💬 NLP

Eigenmood Space: Uncertainty-Aware Spectral Graph Analysis of Psychological Patterns in Classical Persian Poetry

This paper introduces "Eigenmood Space," an uncertainty-aware computational framework that analyzes psychological patterns in classical Persian poetry by aggregating confidence-weighted multi-label annotations into spectral graph embeddings, thereby enabling scalable, auditable, and interpretively cautious poet-level inference while explicitly propagating evidence uncertainty.

Original authors: Kourosh Shahnazari, Seyed Moein Ayyoubzadeh, Mohammadali Keshtparvar

Published 2026-02-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Kourosh Shahnazari, Seyed Moein Ayyoubzadeh, Mohammadali Keshtparvar

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a massive library containing thousands of poems written in Persian over the last thousand years. These poems are famous for being beautiful, but also incredibly tricky. They don't say "I am sad" directly; instead, they might say, "The night is dark, and my heart is a broken mirror."

For centuries, experts have had to read these poems one by one, using their intuition to guess the feelings behind the metaphors. But what if you wanted to compare the "emotional fingerprints" of ten different poets across 60,000 poems? Reading them all manually would take a lifetime.

This paper presents a new digital detective tool called Eigenmood Space. Here is how it works, explained simply:

1. The Problem: The "Maybe" Factor

If you ask a standard computer to read these poems, it might confidently say, "This poem is about love!" even when the poem is actually about spiritual confusion. In poetry, being too confident is dangerous.

The authors realized that to do this right, the computer needs to know when it doesn't know.

The Analogy: Imagine a student taking a difficult test. A bad student guesses wildly and gets everything wrong. A smart student knows when to leave a question blank and write "I'm not sure."
The Solution: This system forces the AI to do the same. If a poem is too vague or metaphorical, the AI says, "I abstain" (I'm not sure). It treats this "I don't know" as valuable data, not a mistake.

2. The Process: Weighing the Evidence

The researchers fed 61,573 verses into the system. For every poem, the AI did three things:

Tagged it with psychological concepts (like "Melancholy," "Romantic Obsession," or "Spiritual Narcissism").
Gave a confidence score (e.g., "I'm 80% sure this is about sadness").
Decided to abstain if the poem was too confusing (which happened in 22% of the cases!).

The Creative Analogy: Think of this like a courtroom.

Old way: Every witness (poem) gets one vote.
New way: Every witness gets a vote, but the weight of their vote depends on how sure they are. A witness who says, "I saw the suspect, I'm 90% sure," counts for more than one who says, "Maybe I saw someone, I'm 50% sure." If a witness says, "I wasn't there," their vote is ignored entirely.

3. The Map: "Eigenmood Space"

Once the data was collected, the researchers built a map.

The Baseline: First, they calculated the "average mood" of all the poets combined. This is the "center of the map."
The Divergence: They measured how far each poet strayed from this average.
- Hafez (a very famous poet) was found to be very close to the center. His poetry is a perfect balance of all the common themes. He is the "average" Persian poet.
- Khayyam (another famous poet) was found to be far away on the edge of the map. His poetry is unique, leaning heavily into "Identity Fragmentation" (feeling split inside) and "Melancholy," while avoiding "Romantic Obsession."

The Analogy: Imagine a group of friends at a party.

Most friends are standing in the middle of the room chatting about normal things (The Baseline).
One friend (Khayyam) is standing in the corner, staring at the ceiling, thinking about the meaning of life and death.
Another friend (Parvin) is standing on a table, lecturing everyone about morality.
The tool measures exactly how far and in what direction each poet is standing from the group.

4. The "Spectral" Magic (The Eigenmood)

The most clever part is how they connected the dots. They didn't just look at single emotions; they looked at how emotions dance together.

They built a graph showing that "Sadness" often appears with "Longing," but rarely with "Arrogance."
They used a mathematical trick (Spectral Graph Analysis) to find the "hidden axes" of this dance.
The Result: They created a 3D coordinate system (Eigenmood). Instead of just saying "Poet A is sad," they can say, "Poet A is sad in a specific direction that combines sadness with a sense of broken identity."

5. Why This Matters

This isn't just about counting words. It's about respecting the mystery of poetry.

Auditable: If a human scholar wants to check the computer's work, they can click on a poet's "unique spot" on the map and see the exact poems that put them there.
Safe: By admitting when it's unsure (abstaining), the system avoids making up fake psychological diagnoses for dead poets. It says, "Here is the evidence we have, and here is where we are unsure."

Summary

The authors built a smart, humble AI that reads thousands of ancient Persian poems. Instead of forcing a simple label on complex art, it weighs the evidence, admits when it's confused, and draws a 3D map showing how each poet's emotional world is unique compared to the rest. It turns the "feeling" of poetry into a measurable, visual landscape, all while keeping the door open for human experts to interpret the nuances.

1. Problem Statement

Classical Persian poetry represents a vast, historically sustained archive of affective life expressed through metaphor, intertextuality, and rhetorical indirection. While this richness makes "close reading" indispensable, it creates significant barriers for reproducible, large-scale computational analysis.

The Challenge: Standard sentiment analysis or fixed-lexicon approaches fail to capture the layered, non-literal nature of poetic emotion (e.g., a single couplet expressing both longing and renunciation).
The Epistemic Risk: Applying modern psychological constructs to pre-modern texts risks anachronism and overconfident labeling. Furthermore, ignoring the inherent ambiguity of poetry can lead to spurious statistical patterns if uncertainty is not explicitly modeled.
The Gap: There is a lack of frameworks that scale computational analysis to the poet level while preserving uncertainty propagation (abstention and confidence) and capturing the relational structure of affective concepts beyond simple marginal distributions.

2. Methodology

The authors propose an uncertainty-aware computational framework that transforms verse-level annotations into poet-level psychological profiles. The workflow consists of four main stages:

A. Data and Annotation

Corpus: 61,573 verses from 10 classical Persian poets (including Hafez, Saadi, Khayyam, and Parvin) sourced from the Ganjoor digital corpus.
LLM Annotation: Verses were annotated using Gemini 2.5 Flash as a multi-label classifier against a 9-label psychological ontology (e.g., Melancholia, Emotional Dependency, Identity Fragmentation, Spiritual Narcissism).
Uncertainty Signals: The model was instructed to output:
1. Labels: A set of applicable concepts.
2. Confidence Scores: Graded probabilities ( $p_{v,c} \in [0,1]$ ) for each label.
3. Abstention Flag: An explicit signal ( $a_v=1$ ) when the model cannot reliably link the verse to the ontology (treating ambiguity as "non-commitment" rather than negative evidence).
Validation: A stratified 500-verse sample was validated by two psychology domain experts, achieving a macro Cohen's $\kappa$ of 0.818 and an F1 score of 0.794 against the adjudicated reference.

B. Uncertainty-Aware Aggregation

Poet $\times$ Concept Matrix ( $X$ ): Instead of simple counting, the authors aggregate confidence-weighted concept mass.
$X_{i,c} = \sum_{v \in V_i} (1 - a_v) \cdot p_{v,c} \cdot \mathbb{1}[c \in L_v]$
This ensures that uncertain or low-confidence labels contribute less to the final profile.
Probability Distributions: Each poet is represented as a probability distribution $P_i(c)$ over concepts (via row normalization with additive smoothing), compared against a global corpus baseline $P_0(c)$ .

C. Quantifying Individuality (Divergence)

Poet individuality is measured as the divergence from the global baseline using Jensen–Shannon Divergence (JSD) and Kullback–Leibler (KL) Divergence.
This provides a reproducible metric for how distinct a poet's rhetorical-affective patterns are compared to the tradition as a whole.

D. Spectral Graph Analysis (Eigenmood Space)

To capture relational structure (how concepts co-occur), a confidence-weighted co-occurrence graph is built where edge weights represent the strength of concept coupling.
Laplacian Spectral Decomposition: The graph Laplacian is decomposed to derive Eigenmood embeddings.
- Unlike PCA (which finds variance in marginal prevalence), Eigenmood axes represent directions of deviation informed by the empirical coupling of concepts.
- Poets are projected onto these axes ( $z_i^{(k)}$ ), allowing for the retrieval of verses that exemplify specific spectral directions (e.g., "Internal Projection vs. Identity Fragmentation").

E. Robustness and Bias Diagnostics

Thresholding: The framework tests stability by filtering out low-confidence labels ( $\tau \ge 0.5, 0.7$ ).
Selection Bias Analysis: Abstention is treated as an explicit category to measure how "missingness" affects poet rankings.
Bootstrap Uncertainty: Non-parametric bootstrapping is used to estimate confidence intervals for divergence scores, particularly for poets with smaller subcorpora.

3. Key Results

Substantial Uncertainty: 22.2% of verses were abstained (13,678 verses), with "no clear psychological signal" being the primary reason. This underscores that uncertainty is a structural feature of the data, not a marginal edge case.
Poet Individuality:
- Khayyam emerged as the most divergent poet ( $D_{JS} = 0.0901$ ), characterized by high Melancholia and Identity Fragmentation but low Emotional Dependency.
- Parvin was the second most divergent ( $D_{JS} = 0.0459$ ), showing high Self-Destructive Idealization and Melancholia.
- Hafez and Shahriar were closest to the baseline, suggesting their affective patterns are representative of the broader corpus norms.
Stability: Individuality rankings remained highly stable ( $\rho > 0.96$ ) even under strict confidence thresholding ( $\tau=0.7$ ) and when switching between confidence-weighted and uniform weighting, validating the robustness of the findings.
Spectral Geometry: The Eigenmood embedding revealed distinct axes:
- EM1: Contrasts Spiritual Narcissism (rhetorical self-distinction) vs. Melancholia/Ambivalent Attachment (sorrowful dependence).
- EM2: Contrasts Internal Projection (inward localization) vs. Identity Fragmentation (paradoxical self).
- EM3: Contrasts Ambivalent Attachment (oscillatory discourse) vs. Identity Fragmentation/Internal Projection.
Selection Bias: Treating abstention as a category shifted the rankings of mid-tier poets (e.g., Eraghi became more distinctive when abstention was included due to his low abstention rate), proving that "missing data" carries meaningful structural information.

4. Key Contributions

Uncertainty-Aware Aggregation: A novel method for aggregating LLM outputs in digital humanities that treats abstention and confidence as first-class variables, preventing ambiguity from being converted into spurious evidence.
Eigenmood Embedding: The introduction of a spectral graph approach to define a "psychological space" where axes are derived from concept co-occurrence rather than just marginal frequency, capturing the relational nature of poetic affect.
Distant-to-Close Workflow: A scalable pipeline that links macro-level poet profiles to micro-level verse retrieval. The system can retrieve specific verses that exemplify a poet's position in the Eigenmood space, providing auditable evidence for computational claims.
Epistemically Modest Framework: The paper explicitly frames its output as operational constructs for comparative analysis rather than clinical diagnoses, addressing the anachronism risk of applying modern psychology to historical texts.

5. Significance and Implications

For Digital Humanities (DH): This work bridges the gap between "distant reading" (statistical aggregation) and "close reading" (interpretive nuance). By propagating uncertainty, it allows scholars to make scalable claims without sacrificing interpretive caution.
For Computational Psychology: It demonstrates how to model "cultural psychology" in literary texts—analyzing the distribution of rhetorical-affective patterns rather than private mental states.
Methodological Rigor: The inclusion of selection-bias diagnostics, bootstrap uncertainty intervals, and human validation sets a new standard for reliability in LLM-based literary analysis.
Cultural Insight: The framework reveals that while many poets share a common "baseline" of melancholic and obsessive themes, outliers like Khayyam and Parvin utilize distinct rhetorical-affective configurations (e.g., existential fragmentation vs. didactic sacrifice) that define their unique literary signatures.

In summary, Eigenmood Space provides a rigorous, auditable, and uncertainty-aware methodology for analyzing the psychological dimensions of classical literature, transforming the challenge of poetic ambiguity from a barrier into a quantifiable feature of the analysis.