PCA-SIFT is an extension to SIFT which aims to reduce SIFT's high dimensionality (128 dimensions) by applying PCA to the gradient image patches. However PCA is not a discriminative representation for recognition due to its global feature nature and unsupervised algorithm. In addition, linear methods such as PCA and ICA can fail in the case of non-linearity. In this paper, we propose a new discriminative method called Supervised Kernel ICA (SKICA) that uses a non-linear kernel approach combined with Supervised ICA-based local image descriptors. Our approach blends the advantages of supervised learning with nonlinear properties of kernels. Using five different test data sets we show that the SKICA descriptors produce better object recognition performance than other related approaches with the same dimensionality. The SKICA-based representation has local sensitivity, non-linear independence and high class separability providing an effective method for local image descriptors.