Density-based spatial clustering of applications with noise (DBSCAN) is the most commonly used density-based clustering algorithm but may not be sufficient when the input data type is heterogeneous in terms of textual description. When we aim to discover clusters of geo-tagged records relevant to a particular point of interest (POI) on social media, examining only one type of input data (e.g., the tweets relevant to a POI) may draw an incomplete picture of clusters due to noisy regions. To overcome this problem, we introduce DBSTexC , a newly defined density-based clustering algorithm using spatio-textual information on social media (e.g., Twitter). We first characterize the POI-relevant and POI-irrelevant geo-tagged tweets as the texts that include and do not include a POI name or its semantically coherent variations, respectively. By leveraging the proportion of the POI-relevant and POI-irrelevant tweets, the proposed algorithm demonstrates much higher clustering performance than the DBSCAN case in terms of F1 score and its variants. While DBSTexC performs exactly as DBSCAN with the textually homogeneous inputs, it far outperforms DBSCAN with the textually heterogeneous inputs. Furthermore, to further improve the clustering quality by fully capturing the geographic distribution of geo-tagged points, we present fuzzy DBSTexC ( F-DBSTexC ), an extension of DBSTexC , which incorporates the notion of fuzzy clustering into the DBSTexC . We then demonstrate the consistent superiority of F-DBSTexC over the original DBSTexC via intensive experiments. The computational complexity of our algorithms is also analytically and numerically shown.