#
User Authentication Based on Handwriting Analysis of Pen-Tablet Sensor Data Using Optimal Feature Selection Model^{ †}

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

- User authentication using motion sensor data of pen-tablet devices.
- A quantitative analysis of pen-tablet sensor data using kinematic and statistical features extraction model.
- Introduce optimal feature selection model combination of filter-based approach and wrapper approach.
- An efficient and robust writer identification model using support vector machine (SVM), logistic regression (LR), and random forest (RF) classifier.

## 2. Literature Review

## 3. Proposed Model

#### 3.1. Pen Tablet Handwriting Data Collection

#### 3.2. Parameters of Pen Tablet Handwriting Data

**Writing Time:**Every person consumes a different amount of time for his/her writing depending on the writing speed. Someone writes very slowly, someone writes moderately and someone writes very fast. After analysis, it is found that for those who write very fast, their handwriting style changes like their baseline changed over time such as rising, straight, falling, erratic, etc.**Pen Pressure:**Pen pressure is the most vital attribute of individual handwriting. Pen pressure of every individual is different from each other in terms of heavy or light. In our collected, dataset, the pressure of a person is not the same for each iteration. The pressure range of some person is (2345–6595) and some other person is (1978–22905).**X-axis:**The X-axis represents the writing position of a person from X-axis. We have taken a single keyword 5 times by the same person. It is noticed that the X-axis position value for each of the 5 cases is very close to each other which indicates that the X-axis value remains almost the same for each case for the same person. It ensures that the X-axis value is a promising attribute that can uniquely identify one person from another.**Y-axis:**The Y-axis indicates the writing position of a person from Y-axis. This position is different from each other. Like the X-axis position value, the Y-axis position value remains very similar in each iteration of the same person. The range of Y-axis value for some person is (1110–1201) and that of some other person has (1200–1350). Figure 3 shows x-axis and y-axis values for different persons for the same keyword.

- 5.
**Horizontal Angle**: The horizontal angle is the dimension of an angle within two lines, rising from the same spot. This angle is automatically measured by the pen tablet. To uniquely identify a user, the horizontal angle is one of the major attributes of our work. The maximum range of horizontal angles in the data set is below 500. Figure 4 shows that the horizontal angle remains constant over time.- 6.
**Vertical Angle**: The vertical angels are the opposite angels to each other after passing two lines. This is also a major attribute of this research work to identify a user uniquely. In the data set, the maximum vertical angle is below 800. Figure 4 shows the horizontal and vertical angle of the same person which is kind of constant over time.

#### 3.3. Handwriting Data Preprocessing

#### 3.4. Feature Extraction

#### 3.4.1. Statistical Features

#### 3.4.2. Kinematic Features

_{n}from that of X

_{n−1}. The mathematical formula of X-axis velocity is:

#### 3.5. Optimal Feature Selection

#### 3.5.1. Hybrid Feature Selection Model

Algorithm 1: SFFS Algorithm |

Input: The set of all features X = {x_{1}, x_{2}, …, x_{n}}Output: A subset of features Y = {y _{i}|i = 1,2,3,…, n; y_{i} $\u03f5$ X}Where, n = (0,1,2,…, m) Steps: 1. X _{0} = {Ø}2. Select the best feature Y ^{+}Update: X _{N}_{+1} = X_{N} + Y^{+} = +13. Select the best feature Y ^{−}4. If I(X _{N} − Y^{−}) > I(X_{N}); [(Y) = criterion function]Then, X _{N}_{+1} = X_{N} − Y^{−}; N = N + 1Go to step 3. |

#### 3.5.2. Objective Function Based on Discriminant Feature

_{i}and y

_{i}are features values of points.

#### 3.6. User Authentication Using Classification Algorithm

_{i}, sv

_{j}) is the kernel function, and sv

_{i}and sv

_{j}are the input data, and parameter σ is a set by the user. The σ used here to determine the width of the kernel function k. Note that, if σ values are small, then overtraining may occur. Again, if σ values are large, then the basis function puts an oval around the points without describing their shapes or patterns [36].

## 4. Experimental Result Analysis

_{1}~f

_{30}). These feature vectors are directly applied to the filter approach for optimal feature selection. The filter technique is executed by two different SFFS algorithms on the two randomly splitted datasets containing equal numbers of data. Individual SFFS algorithm generates separate optimal feature sets from both datasets. This whole process is repeated for 4 iterations. Finally, the filter technique generates 10 sub-optimal feature sets from the 30 datasets. Then the 10 sub-optimal feature sets are forwarded to the wrapper approach, where the classification accuracies are measured using SVM, LR, and RF for each of the sub-optimal feature vectors. Table 5 shows the 10 sub-optimal feature sets after the filter approach. In our experiment, firstly, we have done the best optimal feature selection process with SVM and the evaluation is also done with the same classifier that is SVM. The classification accuracy using SVM is about 98% which shows the practicality of our system. However, to prove the stability of our system, we implemented our model with two additional machine learning algorithms such as LR and RF classifier. For that, the feature selection and evaluation processes are done using LR and RF accordingly following the same procedure of SVM. From the experimental analysis, it is found that the LR and RF provide satisfactory results and SVM perform outstanding which makes our claim stronger for the proposed model.

_{13}, f

_{14}, f

_{16}, f

_{22}} with the best accuracy of 98.0% whereas the accuracy without feature selection is 93% using SVM. Using LR with the combination of best optimal features {f

_{6}, f

_{9}, f

_{23}} provides the best accuracy of 92.2% whereas the accuracy without feature selection is 86% only. Again, using RF with the combination of best optimal features {f

_{4}, f

_{5}, f

_{27}} provides the best accuracy of 94.6% whereas the accuracy without feature selection is 90%. These selected best features are then used in the validation process to check the overall accuracy of our proposed model of user identification. Our proposed model provides efficient and satisfactory writer identification with limited computational resources and hardware cost which prove the practicality of our system.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Writing graph with the x-axis, y-axis values for different persons for the same keyword: (

**a**) Person 1 (

**b**) Person 2 (

**c**) Person 3.

**Figure 7.**Process of objective value calculation: (

**a**) Within-class compactness (

**b**) between-class distance.

**Figure 9.**Sample Handwriting Features for Different Persons: (

**a**) average pressure (

**b**) average velocity (

**c**) average writing start velocity (

**d**) average writing end velocity.

**Figure 10.**Classification accuracy of different sub-optimal feature sets in wrapper approach: (

**a**) estimated by support vector machine (SVM) (

**b**) estimated by logistic regression (LR) (

**c**) estimated by random forest (RF).

**Figure 17.**Classification accuracy for different persons with and without feature selection using SVM.

**Figure 19.**Class-wise accuracy (%) comparison of the proposed model with state-of-the-art image-based system.

Time | Pressure | X-Axis | Y-Axis | Horizontal Angle | Vertical Angle |
---|---|---|---|---|---|

6143.52 | 6787 | 346 | 1214 | 160 | 410 |

6151.46 | 8707 | 346 | 1214 | 160 | 420 |

6159.44 | 15,671 | 346 | 1214 | 161 | 420 |

6166.47 | 15,847 | 346 | 1214 | 160 | 430 |

6174.52 | 16,391 | 346 | 1214 | 161 | 430 |

Features | Equation | Features | Equation |
---|---|---|---|

Mean | $\mu =\frac{1}{N}{\displaystyle {\displaystyle \sum}_{i=1}^{N}}{x}_{i}$ | Cross-Correlation | ${\rho}_{i,j}=\frac{{X}_{i,j}}{\sqrt{{\sigma}_{i}^{2}{\sigma}_{j}^{2}}}$ |

Median | $\mathrm{M}=\left(\frac{\frac{n}{2}-cf}{f}\right)\left(w\right)+{L}_{m}$ | Absolute Mean value | ${A}_{m}=\mu \left(ab{s}_{x}\right)$ |

Maximum | MAX(M) | Shape Factor | $\mathrm{SF}=\frac{{X}_{rms}}{{A}_{m}}$ |

Minimum | Minimum MIN(M) | Energy | $E={\displaystyle {\displaystyle \sum}_{i=1}^{N}}{\left|{x}_{i}\right|}^{2}$ |

Standard Deviation of Pressure | ${P}_{sd}=\frac{\sqrt{{{\displaystyle \sum}}_{n=1}^{N}\left({P}_{n}-{P}_{mean}\right)}}{N}$ | RMS Frequency | $RM{S}_{fr}=\mu \left(\sqrt{\left(fr{x}_{1}^{2}\right)+fr{x}_{2}^{2}+\cdots +fr{x}_{n}^{2}}\right)$ |

Skewness | ${P}_{skw=}\frac{{{\displaystyle \sum}}_{n=1}^{N}{\left({P}_{n}-\overline{P}\right)}^{3}/N\text{}}{{P}_{sd}{}^{3}}$ | Peak to Peak | $PPV=MAX\left(M\right)-MIN\left(M\right)$ |

Kurtosis | ${P}_{k=}\frac{{{\displaystyle \sum}}_{n=1}^{N}{\left({P}_{n}-\overline{P}\right)}^{4}/N}{{({P}_{sd})}^{4}}$ | SRA | $SF=\mu \left(\sqrt[2]{absX}\right)$ |

Variance | ${\sigma}^{2}=\frac{\sum {\left(x-\mu \right)}^{2}}{N}$ | Impulse Factor | $i=\frac{{x}_{peak}}{{x}_{mean}}$ |

Correlation Coefficient | $\mathrm{r}=\frac{n\left(\sum xy\right)-\left(\sum x\right)\left(\sum y\right)}{\left[n\sum {x}^{2}-{\left(\sum x\right)}^{2}\right]\left[n\sum {y}^{2}-{\left(\sum y\right)}^{2}\right]}$ | Margin Factor | $MF={x}_{peak}/{x}_{sra}$ |

Root mean Square | ${X}_{rms}=\sqrt{\frac{1}{N}\left({x}_{1}{}^{2}+{x}_{2}{}^{2}+\cdots +{x}_{n}{}^{2}\right)}$ | Energy Center | $FC=\sqrt{{f}_{1}{f}_{2}}$ |

Features | Equation | Features | Equation |
---|---|---|---|

Average Pressure | $\mathrm{P}\mathrm{\_mean}=\frac{1}{\mathrm{N}}\ast {{\displaystyle \sum}}_{\mathrm{n}=1}^{\mathrm{N}}\left({\mathrm{P}}_{\mathrm{n}}\right)$ | Peak Pressure | $\mathrm{P}\mathrm{\_peak}=1\le \mathrm{n}\le \mathrm{Nmax}\text{}({\mathrm{P}}_{\mathrm{n}})$ |

Average Velocity | ${\mathrm{V}}_{\mathrm{mean}=}\frac{\sqrt{{\left\{{\mathrm{x}}_{\mathrm{n}}-{\mathrm{x}}_{\mathrm{n}+1}\right\}}^{2}+{\left\{{\mathrm{y}}_{\mathrm{n}}-{\mathrm{y}}_{\mathrm{n}+1}\right\}}^{2}}}{{\mathrm{t}}_{\mathrm{n}+1}-{\mathrm{t}}_{\mathrm{n}}}$ | Peak Velocity | ${\mathrm{V}}_{\mathrm{max}=}{\mathrm{max}}_{1\le \mathrm{n}\le \mathrm{N}}\frac{\sqrt{{\left\{{\mathrm{x}}_{\mathrm{n}}-{\mathrm{x}}_{\mathrm{n}+1}\right\}}^{2}+{\left\{{\mathrm{y}}_{\mathrm{n}}-{\mathrm{y}}_{\mathrm{n}+1}\right\}}^{2}}}{{\mathrm{t}}_{\mathrm{n}+1}-{\mathrm{t}}_{\mathrm{n}}}$ |

Average Start Position of Pen | ${\mathrm{P}}_{\mathrm{start}=}\frac{1}{\mathrm{N}\ast 0.05}{\displaystyle {\displaystyle \sum}_{\mathrm{n}=1}^{\mathrm{N}\ast 0.05}}{\mathrm{P}}_{\mathrm{n}}$ | Average End Position of Pen | ${\mathrm{P}}_{\mathrm{End}=}\frac{1}{\mathrm{N}\ast 0.05}{\displaystyle {\displaystyle \sum}_{\mathrm{n}=1}^{\mathrm{N}\ast 0.95}}{\mathrm{P}}_{\mathrm{n}}$ |

Average Writing Start Velocity | ${\mathrm{V}}_{\mathrm{start}=}\frac{1}{\mathrm{N}\ast 0.05}\text{}$ $\displaystyle \sum}_{\mathrm{n}=1}^{\mathrm{N}\ast 0.05}}\frac{\sqrt{{\left\{{\mathrm{x}}_{\mathrm{n}}-{\mathrm{x}}_{\mathrm{n}+1}\right\}}^{2}+{\left\{{\mathrm{y}}_{\mathrm{n}}-{\mathrm{y}}_{\mathrm{n}+1}\right\}}^{2}}}{{\mathrm{t}}_{\mathrm{n}+1}-{\mathrm{t}}_{\mathrm{n}$ | Average Writing End Velocity | ${\mathrm{V}}_{\mathrm{End}}=$ $\frac{1}{\mathrm{N}\ast 0.05}$ $\displaystyle \sum}_{\mathrm{n}-1}^{\mathrm{N}\ast 0.95}}\frac{\sqrt{{\left\{{\mathrm{x}}_{\mathrm{n}}-{\mathrm{x}}_{\mathrm{n}+1}\right\}}^{2}+{\left\{{\mathrm{y}}_{\mathrm{n}}-{\mathrm{y}}_{\mathrm{n}+1}\right\}}^{2}}}{{\mathrm{t}}_{\mathrm{n}}-{\mathrm{t}}_{\mathrm{n}+1$ |

Horizontal Velocity | ${\mathrm{V}}_{\mathrm{h}}={\displaystyle {\displaystyle \sum}_{\mathrm{n}=1}^{\mathrm{N}}}\frac{{\mathrm{x}}_{\mathrm{n}+1}-{\mathrm{x}}_{\mathrm{n}}}{{\mathrm{t}}_{\mathrm{n}+1}-{\mathrm{t}}_{\mathrm{n}}}$ | Vertical Velocity | ${\mathrm{V}}_{\mathrm{v}}={\displaystyle {\displaystyle \sum}_{\mathrm{n}=1}^{\mathrm{N}}}\frac{{\mathrm{y}}_{\mathrm{n}+1}-{\mathrm{y}}_{\mathrm{n}}}{{\mathrm{t}}_{\mathrm{n}+1}-{\mathrm{t}}_{\mathrm{n}}}$ |

No. of Keywords | No. of Writing for Each Keywords | Data Samples for One Person | Training and Feature Selection Data | Test Data | |
---|---|---|---|---|---|

Class 1 | 10 | 5 | 50 | 30 | 20 |

Class 2 | 10 | 5 | 50 | 30 | 20 |

Class 3 | 10 | 5 | 50 | 30 | 20 |

… | … | … | … | … | … |

Class 25 | 10 | 5 | 50 | 30 | 20 |

Total Data: 1250 | Total Train Data: 750 | Total Test Data: 500 |

Sub-Optimal Feature Sets in Filter Approach | |||||||||
---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

{f_{2} f_{5} f_{7} f_{9}} | {f_{3} f_{4} f_{8} f_{10}} | {f_{13} f_{14} f_{16} f_{22}} | {f_{6} f_{9} f_{23}} | {f_{8} f_{13} f_{15} f_{21}} | {f_{1} f_{12} f_{24}} | {f_{4} f_{5} f_{27}} | {f_{6} f_{13} f_{19} f_{29}} | {f_{11} f_{17} f_{28}} | {f_{9} f_{20} f_{26} f_{30}} |

**Table 6.**Classification Accuracy of Best Optimal Features after Feature Selection with Wrapper Approach.

Machine Learning Algorithms | |||
---|---|---|---|

Using SVM | Using LR | Using RF | |

Best Optimal Feature | {f_{13}, f_{14}, f_{16}, f_{22}} | {f_{6}, f_{9}, f_{23}} | {f_{4}, f_{5}, f_{27}} |

Best Accuracy | 98.0% | 92.2% | 94.1% |

No. of Persons | SVM Classifier (with Feature Selection) | |||
---|---|---|---|---|

Accuracy | Precision | Recall | F1 Score | |

5 | 98.00 | 98.00 | 98.00 | 98.00 |

10 | 97.00 | 97.13 | 97.00 | 97.06 |

15 | 97.30 | 97.25 | 97.35 | 97.30 |

20 | 96.75 | 97.00 | 96.20 | 96.60 |

25 | 96.20 | 96.00 | 96.30 | 96.15 |

Ref # | Classifier | Feature | Result/Accuracy | Input Data Type | Comments |
---|---|---|---|---|---|

[5] | RF, KNN | Keystrokes Dynamic | Achieved an EER of 2.9% | Image-based | Considered only 3 typing positions |

[11] | KNN, SVM | Hand Radiographs | 97% | Image-based | Suffers from high computational Cost |

[28] | Minimum Distance, Bayes | Dynamic Features | 95% | Pen-tablet data | Focused only on the small scale writing samples |

[30] | Hamming Distance, Nearest neighbor | Histogram | 91.17% | Image-based | Writer’s information lost due to stretching the images |

[32] | AlexNet | Implicit and explicit information | 92% | Image-based | Resizing handwriting patches loss write’s intrinsic information |

[34] | ResNet | Handwriting thickness descriptor (HTD) | 97% | Image-based | High Computational cost, Multimodal descriptions needed |

Proposed Model | SVM, LR, RF | Optimal Features (kinematic and statistics) | 98% | Pen-tablet sensor data (numerical value) | Pen-tablet data are more robust in terms of noise effect compare to image-based, low computational cost |

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## Share and Cite

**MDPI and ACS Style**

Begum, N.; Akash, M.A.H.; Rahman, S.; Shin, J.; Islam, M.R.; Islam, M.E. User Authentication Based on Handwriting Analysis of Pen-Tablet Sensor Data Using Optimal Feature Selection Model. *Future Internet* **2021**, *13*, 231.
https://doi.org/10.3390/fi13090231

**AMA Style**

Begum N, Akash MAH, Rahman S, Shin J, Islam MR, Islam ME. User Authentication Based on Handwriting Analysis of Pen-Tablet Sensor Data Using Optimal Feature Selection Model. *Future Internet*. 2021; 13(9):231.
https://doi.org/10.3390/fi13090231

**Chicago/Turabian Style**

Begum, Nasima, Md Azim Hossain Akash, Sayma Rahman, Jungpil Shin, Md Rashedul Islam, and Md Ezharul Islam. 2021. "User Authentication Based on Handwriting Analysis of Pen-Tablet Sensor Data Using Optimal Feature Selection Model" *Future Internet* 13, no. 9: 231.
https://doi.org/10.3390/fi13090231