Interpretable Semantic Gradients in SSD: A PCA Sweep Approach and a Case Study on AI Discourse

Supervised Semantic Differential (SSD) is an emerging mixed-method approach designed to analyze how text semantics vary with individual difference variables. The method is inspired by long-standing psychological semantic differential methods that measure the connotative meaning of concepts via polar concept opposites (e.g., warm/cold, strong/weak) and by modern distributional semantics, where word embeddings model relational structure in language use. SSD combines these traditional and modern approaches by estimating a semantic gradient in an embedding space and interpreting its poles through clustering and text retrieval. Although SSD applies PCA to reduce redundant dimensions in small corpora, there is currently no systematic method for choosing the number of components to retain, introducing avoidable researcher degrees of freedom, increasing the risk of overfitting, reducing the transparency of the analysis pipeline, and potentially biasing substantive interpretations of the resulting semantic gradients.

SSD lacks a systematic standard for selecting PCA dimensions, leading to excessive researcher freedom, increased risk of overfitting, reduced analysis transparency, and potentially biased substantive interpretations of the resulting semantic gradients. While original results were relatively stable across similar component ranges, leaving the choice of dimensionality to the researcher introduces avoidable researcher degrees of freedom, thereby increasing the risk of overfitting, reducing the transparency of the analysis pipeline, and potentially biasing substantive interpretations of the resulting semantic gradients.

The paper introduces a novel PCA sweep approach to optimize dimension selection in SSD. This method selects the appropriate number of dimensions K by jointly optimizing representation capacity, gradient interpretability, and stability. Specifically, the PCA sweep evaluates a sequence of K values, fits SSD at each K, and tracks cluster coherence, gradient alignment, and result stability based on cosine differences. Unlike traditional methods, this approach considers not only representation capacity but also integrates gradient interpretability and stability, ensuring reliable semantic analysis.

• �� The PCA sweep method evaluates a sequence of K values and fits SSD at each K.
• �� Calculates cluster coherence at each K as an interpretability criterion.
• �� Assesses gradient alignment with clusters and result stability based on cosine differences.
• �� Selects the appropriate dimension K by jointly optimizing representation capacity, gradient interpretability, and stability.
• �� Applies plateau-sensitive smoothing using a local neighborhood average to emphasize broad, stable plateaus over sharp spikes.

The experimental design is based on a dataset of short posts about artificial intelligence written by Prolific participants who also completed Admiration and Rivalry narcissism scales. Tokenization and linguistic preprocessing were performed using spaCy, and embeddings were generated using the Dolma GloVe model. The PCA sweep method evaluates a sequence of K values, fits SSD at each K, and tracks cluster coherence, gradient alignment, and result stability based on cosine differences. The number of clusters was chosen by silhouette from a range, and other settings followed the original SSD configuration.

For the Admiration-related semantic gradient, the model explained 19% of the variance (R²_adj = 0.19, F = 6.32, p < 0.0001, r = 0.47), contrasting optimistic AI collaboration with distrustful and derisive discourse. The Rivalry model did not reach significance (R²_adj = 0.03, p = 0.095), indicating no robust semantic alignment for this trait. Comparison with a high-dimensional PCA solution showed it produced diffuse, weakly structured clusters, underscoring the value of the sweep-based choice of K.

The PCA sweep method can be directly applied in scenarios requiring analysis of text semantics in relation to individual differences, such as psychological research and social science studies. By reducing researcher degrees of freedom and enhancing analysis transparency and stability, this method provides a more reliable tool for semantic analysis in these fields.

The case study is based on a relatively small dataset of AI-related short posts, limiting the generalizability of semantic gradients to other populations and task contexts. The analysis operates at the level of whole-text representations rather than concept-specific lexicon-based PCVs, which may blur finer-grained semantic distinctions. The PCA sweep addresses only one source of flexibility in SSD, namely dimensionality selection, while other design choices like embedding model selection remain open. Future directions include developing similarly principled criteria for upstream modeling choices, particularly the selection of the embedding model.