While deep convolutional neural networks (DCNNs) have demonstrated superiority in their ability to classify image data, one of the primary downsides of DCNNs is that their training normally requires large sets of labeled "ground truth" images. For that reason, DCNNs do not provide an effective solution in many real-world problems in which large sets of labeled images are not available. Here we propose to use the quick learning if SVMs to provide a solution for learning from small image datasets in a non-parametric manner. Experimental results show that while "conventional" DCNN architectures such as ResNet-50 outperform SVMnet when the size of the training set is large, SVMnet provides a much higher accuracy when the number of "ground truth" training samples is small.