Gaussian decomposition of $\ion{H}{i}$ surveys

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In the previous papers of this series, we have decomposed into Gaussian components all the HI 21-cm line profiles of the Leiden-Argentina-Bonn (LAB) database, and studied statistical distributions of the obtained Gaussians. Now we are interested in separation from the general database of the components the "clouds" of closely spaced similar Gaussians. In this paper we describe the new cloud-finding algorithm. To separate the clouds of similar Gaussians, we start with the single-link hierarchical clustering procedure in five-dimensional (longitude, latitude, velocity, Gaussian width and height) space, but make some modifications to accommodate it to the large number of components. We also use the requirement that each cloud may be represented at any observed sky position by only one Gaussian and take into account the similarity of global properties of the merging clouds. As a test, we apply the algorithm for finding the clouds of the narrowest HI 21-cm line components. Using the full sky search for cold clouds, we easily detect the coldest known HI clouds and demonstrate that actually they are a part of a long narrow ribbon of cold clouds. We model these clouds as a part of a planar gas ring, deduce their spatial placement, and discuss their relation to supernova shells in the solar neighborhood. We conclude that the proposed algorithm satisfactorily solves the posed task. We guess that the study of the narrowest HI 21-cm line components may be a useful tool for finding the structure of neutral gas in solar neighborhood.