# A Survey of Handwritten Character Recognition with MNIST and EMNIST

^{*}

## Abstract

**:**

## 1. Introduction

## 2. MNIST Database

#### 2.1. Acquisition and Data Format

#### 2.2. State of the Art

## 3. EMNIST Database

#### 3.1. Acquisition and Data Format

- Storing original images in NIST SD 19 as 128 × 128-pixels black and white images.
- Applying a Gaussian blur filter to soften edges.
- Removing empty padding to reduce the image to the region of interest.
- Centering the digit in a square box preserving the aspect ration.
- Adding a blank padding of 2-pixels per side.
- Downsampling the image 28 × 28 pixels using bi-cubic interpolation.

- By_Class: in this schema classes are digits [0–9], lowercase letters [a–z] and uppercase letters [A–Z]. Thus, there are 62 different classes.
- By_Merge: this schema addresses the fact that some letters are quite similar in their lowercase and uppercase variants, thus both classes can be fused. In particular, these letter are ‘c’, ‘i’, ‘j’, ‘k’, ‘l’, ‘m’, ‘o’, ‘p’, ‘s’, ‘u’, ‘v’, ‘w’, ‘x’, ‘y’ and ‘z’. This schema contains 47 classes.

- Balanced: both By_Class and By_Merge datasets are very unbalanced when it comes to letters, a fact that could negatively impact the classification performance. This dataset takes the By_Merge dataset and reduces the number of instances from 814,255 (total number of samples in NIST Special Database 19) to only 131,600, guaranteeing that there is an equal number of samples per each label.
- Digits: similar to MNIST, but from a different source and with 280,000 instances.
- Letters: this dataset contains mixed lowercase and uppercase letteres, thus containing 26 classes and a total of 145,600 samples.

#### 3.2. State of the Art

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

BFGS | Broyden–Fletcher–Goldfarb–Shanno algorithm |

CG | Conjugate gradient |

C-SVDD | Centering support vector data description |

CNN | Convolutional neural network |

COSFIRE | Combination of shifted filter responses |

DCT | Discrete cosine transform |

DWT | Discrete wavelet transform |

ELM | Extreme learning machine |

EMNIST | Extended MNIST |

K-NN | k-nearest neighbors |

MNIST | Mixed National Institute of Standards and Technology |

NN | Neural network |

PCA | Principal component analysis |

RNN | Recurrent neural network |

SIFT | Scale-invariant feature transform |

SVM | Support vector machine |

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**Table 1.**Side-by-side comparison of the most competitive (error rate < 1%) results found in the state of the art for the MNIST database with data augmentation or preprocessing. Best achieved performances are boldfaced.

Technique | Test Error Rate |
---|---|

NN 6-layer 5,700 hidden units [12] | 0.35% |

MSRV C-SVDDNet [46] | 0.35% |

Committee of 25 NN 2-layer 800 hidden units [11] | 0.39% |

RNN [48] | 0.45% |

K-NN (P2DHMDM) [6] | 0.52% |

COSFIRE [49] | 0.52% |

K-NN (IDM) [6] | 0.54% |

Task-driven dictionary learning [51] | 0.54% |

Virtual SVM, deg-9 poly, 2-pixel jit [8] | 0.56% |

RF-C-ELM, 15,000 hidden units [21] | 0.57% |

PCANet (LDANet-2) [50] | 0.62% |

K-NN (shape context) [5] | 0.63% |

Pooling + SVM [52] | 0.64% |

Virtual SVM, deg-9 poly, 1-pixel jit [8] | 0.68% |

NN 2-layer 800 hidden units, XE loss [9] | 0.70% |

SOAE-$\sigma $ with sparse connectivity and activity [53] | 0.75% |

SVM, deg-9 poly [4] | 0.80% |

Product of stumps on Haar f. [7] | 0.87% |

NN 2-layer 800 hidden units, MSE loss [9] | 0.90% |

CNN (2 conv, 1 dense, relu) with DropConnect [24] | 0.21% |

Committee of 25 CNNs [20] | 0.23% |

CNN with APAC [28] | 0.23% |

CNN (2 conv, 1 relu, relu) with dropout [24] | 0.27% |

Committee of 7 CNNs [19] | 0.27% |

Deep CNN [18] | 0.35% |

CNN (2 conv, 1 dense), unsup pretraining [16] | 0.39% |

CNN, XE loss [9] | 0.40% |

Scattering convolution networks + SVM [41] | 0.43% |

Feature Extractor + SVM [14] | 0.54% |

CNN Boosted LeNet-4 [4] | 0.70% |

CNN LeNet-5 [4] | 0.80% |

**Table 2.**Side-by-side comparison of the most competitive (error rate < 1%) results found in the state of the art for the MNIST database without data augmentation or preprocessing. Best achieved performances are boldfaced.

Technique | Test Error Rate |
---|---|

HOPE+DNN with unsupervised learning features [47] | 0.40% |

Deep convex net [10] | 0.83% |

CDBN [54] | 0.82% |

S-SC + linear SVM [56] | 0.84% |

2-layer MP-DBM [58] | 0.88% |

DNet-kNN [55] | 0.94% |

2-layer Boltzmann machine [57] | 0.95% |

Batch-normalized maxout network-in-network [29] | 0.24% |

Committees of evolved CNNs (CEA-CNN) [65] | 0.24% |

Genetically evolved committee of CNNs [66] | 0.25% |

Committees of 7 neuroevolved CNNs [64] | 0.28% |

CNN with gated pooling function [30] | 0.29% |

Inception-Recurrent CNN + LSUV + EVE [60] | 0.29% |

Recurrent CNN [31] | 0.31% |

CNN with norm. layers and piecewise linear activation units [32] | 0.31% |

CNN (5 conv, 3 dense) with full training [45] | 0.32% |

MetaQNN (ensemble) [61] | 0.32% |

Fractional max-pooling CNN with random overlapping [34] | 0.32% |

CNN with competitive multi-scale conv. filters [33] | 0.33% |

CNN neuroevolved with GE [63] | 0.37% |

Fast-learning shallow CNN [35] | 0.37% |

CNN FitNet with LSUV initialization and SVM [59] | 0.38% |

Deeply supervised CNN [27] | 0.39% |

Convolutional kernel networks [36] | 0.39% |

CNN with Multi-loss regularization [37] | 0.42% |

MetaQNN [61] | 0.44% |

CNN (3 conv maxout, 1 dense) with dropout [17] | 0.45% |

Convolutional highway networks [38] | 0.45% |

CNN (5 conv, 3 dense) with retraining [45] | 0.46% |

Network-in-network [39] | 0.47% |

CNN (3 conv, 1 dense), stochastic pooling [25] | 0.49% |

CNN (2 conv, 1 dense, relu) with dropout [24] | 0.52% |

CNN, unsup pretraining [17] | 0.53% |

CNN (2 conv, 1 dense, relu) with DropConnect [24] | 0.57% |

SparseNet + SVM [15] | 0.59% |

CNN (2 conv, 1 dense), unsup pretraining [16] | 0.60% |

DEvol [62] | 0.60% |

CNN (2 conv, 2 dense) [40] | 0.62% |

Boosted Gabor CNN [42] | 0.68% |

CNN (2 conv, 1 dense) with L-BFGS [43] | 0.69% |

Fastfood 1024/2048 CNN [44] | 0.71% |

Feature Extractor + SVM [14] | 0.83% |

Dual-hidden Layer Feedforward Network [21] | 0.87% |

CNN LeNet-5 [4] | 0.95% |

**Table 3.**Side-by-side comparison of the results for the EMNIST dataset, including works using similar datasets from NIST Special Database 19. Best results are boldfaced. Results marked with a star (*) indicate that they refer to works using samples from NIST SD 19 which are similar but not equivalent to EMNIST (samples are the same, but they are not submitted to the preprocessing stage used in EMNIST, described in the text).

Technique | By_Class | By_Merge | Balanced | Letters | Digits |
---|---|---|---|---|---|

DWT-DCT + SVM [71] | – | – | – | 89.51% | 97.74% |

Linear classifier [67] | 51.80% | 50.51% | 50.93% | 55.78% | 84.70% |

OPIUM [67] | 69.71% | 72.57% | 78.02% | 85.15% | 95.90% |

SVMs (one against all + sigmoid) [86] | – | – | – | – | 98.75% * |

Multi-layer perceptron [88] | – | – | – | – | 98.39% * |

Hidden Markov model [91] | – | – | – | 90.00% * | 98.00% * |

Record-to-record travel [89] | – | – | – | 93.78% * | 96.53% * |

PSO + fuzzy ARTMAP NNs [87] | – | – | – | – | 96.49% * |

Multi-layer perceptron [90] | – | – | – | 87.79% * | – |

CNN (6 conv + 2 dense) [85] | – | – | 90.59% | – | 99.79% |

Markov random field CNN [73] | 87.77% | 90.94% | 90.29% | 95.44% | 99.75% |

TextCaps [76] | 90.46% | 95.36% | 99.79% | ||

CNN (2 conv + 1 dense) [75] | 87.10% | – | – | – | – |

Committees of neuroevolved CNNs [64] | – | – | – | 95.35% | 99.77% |

Deep convolutional ELM [78] | – | – | – | – | 99.775% |

Parallelized CNN [74] | – | – | – | – | 99.62% |

CNN (flat; 2 conv + 1 dense) [79] | – | – | 87.18% | 93.63% | 99.46% |

EDEN [80] | – | – | – | 88.30% | 99.30% |

Committee of 7 CNNs [19] | 88.12% * | – | – | 92.42% * | 99.19% * |

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**MDPI and ACS Style**

Baldominos, A.; Saez, Y.; Isasi, P.
A Survey of Handwritten Character Recognition with MNIST and EMNIST. *Appl. Sci.* **2019**, *9*, 3169.
https://doi.org/10.3390/app9153169

**AMA Style**

Baldominos A, Saez Y, Isasi P.
A Survey of Handwritten Character Recognition with MNIST and EMNIST. *Applied Sciences*. 2019; 9(15):3169.
https://doi.org/10.3390/app9153169

**Chicago/Turabian Style**

Baldominos, Alejandro, Yago Saez, and Pedro Isasi.
2019. "A Survey of Handwritten Character Recognition with MNIST and EMNIST" *Applied Sciences* 9, no. 15: 3169.
https://doi.org/10.3390/app9153169