We propose a clustering-analysis approach that addresses the bandpass filter (BPF) detection problem in the analysis of the peak position of the interference envelope in vertical-scanning wideband interferometry. Our approach exploits the fact that the fringe signal formed by a wideband light source is a superposition of deterministic fringe signals and noise. Consequently, two clusters can be specified in advance for use in the k-means clustering analysis. We describe our measurement procedure and its development using a two-means method-based spectrum selection scheme based on the constituent characteristics of interference fringes. The details of our approach are introduced within the framework of femtosecond optical frequency comb-based interferometry. Our experimental results demonstrate the superiority of the proposed algorithm over the conventional heuristic threshold-based BPF estimation for envelope peak determination.