to one of three classes, ensuring low latency and adaptability in dynamic scenarios.
• Unified methodologies like vector-space encoding, Bayesian models, and triplet embeddings enhance accuracy across domains such as astrophysics, telecommunications, and conflict analysis.
• Efficient deployment is achieved via microservices, compact models, and robust handling of missing or imbalanced data, enabling real-time updates in resource-constrained environments.

Real-time three-way classification refers to algorithms and systems capable of assigning a newly observed instance to one of three categories with low latency, under constraints inherent to streaming or event-driven environments. The three categories may be problem-specific (e.g., signal, anomaly, other), may emerge from three-way decision theory (accept/reject/neutral), or may correspond to multiclass frameworks where the classifier must rapidly and accurately resolve among three possible classes or paradigms in a unified way. This capability is crucial in domains such as event monitoring, real-time communication, scientific instrumentation, and conflict analysis, where prompt and accurate classification is required for effective decision making or resource allocation.

1. Formal Models and Unification Across Paradigms

Real-time three-way classification encompasses a variety of formal approaches:

• Unified Output Representation: The online universal classifier of Ashfahani and Pratama (Er et al., 2016) encodes all labels as $L$-dimensional binary vectors. Binary, multi-class, and multi-label problems are uniformly addressed by maintaining a mapping $f: \mathbb{R}^n \to \mathbb{R}^L$, where the postprocessing step (elementwise Heaviside) yields direct assignment to exactly one, several, or none of the $L$ labels, according to the count of active entries. The classification regime is determined online, and all update and inference routines are agnostic to the paradigm.
• Three-Way Decision Theory: The TWDCAMs (Three-Way Decisions-Based Conflict Analysis Models) trisect a universe of objects (agents or issues) into agreement (POS), disagreement (NEG), and neutral (BND) subsets according to evaluation functions and thresholded acceptance/rejection regions (Lang, 2019). These models subsume earlier special cases (SMZCAM, FQWCAM) and support dynamic, real-time implementation through O(1)-complexity updates where new evidence or votes are incorporated instantaneously.
• Bayesian Multiclassification and Event Filtering: In astrophysics, Mahabal et al. (Mahabal et al., 2011) realized real-time three-way classification among supernovae, cataclysmic variables, and blazars by leveraging a Bayesian framework with joint density modeling of observational increments. Each class is associated with separate prior and likelihood components, allowing probabilistic discrimination in under two seconds per event in the CRTS pipeline.

These formalizations enable a unified treatment of three-way classification under both supervised and semi-supervised learning, in both batch and online regimes. The choice of framework—vector-space encoding, probabilistic modeling, or explicit decision sets—is domain-dependent and often dictated by the structure of input features and the semantic meaning of the three categories.

2. Core Methodologies

Multiple architectures have been successfully deployed for real-time three-way classification, tailored to streaming and high-throughput demands:

• Online Extreme Learning Machines (ELM): A single-hidden-layer feedforward network with fixed random input weights and output weights updated via recursive least squares provides the backbone in (Er et al., 2016). Label vectors are treated uniformly, and the Heaviside threshold plus count of active outputs determines the three-way paradigm. Key steps include initial block least-squares fit, followed by per-sample or mini-batch recursive updates for rapid adaptation.
• Triplet-network and Few-shot Embedding: In SpeckleNN (Wang et al., 2023), a twin (triplet) neural network backbone embeds input patterns into a normalized space optimized via triplet loss. Three-way classification proceeds by comparing the distance of query embeddings to class prototypes computed from sparse, labeled support sets. Adjustment for new classes is achieved by simply extending the support set and prototype pool, with no retraining.
• Probabilistic/Bayesian Event Classification: The CRTS pipeline (Mahabal et al., 2011) models feature likelihoods for each of three astrophysical event types, combining color, contextual, and empirical light-curve likelihoods within a Bayesian updating rule for online decision making. Missing or incomplete features are handled by dropping unmatched terms, maintaining robustness in event-driven environments.
• Efficient Low-latency Models via Knowledge Distillation: In voice communications, real-time three-way classification is achieved by distilling a high-capacity CNN into gradient-boosted trees (LightGBM), achieving sub-2ms inference per 1s audio window and >98% transfer accuracy on coarse class assignments (Altwlkany et al., 28 Oct 2024). Knowledge distillation with class aggregation (from, e.g., 527 AudioSet classes to three coarse categories) allows for major computational savings and seamless adaptation.
• Compact 1D Convolutional Neural Networks (CNN) for Signal Data: The LibIQ framework (Olimpieri et al., 15 May 2025) employs a streamlined 1D-CNN with three convolutional blocks, global average pooling, and a 3-class softmax head for RF spectrum classification. Accurate three-way assignment is achieved in <2 ms total latency, suitable for strict O-RAN network timing constraints.
• Three-Way Decision Rules via Evaluation Functions: TWDCAMs proceed by maintaining two evaluation functions (acceptance and rejection evaluations), classifying objects into three regions via two thresholds (Lang, 2019). These rules reduce to simply checking two inequalities after each real-time update.

3. Real-Time Requirements, System Integration, and Scalability

Across domains, three-way classifiers must process high-velocity data streams, impose low computational overhead, and adapt to evolving distributions. Key system aspects include:

• Low Latency Updates and Prediction: The online universal classifier (Er et al., 2016) achieves update times <1 ms/sample, with post-processing to detect the classification regime in O(L) time. LibIQ (Olimpieri et al., 15 May 2025) demonstrates end-to-end latency <4 ms for RF sample classification in O-RAN, with componentwise breakdown for each stage. Voice classification with distilled LightGBM models (Altwlkany et al., 28 Oct 2024) attains ≳580 samples/s throughput even on CPU.
• Microservice and Event-driven Deployment: Real-time transient classification in CRTS (Mahabal et al., 2011) and large-scale dApp-based signal detection (Olimpieri et al., 15 May 2025) are implemented as microservices communicating via queues for scalable pipeline execution and parallel feature extraction.
• Adaptivity and Feedback Loops: The CRTS pipeline incorporates nightly retraining from operator and crowd feedback, distributed microservice deployment, and automatic adjustment of priors for class balance. TWDCAMs admit immediate O(1) updates per evidence arrival, supporting live reclassification upon each new event.
• Resource Constraints and Edge Deployability: Compact model design (LightGBM, shallow CNNs) and class aggregation techniques permit deployment on resource-constrained hardware (e.g., edge nodes in O-RAN, telephony data centers) without sacrificing accuracy (Altwlkany et al., 28 Oct 2024, Olimpieri et al., 15 May 2025).

4. Empirical Performance and Evaluation Metrics

Empirical assessment consistently demonstrates that state-of-the-art three-way classifiers closely match or exceed the accuracy of specialized baseline models, while providing substantial gains in latency and adaptability:

System / Paper	Task/Domain	Overall Accuracy	Latency / Throughput
Ashfahani & Pratama (Er et al., 2016)	Binary, multi-class, multi-label streams	±1–3% of best baseline	<1 ms/sample (train), <10 ms/test
Mahabal et al. (Mahabal et al., 2011)	Optical transient classification	>85% average recall	≲2 s/inference, 100 events/minute
SpeckleNN (Wang et al., 2023)	SPI speckle pattern, 3-way	98% (full), 94% (gappy)	2 ms/pattern (GPU), 100+ patterns/s (CPU)
Infobip/Audio (Altwlkany et al., 28 Oct 2024)	Early media (audio), 3-way	99.3% overlap teacher	1.7 ms (LightGBM), 68 ms (CNN)
LibIQ (Olimpieri et al., 15 May 2025)	RF spectrum, 3-way	97.8% average	0.9–2.3 ms inference, <10 ms end-to-end

Additional metrics include Hamming loss (multi-label), macro-F₁ scores (imbalanced data), precision/recall/FPR per class, robustness to missing data (random masking in SpeckleNN (Wang et al., 2023)), and resource utilization (CPU load, RAM footprint).

5. Handling of Missing, Imbalanced, and Dynamic Data

Real-time three-way classification systems incorporate explicit strategies for addressing unreliable or incomplete input and nonstationary class distributions:

• Imbalanced Classes: Initial class priors are adjusted via Dirichlet hyper-priors or periodic reestimation based on observed frequencies (Mahabal et al., 2011). Synthetic resampling/oversampling (SMOTE-like) techniques are applied in feature subspace for rare class support.
• Missing Data: In CRTS (Mahabal et al., 2011), absence of certain features (e.g., missing color photometry) leads to the omission of the corresponding likelihood factor; posteriors are renormalized over observed features only.
• Concept Drift and Nonstationarity: While the ELM-based classifier (Er et al., 2016) does not include built-in drift detection, the architecture supports potential extensions via decay factors or drift detectors. CRTS pipelines retrain likelihoods and priors based on ongoing feedback. TWDCAMs update sufficient statistics incrementally, ensuring instant adaptation.
• Robustness to Sparsity: SpeckleNN (Wang et al., 2023) is inherently robust to sparsity via random masking; accuracy deteriorates by only 4% under 75% detector masking.

6. Extensions, Limitations, and Theoretical Underpinnings

Real-time three-way classification approaches benefit from substantial extensibility but are subject to technical and theoretical constraints:

• Limitations: Matrix update costs in ELM-based methods scale quadratically with hidden size (Er et al., 2016); random initialization can affect stability and accuracy, requiring tuning. Concept drift and long-term memory are largely unsupported natively.
• Extensions: Sparse or budgeted online updates, kernelization, semi-supervised extensions, active querying strategies, and integration with external drift detectors are highlighted as practical avenues (Er et al., 2016).
• Generalization to Arbitrary Trisecting: The TWDCAM formalism (Lang, 2019) provides principled trisecting of universes via two evaluation functions, permitting adaptation of the methodology to scenarios outside classification, such as conflict analysis or multi-agent decision support.
• Model Specialization and Reduction: Theoretical results confirm that commonly used two-way decision models emerge as special cases in the three-way decision framework (Lang, 2019).

A plausible implication is that continued integration of evaluation-function-based partitioning and unified embedding techniques can further universalize real-time three-way classification, leading to modular, extensible systems adaptable to a broad spectrum of data modalities and operating constraints.

7. Application Domains and Deployment Practices

Real-time three-way classification has been deployed in diverse domains, each leveraging specific technical attributes of the core methodologies:

• Astronomy and Astrophysics: Near-real-time filtering and categorization of transient celestial phenomena (Mahabal et al., 2011).
• Voice and Media Communication: Discrimination of early media classes in VoIP and telephony, with minimal compute use (Altwlkany et al., 28 Oct 2024).
• X-ray and Photon Science: Classification of diffraction and speckle patterns in single-particle imaging datasets with scarce labels (Wang et al., 2023).
• Wireless Networking: O-RAN deployments for spectrum monitoring and interference/beamforming support (Olimpieri et al., 15 May 2025).
• Conflict Analysis and Social Science: Partitioning of agents/issues into agreement/disagreement/neutral trichotomies for decision support (Lang, 2019).

Best practices for application include modular pipeline decomposition, judicious selection of computational primitives (e.g., CNN blocks, GBT depth), class aggregation for problem-specific granularity, end-to-end latency monitoring, and continuous updating via operator or crowd-labeled feedback (Mahabal et al., 2011, Altwlkany et al., 28 Oct 2024).

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In summary, real-time three-way classification unifies methodologies and architectures that support low-latency, accurate assignment of streaming data or events into three paradigms, leveraging advances in universal output encoding, probabilistic modeling, twin-net embeddings, compact gradient-boosted models, and abstract decision-theoretic partitioning. State-of-the-art systems demonstrate that generality, efficiency, and adaptability can be simultaneously achieved across diverse, resource-constrained, and rapidly evolving domains (Er et al., 2016, Lang, 2019, Mahabal et al., 2011, Wang et al., 2023, Altwlkany et al., 28 Oct 2024, Olimpieri et al., 15 May 2025).