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The Growing Self Organizing Map (GSOM) algorithm is a variant of the Self Organizing Map (SOM). It has a dynamically growing structure that adapts to the natural structure of the data.It has been identified that the growing of the GSOM can get negatively affected when used with very large dimensional data such as those in text and DNA data sets. This paper addresses these issues and presents a modified version of the GSOM called the High Dimensional GSOM (HDGSOM). The algorithm and experimental results showing the improved performance of the HDGSOM are also presented.