A Novel Mathematical Framework for Objective Characterization of Ideas
B. Sankar, Dibakar Sen
TL;DR
This work tackles the challenge of objectively evaluating the abundance of ideas generated by CAI systems and humans during ideation. It proposes a vector-embedding framework that converts ideas into high-dimensional representations, then uses UMAP, DBSCAN, and PCA to analyze the idea space for meaningful structure, dispersion, and clusters. Empirical results demonstrate semantic validity of embeddings, usefulness in aiding diverse idea selection by novices, and robust objective metrics for distribution and dispersion of ideas. The approach offers transparent, scalable, and reproducible evaluation that complements subjective judgments, with strong implications for accelerating the ideation phase in product design.
Abstract
The demand for innovation in product design necessitates a prolific ideation phase. Conversational AI (CAI) systems that use Large Language Models (LLMs) such as GPT (Generative Pre-trained Transformer) have been shown to be fruitful in augmenting human creativity, providing numerous novel and diverse ideas. Despite the success in ideation quantity, the qualitative assessment of these ideas remains challenging and traditionally reliant on expert human evaluation. This method suffers from limitations such as human judgment errors, bias, and oversight. Addressing this gap, our study introduces a comprehensive mathematical framework for automated analysis to objectively evaluate the plethora of ideas generated by CAI systems and/or humans. This framework is particularly advantageous for novice designers who lack experience in selecting promising ideas. By converting the ideas into higher dimensional vectors and quantitatively measuring the diversity between them using tools such as UMAP, DBSCAN and PCA, the proposed method provides a reliable and objective way of selecting the most promising ideas, thereby enhancing the efficiency of the ideation phase.