The internet of things devices suffer of low memory while good accuracy is needed. Designing suitable algorithms is vital in this subject. This paper proposes a feed forward LogNNet neural network which uses a semi-linear Henon type discrete chaotic map to classify MNIST-10 dataset. The model is composed of reservoir part and trainable classifier. The aim of reservoir part is transforming the inputs to maximize the classification accuracy using a special matrix filing method and a time series generated by the chaotic map. The parameters of the chaotic map are optimized using particle swarm optimization with random immigrants. The results show that the proposed LogNNet/Henon classifier has higher accuracy and same RAM saving comparable to the original version of LogNNet and has broad prospects for implementation in IoT devices. In addition, the relation between the entropy and accuracy of the classification is investigated. It is shown that there exists a direct relation between the value of entropy and accuracy of the classification.