Mining frequent patterns is a fundamental and essential problem in many data mining applications. Mining frequent closed itemsets provides complete and non-redundant results for frequent pattern analysis. The growth of bioinformatics has resulted in datasets with new characteristics. These datasets typically contain a large number of columns. Such high-dimendional datasets pose a great challenge for existing closed frequent pattern discovery algorithms. This paper presents a survey of the various algorithms for mining frequent closed itemsets in very high dimensional data along with a hierarchy organizing the algorithms by their characteristics. We compare two row enumeration-based algorithms, discuss an algorithm which is designed to automatically switch between feature enumeration and row enumeration during the mining process based on the characteristics of the data subset being considered, and finally point out the research direction in this field.