# Segmentation of Gait Sequences in Sensor-Based Movement Analysis: A Comparison of Methods in Parkinson’s Disease

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Peak Detection

#### 2.2. Multi-subsequence Dynamic Time Warping

- Distance matrix $\mathbf{D}$: The elements of $\mathbf{D}$ represent the pairwise distance between the elements of the template X and the gait sequence Y. The size of the matrix $\mathbf{D}$ is $M\times T$. In the case of including several axes, separate distance matrices are computed and they are all summed up to construct a single distance matrix [33].
- Accumulated cost matrix $\mathbf{C}$: represents the distance between the template and the gait sequence as well as the accumulated costs of warping the template to parts of the gait sequence. The bottom row of matrix $\mathbf{C}$ is as follows:$$\mathbf{C}(1,t)=\mathbf{D}(1,t)\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\forall t\in \{1,\cdots ,T\}$$The first column is:$$\mathbf{C}(m,1)=\sum _{i=1}^{M}\mathbf{D}(i,1)\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\forall m\in \{1,\cdots ,M\}$$The remaining elements are calculated in a recursive manner as$$\begin{array}{c}\hfill \mathbf{C}(m,t)=\mathbf{D}(m,t)+min\left\{\mathbf{C}\right(m-1,t-1),\mathbf{C}(m-1,t),\mathbf{C}(m,t-1\left)\right\}\\ \hfill \forall m\in \{1,\cdots ,M\},t\in \{1,\cdots ,T\}\end{array}$$
- Distance function $\Delta $: The top row of matrix $\mathbf{C}$ represents the accumulated costs for warping the stride template X to the gait sequence Y and can be considered as a matching function $\Delta :[1:T]\to \mathbb{R}$.
- Warping path P: Warping path $P=({p}_{1},{p}_{2},\cdots ,{p}_{L})$ of length L with elements ${p}_{l}$ for $l\in \{1,\cdots ,L\}$ presents a good match between X and Y. Local minimums of the matching function $\Delta $ are considered as the end points of warping paths and starting points are obtained by backtracking on the accumulated cost matrix. A threshold should be chosen in order to select these local minimums in such a way to find the maximum number of relevant strides in the sequence.
- Boundary conditions for a complete stride:
- Start of warping path P is in the top row of the cost matrix $\mathbf{C}$.
- End of warping path P is in the bottom row of cost matrix $\mathbf{C}$.
- Condition to ensure warping path monotonically decreases:$${p}_{l+1}-{p}_{l}\in \{(1,0),(0,1),(1,1)\}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}for\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}l\in \{1,\cdots ,L\}$$

#### 2.3. Hierarchical Hidden Markov Models

## 3. Evaluation Study

#### 3.1. Data Collection and Setup

#### 3.2. Manual Data Labeling

#### 3.3. Implementation of Peak Detection

#### 3.4. Implementation of Euclidean DTW

#### 3.5. Implementation of Probabilistic DTW

#### 3.6. Implementation of hHMM

#### 3.7. Performance Assessment

## 4. Experimental Results

## 5. Discussion and Conclusion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Topology of a two-level hierarchical hidden Markov model (hHMM). Large circles represent states in the first level of the model. Each state in turn is an HMM with sub-states (dark circles). Here, we applied left-to-right HMMs in the second level.

**Figure 2.**(

**Left**) Shimmer sensor placement and axes definition (AX, AY and AZ form three dimensions of accelerometer and GX, GY and GZ form three dimensions of gyroscope); (

**Right**) Accelerometer and gyroscope data for one exemplary stride.

**Figure 3.**Labeling of an example of gyroscope signal including two strides, the following transition (non-stride) movement, and rest.

**Figure 4.**Template based on average of (

**Left**) a three-dimensional accelerometer signal, (

**Right**) a three-dimensional gyroscope signal. Signals AX, GX, and GY have a very low variation.

**Figure 5.**Mean ± STD of precision, recall and F-score for four methods. Asterisks represent a 5% significant difference between methods corresponding to 95% confidence interval.

Signal Combination | GZ | AXGZ | AYGZ | AXAYGZ |
---|---|---|---|---|

Threshold (steps of 5) | 10–25 | 20–30 | 20–30 | 25–40 |

Signal Combination | GZ | AXGZ | AYGZ | AXAYGZ |
---|---|---|---|---|

Threshold (steps of 1) | 8–15 | 8–15 | 8–15 | 8–15 |

Parameters | Values |
---|---|

Sliding window length (s) (steps of 0.20) | 0.10–0.70 |

Number of sub-states for stride | transition | rest (steps of 2) | 4–12 | 2–4 | 1 |

Number of Gaussian mixture model (GMM) components (steps of 2) | 8–12 |

Number of principal components (steps of 2) | 1–15 |

Method | Precision (%) | Recall (%) | F-score (%) |
---|---|---|---|

hHMM | 98.5 ± 0.4 | 93.5 ± 1.9 | 95.9 ± 0.9 |

eDTW | 94 ± 1.2 | 93.5 ± 0.8 | 93.8 ± 0.5 |

Peak detection | 87.4 ± 1.2 | 95.9 ± 1.8 | 91.5 ± 0.4 |

pDTW | 91.8 ± 2.1 | 90.1 ± 2.2 | 90.9 ± 1.4 |

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**MDPI and ACS Style**

Haji Ghassemi, N.; Hannink, J.; Martindale, C.F.; Gaßner, H.; Müller, M.; Klucken, J.; Eskofier, B.M.
Segmentation of Gait Sequences in Sensor-Based Movement Analysis: A Comparison of Methods in Parkinson’s Disease. *Sensors* **2018**, *18*, 145.
https://doi.org/10.3390/s18010145

**AMA Style**

Haji Ghassemi N, Hannink J, Martindale CF, Gaßner H, Müller M, Klucken J, Eskofier BM.
Segmentation of Gait Sequences in Sensor-Based Movement Analysis: A Comparison of Methods in Parkinson’s Disease. *Sensors*. 2018; 18(1):145.
https://doi.org/10.3390/s18010145

**Chicago/Turabian Style**

Haji Ghassemi, Nooshin, Julius Hannink, Christine F. Martindale, Heiko Gaßner, Meinard Müller, Jochen Klucken, and Björn M. Eskofier.
2018. "Segmentation of Gait Sequences in Sensor-Based Movement Analysis: A Comparison of Methods in Parkinson’s Disease" *Sensors* 18, no. 1: 145.
https://doi.org/10.3390/s18010145