# Critical Examination of the Parametric Approaches to Analysis of the Non-Verbal Human Behavior: A Case Study in Facial Pre-Touch Interaction

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Participants

- “female” touchers and “female” evaluators
- “female” touchers and “male” evaluators
- “male” touchers and “female” evaluators
- “male” touchers and “male” evaluators

#### 2.2. Paradigm

#### 2.3. Data Acquisition

#### 2.4. Analysis

#### 2.5. Ethics Statement

## 3. Results

#### 3.1. Rmse

#### 3.2. Coefficient of Determination ${R}^{2}$

#### 3.3. Investigation of the Training Process

## 4. Discussion

## 5. Limitations and Future Direction

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Experimental Setup. (

**a**) An instance of toucher-evaluator interaction. The two Kinect V2 sensors that were mounted behind the evaluators’ seat to automatically track the touchers’ hand and the evaluators’ face positions are visible in this figure. (

**b**) Toucher-evaluator interaction settings. The toucher (i.e., T) moves along the positions 0 through 8 and stretches her hand toward the face of the evaluator (i.e., E) who is seated in the middle. The two Kinect V2 sensors mounted behind the evaluator collect the joint and the head positions of the toucher and the evaluator.

**Figure 2.**Pre-touch distance surface. (

**a**) Full participant’s pre-touch distance (cm) grid along the azimuth and elevation angles. Azimuth and elevation angles are within −89.00 and +89.00 degrees. The color-bar on the side indicates the pre-touch distance value (in cm) in each cell of the azimuth-elevation grid whose cells are constructed by 1-degree increment along these angles’ directions. Grey cells in this subplot show the areas in which no pre-touch distance was available. (

**b**) 3-D heatmap of pre-touch surface around the face using the modified grid that includes 5664 facial-area pre-touch data points. The azimuth and elevations angles of these samples are within [−80.00, …, +80.00] and [−32.00, …, +53.00], respectively. The z-axis corresponds to the distance of the touchers’ hand from the touchees’ face (i.e., distance at which the touchers were asked by the touchees to stop approaching hand to get any closer). (

**c**) Distribution of touchers’ pre-touch data points around the touchees’ face area. Points are plotted in different shades of grey for better visualization purpose. These data points correspond to the locations where the touchers were asked by the touchee to stop approaching their face. Coordinates of these data points correspond to toucher’s hand distance (x-axis, in cm), azimuth angle (y-axis, in degree), and elevation angle (z-axis, in degree) with respect to the touchees’ face. (

**d**) Schematic diagram of the face’s orientation with respect to the azimuth and elevation angles as shown in subplot (

**b**).

**Figure 3.**Root-mean-squared-error (RMSE) when the models trained using (

**a**) polynomial degree 0 (

**b**) polynomial degree 4. The horizontal bars correspond to the difference between the polynomial degrees for each model and the vertical bars are associated with the difference between models in each polynomial degree settings. The asterisks indicate the significance in their differences (***: p < 0.001).

**Figure 4.**Coefficient of Determination (${R}^{2}$) when the models trained using (

**a**) polynomial degree 0 (

**b**) polynomial degree 4. The horizontal bars correspond to the difference between the polynomial degrees for each model and the vertical bars are associated with the difference between models in each polynomial degree settings. The asterisks indicate the significance in their differences (***: p < 0.001).

**Figure 5.**Subplots (

**a**) through (

**c**): estimated 2-D heatmap surfaces by models trained on the entire facial-area pre-touch distances. In each of these subplots, the z-axis corresponds to the facial pre-touch distances that were estimated by these models. The x- and y-axes correspond to the elevation azimuth and elevation angles associated with these distances (i.e., the feature inputs) to these models. (

**a**) GP appears to perfectly fit the data during its learning, thereby resulting in an overfitted model. (

**b**) SVR discards the differences between pre-touch distances and instead finds the hyper/plane that best suites its optimization criterion i.e., minimization of the orthogonal distances between pre-touch data and the candidate boundary. It is apparent that in 3D space of the facial pre-touch distances a hemisphere is the best candidate. (

**c**) Lasso’s learning process appears to better balance the balanced bias-variance tradeoff while satisfying its criterion that is to keep the entries of its learned weight matrix small (i.e., potentially as coarse-grained as possible), thereby allowing for a better generalization to novel cases. The middle row gives the top-view of the surfaces that were estimated by each of these models.

**Figure 6.**Distribution of estimated pre-touch distances by each of these models. This subplot verifies that GP perfectly matched (i.e., overfitted) the data and that SVR’s estimate resulted in a uniform boundary in the form of a hemisphere around the face area.

**Table 1.**RMSE values using Lasso, SVR, and GP. Entries M${}_{i}$ and SD${}_{i}$, i = $0,4$ refer to the mean and the standard deviation of RMSEs associated with these models while using polynomial degrees 0 (i.e., no polynomial degree) and 4.

Models | p < | W(26) | r | M_{0} | SD_{0} | M_{4} | SD_{4} |
---|---|---|---|---|---|---|---|

Lasso | 0.001 | 36.57 | 1.16 | 8.19 | 0.85 | 5.79 | 1.60 |

SVR | 0.001 | 12.19 | 0.39 | 8.07 | 0.84 | 7.69 | 0.85 |

GP | 0.001 | 19.64 | 0.62 | 16.79 | 3.64 | 14.27 | 2.70 |

**Table 2.**Pairwise models’ RMSE comparison. Subscripts 0 and 4 correspond to the case of polynomial degree 0 (i.e., no polynomial degree) and 4.

Models | p_{0}< | W_{0}(26) | r_{0} | p_{4}< | W_{4}(26) | r_{4} |
---|---|---|---|---|---|---|

Lasso vs. GP | 0.001 | 12.22 | 0.86 | 0.001 | 12.21 | 0.86 |

Lasso vs. SVR | = 0.31 | 1.03 | 0.07 | 0.001 | 8.00 | 0.57 |

Lasso vs. Fixed | 0.001 | 14.11 | 1.00 | 0.001 | 14.11 | 0.86 |

SVR vs. GP | 0.001 | 12.22 | 0.86 | 0.001 | 12.20 | 0.86 |

SVR vs. Fixed | 0.001 | 14.11 | 1.00 | 0.001 | 14.11 | 1.00 |

GP vs. Fixed | 0.001 | 14.11 | 1.00 | 0.001 | 14.11 | 1.00 |

**Table 3.**Effect of polynomial degree on improving the coefficient of determination (${R}^{2}$) in Lasso, SVR, and GP. M${}_{i}$ and SD${}_{i}$, i = $0,4$ refer to the mean and the standard deviation of RMSEs associated with these models while using polynomial degrees 0 (i.e., no polynomial degree) and 4.

Models | p < | W(26) | r | M${}_{0}$ | SD${}_{0}$ | M${}_{4}$ | SD${}_{4}$ |
---|---|---|---|---|---|---|---|

Lasso | 0.001 | 36.74 | 1.16 | −0.06 | 0.08 | 0.44 | 0.30 |

SVR | 0.001 | 29.08 | 0.92 | −0.03 | 0.09 | 0.06 | 0.11 |

GP | 0.001 | 10.29 | 0.33 | −2.47 | 0.93 | −2.05 | 0.84 |

**Table 4.**Coefficient of determination (${R}^{2}$). Comparison of the use of average with Lasso, SVR, and GP with and without polynomial degrees. Subscripts 0 and 4 correspond to the case of polynomial degree 0 (i.e., no polynomial degree) and 4.

Models | p < | W(26) | r | p < | W(26) | r |
---|---|---|---|---|---|---|

Lasso | 0.001 | 27.39 | 0.87 | 0.001 | 47.84 | 1.51 |

SVR | 0.001 | 4.51 | 0.14 | 0.001 | 37.27 | 1.18 |

GP | 0.001 | 22.90 | 0.72 | 0.001 | 52.62 | 1.66 |

**Table 5.**Pairwise model’s ${R}^{2}$ comparison. Subscripts 0 and 4 correspond to the case of polynomial degree 0 (i.e., no polynomial degree) and 4.

Models | p${}_{0}$< | W${}_{0}$(26) | r${}_{0}$ | p${}_{4}$< | W${}_{4}$(26) | r${}_{4}$ |
---|---|---|---|---|---|---|

Lasso vs. GP | 0.001 | 12.22 | 0.86 | 0.001 | 12.21 | 0.86 |

Lasso vs. SVR | 0.001 | 4.95 | 0.35 | 0.001 | 6.84 | 0.48 |

Lasso vs. Fixed | 0.001 | 14.11 | 1.00 | 0.001 | 14.11 | 1.00 |

SVR vs. GP | 0.001 | 12.22 | 0.86 | 0.001 | 12.20 | 0.86 |

SVR vs. Fixed | 0.001 | 14.11 | 1.00 | 0.001 | 14.11 | 1.00 |

GP vs. Fixed | 0.001 | 14.11 | 1.00 | 0.001 | 14.11 | 1.00 |

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**MDPI and ACS Style**

Keshmiri, S.; Shiomi, M.; Shatani, K.; Minato, T.; Ishiguro, H. Critical Examination of the Parametric Approaches to Analysis of the Non-Verbal Human Behavior: A Case Study in Facial Pre-Touch Interaction. *Appl. Sci.* **2020**, *10*, 3817.
https://doi.org/10.3390/app10113817

**AMA Style**

Keshmiri S, Shiomi M, Shatani K, Minato T, Ishiguro H. Critical Examination of the Parametric Approaches to Analysis of the Non-Verbal Human Behavior: A Case Study in Facial Pre-Touch Interaction. *Applied Sciences*. 2020; 10(11):3817.
https://doi.org/10.3390/app10113817

**Chicago/Turabian Style**

Keshmiri, Soheil, Masahiro Shiomi, Kodai Shatani, Takashi Minato, and Hiroshi Ishiguro. 2020. "Critical Examination of the Parametric Approaches to Analysis of the Non-Verbal Human Behavior: A Case Study in Facial Pre-Touch Interaction" *Applied Sciences* 10, no. 11: 3817.
https://doi.org/10.3390/app10113817