Clustering of video sequences is essential in order to perform video summarization. Because of the high spatial and temporal dimensions of the video data, dimensionality reduction becomes imperative before performing Euclidean distance based clustering. In this paper, we present non-adaptive dimensionality reduction approaches using random projections on the video data. Assuming the data to be a realization from a mixture of Gaussian distributions allows for further reduction in dimensionality using random projections. The performance and computational complexity of the K-means and the K-hyperline clustering algorithms are evaluated with the reduced dimensional data. Results show that random projections with an assumption of Gaussian mixtures provides the smallest number of dimensions, which leads to very low computational complexity in clustering.