Modern deep neural networks (DNNs) become frail when the datasets contain noisy (incorrect) class labels. Robust techniques in the presence of noisy labels can be categorized into two folds: developing noise-robust functions or using noise-cleansing methods by detecting the noisy data. Recently, noise-cleansing methods have been considered as the most competitive noisy-label learning algorithms. Despite their success, their noisy label detectors are often based on heuristics more than a theory, requiring a robust classifier to predict the noisy data with loss values. In this paper, we propose a novel detector for filtering label noise. Unlike most existing methods, we focus on each data's latent representation dynamics and measure the alignment between the latent distribution and each representation using the eigen decomposition of the data gram matrix. Our framework, coined as filtering noisy instances via their eigenvectors (FINE), provides a robust detector with derivative-free simple methods having theoretical guarantees. Under our framework, we propose three applications of the FINE: sample-selection approach, semi-supervised learning approach, and collaboration with noise-robust loss functions. Experimental results show that the proposed methods consistently outperform corresponding baselines for all three applications on various benchmark datasets.