We investigate different approaches for efficient feature space reduction and compare different methods for cell classification. The application context is the development of automatic methods for analysing fluorescence microscopy images with the goal to identify those genes that are involved in the mitosis of human cells (cell division). We distinguish four cell classes comprising interphase cells, mitotic cells, apoptotic cells, and cells with clustered nuclei. Feature space reduction was performed using the Principal Component Analysis and Independent Component Analysis methods. Six classification methods were examined including unsupervised clustering algorithms such as K-means, Hard Competitive Learning, and Neural Gas as well as Hierarchical Clustering, Support Vector Machines, and Random Forests classifiers. Detailed results on the cell image classification accuracy and computational efficiency achieved using different feature sets and different classification methods are reported.