We present a hierarchical clustering method for a dataset based on the deep structure of the probability density function (PDF) of the data in the scale space. The data clusters correspond to the modes of the PDF, and their hierarchy is determined by regarding the nonparametric estimation of the PDF with the Gaussian kernel as a scale-space representation. It is shown that the number of clusters is statistically deterministic above a certain critical scale, even though the positions of the data points are stochastic. Such a critical scale is estimated by analysing the distribution of cluster lifetime in the scale space, and statistically valid clusters are detected above the critical scale. This cluster validation using the critical scale can be recursively employed according to the hierarchy of the clusters.