Emotional Dimensions: Valence, Arousal, Dominance

• Emotional dimensions are defined by valence (positivity), arousal (activation), and dominance (control), forming a continuous framework for affect analysis.
• Empirical studies and crowdsourced lexicons validate the VAD model's scalability and application across psychology, NLP, and computational social science.
• Advanced methodologies like regression, clustering, and multimodal fusion map discrete emotions to continuous VAD scores, enhancing sentiment analysis accuracy.

Emotional Dimensions: Valence, Arousal, and Dominance

The Valence–Arousal–Dominance (VAD) model, foundational to dimensional theories of affect, posits that human emotions can be systematically represented as points in a three-dimensional continuous space. Valence encodes the positivity or negativity (pleasure–displeasure) of an affective state, Arousal measures the level of physiological or psychological activation (calmness–excitement), and Dominance captures the sense of control versus submission (power–powerlessness). This trimodal structure, supported by extensive psychometric, neurophysiological, and computational studies, offers a scalable framework for emotion research in psychology, linguistics, NLP, affective computing, computational social science, and speech synthesis.

1. Theoretical Foundations and Dimensional Definitions

The VAD model arises from early psychometric factor analyses (Osgood et al., 1957), which identified three largely orthogonal factors (Evaluation, Potency, Activity) underlying human similarity judgments of affective language. Russell’s Core Affect theory refined these as Valence (pleasure–displeasure), Arousal (activation–deactivation), and subsequently Dominance (degree of control or agency) (Mohammad, 30 Mar 2025). Major lexicons and empirical studies (e.g., NRC VAD Lexicon v2, Warriner et al. 2013) anchor these dimensions as follows:

• Valence (V): Degree of positivity/negativity, e.g., “happy” (high V) vs. “sad” (low V).
• Arousal (A): Intensity or activation, e.g., “excited” (high A) vs. “bored” (low A).
• Dominance (D): Perceived agency or control, e.g., “powerful” (high D) vs. “helpless” (low D).

Scales are typically continuous: –1, 1, 1, 9, or [1, 5]/[1, 10] in annotation schemes (Mohammad, 30 Mar 2025, Mohammad, 25 Nov 2025, Buechel et al., 2022). Empirical distributions frequently show a positive bias in valence and substantial non-neutrality across all three axes.

2. Psychometric Evidence and Lexicon Development

Large-scale annotation projects employ crowdsourcing with rigorous quality control and aggregation protocols. The NRC VAD Lexicon v2 rates 55,133 English words and phrases on all three dimensions, using seven-point Likert scales mapped to [–1, 1] via linear rescaling:

$y_t = \frac{\bar x_t}{3}$

where $x_t$ is the mean raw annotation per term, and $y_t$ is the rescaled score (Mohammad, 30 Mar 2025, Mohammad, 25 Nov 2025). Split-half reliability (SHR) consistently exceeds 0.95 for all dimensions, confirming high annotation consistency. Multiword expressions (MWEs)—previously underrepresented—are now included, facilitating compositionality studies and enhancing NLP coverage (Mohammad, 25 Nov 2025).

Valence is the most compositionally predictable property (Pearson $r\approx0.72$) for MWEs compared to arousal ($r\approx0.58$) and dominance ($r\approx0.55$); however, semantic non-compositionality frequently emerges, indicating that idiomatic expressions have emergent affective properties (Mohammad, 25 Nov 2025).

3. Methodologies for Emotion Analysis and Cross-Model Mapping

Emotion detection in text, speech, and multimodal signals frequently relies on assigning VAD vectors to individual tokens or aggregated textual units. The standard approach computes weighted or unweighted centroidal means:

$$\bar e(d) = \frac{\sum_{w \in d} \lambda(w, d) e(w)}{\sum_{w \in d} \lambda(w, d)}$$

where $\lambda(w, d)$ is the frequency of word $w$ in document $d$, and $x_t$0 is its (V, A, D) vector (Buechel et al., 2019, Mohammad, 30 Mar 2025). Missing lexicon entries are treated as neutral.

Bridging between discrete and continuous affect models is operationalized through regression, clustering, and proxy-based mapping. Wrobel (2025) uses geometric animation proxies followed by self-assessed VAD ratings, yielding robust mappings for discrete labels such as "anger," "joy," and "fear" onto continuous VAD coordinates (Wrobel, 16 Nov 2025). Machine learning architectures (e.g., multimodal fusion models, deep embeddings, transformer-based classification, CAKE-3D representation) impose continuous VAD regression objectives and utilize clustering (e.g., K-means) to enable back-and-forth mapping with categorical classes (Kervadec et al., 2018, Jia et al., 2024, Park et al., 2019). Earth Mover's Distance (EMD) is adopted as a loss for learning ordered VAD targets (Park et al., 2019).

4. Applications Across Domains

4.1 Natural Language Processing and Sentiment Analysis

Lexicon-based and neural approaches leverage VAD for sentiment and emotion analysis at word, sentence, and document levels. EmoBank and NRC VAD Lexicon v2 provide foundational data for supervised and transfer learning in affective NLP (Mohammad, 30 Mar 2025, Buechel et al., 2022). VAD augmentation improves regression and classification accuracy, enables fine-grained affect tracking, and allows for the synthesis of emotion trajectories in long texts (Park et al., 2019, Buechel et al., 2019).

4.2 Speech Synthesis and Affective Computing

Text-to-speech systems can be conditioned on VAD or PAD (Pleasure–Arousal–Dominance) embeddings. Injection points within Tacotron and Transformer-based architectures have been systematically evaluated for style fidelity (Rabiee et al., 2019, Zhou et al., 2024). Interpolating or directly controlling VAD enables generation of a continuum of emotional prosodies, rather than limiting output to a small finite set of categories.

4.3 Organizational and Social Applications

Analysis of developer communications (e.g., Jira issue reports) reveals systematic links between issue priority, temporal evolution, and VAD trajectories, offering scalable indicators of burnout and productivity (Mäntylä et al., 2016). In institutional communication (e.g., central bank press releases), temporal VAD analysis uncovers latent affective arcs aligned with economic indicators and leadership transitions (Buechel et al., 2019).

4.4 LLMs and Representation Learning

Recent work demonstrates that LLMs encode a low-dimensional "emotional manifold" in their hidden states, where the leading principal components align with VAD axes. This internal representation is stable across layers, robust across languages and datasets, and manipulable via learned interventions without semantic degradation (Reichman et al., 24 Oct 2025).

5. Quantitative Properties, Mapping, and Model Evaluation

Across corpora, inter-annotator agreement on VAD (Pearson $x_t$1) routinely ranges from 0.54–0.74 depending on dimension and perspective, with reader-perspective VAD ratings yielding both more intensity and higher inter-rater reliability than writer-perspective (Buechel et al., 2022). Correlation between VAD and discrete categories, both via regression (e.g., k-NN mapping) and through open-vocabulary prediction, matches or exceeds human IAA for most basic emotions.

Experimental results in machine learning settings demonstrate:

• Substantial MSE and correlation improvements in VAD regression via multimodal data and fusion (Jia et al., 2024).
• Macro-F1 gains in discrete emotion classification upon adding the third dominance-like dimension to model bottlenecks (Kervadec et al., 2018).
• For speech synthesis, explicit PAD conditioning yields large improvements in naturalness and the range of affective rendering (Rabiee et al., 2019, Zhou et al., 2024).

Tables derived from recent work exemplify VAD scores of prototypical emotions and MWEs:

Emotion / MWE	Valence	Arousal	Dominance
anger	3.39	8.10	8.00
joy	7.36	7.56	6.49
sadness	3.79	2.99	3.57
"over the moon"	+0.92	+0.64	+0.55
"at the mercy of"	–0.65	–0.20	–0.90

Raw scores are lexicon-specific; normalization to [–1, 1] is standard for cross-system comparability (Wrobel, 16 Nov 2025, Mohammad, 25 Nov 2025).

6. Methodological Considerations and Future Directions

Lexicon-based approaches are limited by coverage, context insensitivity (e.g., negation, sarcasm, intensifiers), and cross-domain semantic drift (e.g., technical jargon in SE). Deep learning models may mitigate these issues via end-to-end training and context-aware representations but depend on high-quality VAD annotations and robust mapping procedures (Mohammad, 30 Mar 2025, Park et al., 2019).

Emerging research is extending VAD frameworks to MWEs, multimodal affect analysis, reversible and differentiable discrete–continuous mappings, and manipulation of affective subspaces in LLMs (Reichman et al., 24 Oct 2025, Mohammad, 25 Nov 2025, Jia et al., 2024). Cross-cultural and cross-linguistic validation, longitudinal affect tracking, compositional modeling, and integration with social cognition dimensions (e.g., warmth, competence) represent active frontiers.

7. Conceptual Impact and Broader Implications

The VAD model offers a unified framework for affect representation, supporting analysis, synthesis, and interpretation of emotions in language, vision, speech, and behavior. It enables bridging disparate data modalities and categorical schemes via continuous, interpretable measures, augments psychological theory with large-scale computational rigor, and underpins data-driven applications from conversational AI to well-being surveillance. Analysis along VAD dimensions has overturned assumptions about the emotive neutrality of institutional communication, improved machine understanding of nuanced affect, and exposed deep, directionally encoded affective subspaces in neural systems (Buechel et al., 2019, Reichman et al., 24 Oct 2025). The ongoing expansion of VAD lexica and resources, combined with methodological advancements in mapping and representation, continues to broaden the theoretical and practical scope of dimensional emotion research.