# A Survey of Handwritten Character Recognition with MNIST and EMNIST
## 2 MNIST Database
### State of the Art
[44] developed a new transform named Adaptative Fastfood to reparameterize the fully connected layers, obtaining a test error rate of 0.71%. An interesting approach is followed by [PERSON] et al. [45], in which they reuse the convolutional kernels previously learned over the ILSVRC-12 dataset, proving that CNNs can learn generic feature extractors than can be reused across tasks, and achieving a test error rate in the MNIST dataset of 0.46% (vs. 0.32% when training the network from scratch). It can be seen how most recent works are based on convolutional neural networks, due to their high performance. However, some exceptions can be noticed. One example is the work by [PERSON] and [PERSON] [46] where they attained a test error rate of 0.35% using a single layer centering support vector data description (C-SVDD) network with multi-scale receptive voting and SIFT (scale-invariant feature transform) features. Also, [PERSON] et al. [47] devised a model (HOPE) for projecting features from raw data, that could be used for training a neural network, that attained a test error rate of 0.40% without data augmentation. [PERSON] et al. [48] proposed a recurrent neural network (RNN) that replaced the convolutional layers by recurrent neural networks that swiped through the image, attaining an error rate of 0.45% with data augmentation. Additional examples with less performance include the work by [PERSON] and [PERSON] [49] who used a combination of shifted filter responses (COSFIRE), attaining an error rate of 0.52%. Also, [PERSON] et al. [PERSON] et al. [50] used a PCA network to learn multi-stage filter banks, and report an error rate of 0.62%. [PERSON] et al. [51] used task-driven dictionary learning, reporting a test error rate of 0.54%, yet using data augmentation. [PERSON] et al. [52] explored the receptive field of pooling, and obtained an error of 0.64%. [PERSON] and [PERSON] [53] explored the application of the sparse connectivity and sparse activity properties to neural networks, obtaining an error rate of 0.75% using a supervised online autoencoder with data augmentation. [PERSON] et al. [54] described convolutional deep belief networks with probabilistic max-pooling achieving an error rate of 0.82%. [PERSON] et al. [55] reported an error of 0.95% using a deep encoder network to perform non-linear feature transformations which are then introduced to K-NN for classification. Finally, [PERSON] et al. [56] used supervised translation-invariant sparse coding with a linear SVM attaining an error rate of 0.84%. Other approach to solve the MNIST classification problem involves so-called \"deep Boltzmann machines\". The first application of this technique was suggested by [PERSON] and [PERSON] [57] and enabled them to report an error rate of 0.95%. Few years later, [PERSON] et al. [58] introduced the multi-prediction deep Boltzmann machine, achieving a test error rate of 0.88%. The reviewed rankings gather most of the works providing very competitive results for the MNIST database. Besides those rankings, we have found a work by [PERSON] and [PERSON] [59] where the authors work in the weights initialization of the CNN and replacing the softmax classifier with SVM, achieving a test error rate of 0.38%, and another work by [PERSON] et al. [60] where inception-recurrent CNNs were used to attain an error of 0.29%. Finally, it is worth mentioning some techniques that automatically optimize the topology of CNNs: MetaQNN [61], which relies on reinforcement learning for the design of CNNs architectures, has reported an error rate on MNIST of 0.44%, and 0.32% when using an ensemble of the best found neural networks. Also, DEvol [62], which uses genetic programming, has obtained a error rate of 0.6%. [PERSON] et al. [63] presented a work in 2018 where the topology of the network is evolved using grammatical evolution, attaining a test error rate of 0.37% without data augmentation and this result was later improved by means of the neuroevolution of committees of CNNs [64] down to 0.28%.