# Kohonen Neural Network Investigation of the Effects of the Visual, Proprioceptive and Vestibular Systems to Balance in Young Healthy Adult Subjects

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Kohonen Neural Network

- i.
- Initialization

_{mn}is associated with the connection from m

^{th}feature of the input vector (representing an input example) to n

^{th}neuron. The number of weights for each neuron is the same as the number of features in the input vector. The weights can be initialized based on prior information or small randomly selected values close to zero. The learning rate and neighborhood size are also initialized (these are defined in step iii). Kohonen network requires the learning termination point to be initialized. The manners this can be achieved are explained in step (iii).

- ii.
- Competition

^{th}training input vector (Xj). Each neuron determines the closeness (or distance) of the current input vector to the weights associated with its connections. The neuron with the closest connection weights to the input vector (i.e., smallest distance) is selected as the winner. When the Euclidean distance is used to determine closeness, the distance (d

_{n}) for neuron n is

- iii.
- Adaptation

**W**

_{-(j_current)}and

**W**

_{-(j_updated)}represent the current and updated weight vectors for the winning neuron respectively. The learning rate (0 < μ ≤ 1) controls the amount of weights changes taking place during each learning iteration. Larger values of μ lead to faster learning but they may reduce adaptation effectiveness. Its initial value is typically chosen heuristically.

- iv.
- Termination of iterations

## 3. Methodology

#### 3.1. Accelerometry Algorithm to Analyse Postural Sway

_{x}, a

_{y,}and a

_{z}are shown as α, β, and γ respectively. They are obtained from their directional cosines cos(α), cos(β), and cos(γ) respectively. The angles φ

_{1}, φ

_{2}, φ

_{3}, φ

_{4}, and φ

_{5}are used for mathematical justifications. The ground displacements from the origin in the x and y directions are d

_{x}and d

_{y}respectively and H represents the ground projection of the COM height. Equations (3)–(5) describe the algorithm’s operation. The units for distance, acceleration and angle were chosen as centimeters (cm), centimeters per second square (cm/s

^{2}), and degrees (°) respectively.

#### 3.2. Accelerometry Device Used for Data Recording

#### 3.3. Participants’ Details and Experimental Procedure

#### 3.4. Data Analysis

#### 3.4.1. Conversion of the Raw Accelerometry Data into Sway Information

_{x}and d

_{y}were obtained using Equations (3)–(5). The subject’s body position, velocity, and acceleration were obtained using Equations (6) and (7), where ${D}_{k}{}_{n}$, ${V}_{k}{}_{n}$, and ${A}_{k}{}_{n}$ are the positional displacements, velocity, and acceleration respectively, ${D}_{k}{}_{RMS}$, ${V}_{k}{}_{RMS}$, and ${A}_{k}{}_{RMS}$ are their corresponding root mean square (RMS) values, k corresponds to the direction of interest, i.e., ML and AP, ${d}_{k}{}_{1}$ is the first term used to remove the inclination offset on the subject’s back.

#### 3.4.2. Clustering of the Postural Sway Information

^{©}(MathWorks

^{®}, Natick, MA, USA) batch algorithm of the Kohonen network was used for training with a Kohonen map size of 10 by 10 neurons (total 100 neurons). A large map was used to explore the relationships between the four conditions of mCTSIB. The default value of the initial neighborhood size (i.e., 3 neurons) was used for the training and the number of training iterations was set to 1000. The entire dataset was used as the training and test set because the interest was to explore the interactions between the conditions of the mCTSIB. Each mCTSIB condition consisted of the data from the 23 subjects and the clustering of the data set was conducted by pairing each condition with condition 1, taking condition 1 as the reference (as condition 1 incorporated all the balance-related sensory systems). Therefore, three examination combinations could be carried out, i.e., conditions: 1 and 2, 1 and 3, and 1 and 4.

^{®}, Massachusetts, USA) batch was used for the implementation of the K-means clustering with the default distance metric, i.e. Euclidean. The processes involved were representing the porotype vectors formed during the first abstraction level by their centroids and then clustering the resulting centroids. The prototype vectors represented the neurons associated with at least one input data. The main issue that needed considering when performing the K-means algorithm, was determining the number of clusters. To this effect, the number of clusters was determined by performing K-means clustering on the resulting centroids of the prototypes formed during the first abstraction level for the different number of clusters (K) varying from 2 to 30 and evaluating the resulting cluster separation, using the Davies-Bouldin (DB) index as the measure of the clustering separation. The DB index is an internal evaluation measure based on the ratio of within to between cluster separations [34]. Usually, the lower the value of the DB index, the better the clustering performance. The DB index was determined using Equation (8).

_{i}, ${\sigma}_{{c}_{j}}$ is the standard deviation of cluster c

_{j}, ${\mu}_{{c}_{i}}$ is mean of cluster c

_{i}, ${\mu}_{{c}_{j}}$ is mean of cluster c

_{j}, DB

_{ij}is an array of DB indices for cluster i with respect to the j

^{th}cluster, where i ≠ j, j = i + 1:k, DB

_{i}is DB index for the i

^{th}cluster. The number of clusters with the minimum DB was used for external evaluation.

#### 3.4.3. Clustering Performance

_{ij}is the number of elements of class j in the i

^{th}cluster, n

_{i}is the total number of elements in the i

^{th}cluster, n is the total number of elements of the dataset, purity

_{i}is the i

^{th}purity of the clustering. ${n}_{i{j}_{i}}$ is the maximum elements of the classes in the i

^{th}cluster, prec

_{i}is the i

^{th}precision. ${m}_{{j}_{i}}$ is the number of elements of the resulting maximum j

^{th}class of the i

^{th}cluster, recall

_{i}is the recall of the i

^{th}cluster. The F-measure of the clustering was obtained by taking the average over all the clusters as

^{©}(version 2017a, MathWorks

^{®}, Massachusetts, USA) batch while the statistical test was carried out using SPSS

^{®}(version 24, IBM, Armonk, NY, USA).

## 4. Results

#### 4.1. Correlation Result

_{τ}(21) = 0.929, p < 0.01) while a significant weak positive correlation existed between the RMS position and RMS velocity r

_{τ}(21) = 0.344, p = 0.022), and the RMS position and RMS acceleration (r

_{τ}(21) = 0.32, p = 0.032) with the level of significance (α) equal to 5%. Thus, RMS position and velocity were used for the subsequent analysis.

#### 4.2. Clustering Results

## 5. Discussions

- i.
- The clustering of the postural sway, based on the RMS measures of the body’s position and velocity of the AP direction, showed larger values of external measures of the clustering performances as compared to similar variables from the ML direction. As a result, it may be inferred that the AP direction was more sensitive to the effect of the information of the sensory system as compared to the ML direction.
- ii.
- Hindrance in the operation of the visual system leads to an increase in the external performance measures of the clustering in the ML direction. In clustering between the eyes open conditions (conditions 1 and 3), the clustering evaluation measures, i.e. purity, precision, recall, and F-measure were 0.5, which was equal to the minimum value that could occur from the clustering. Thus, postural sway in the ML direction is a characteristic of the contribution of the visual system.
- iii.
- Using separate directions resulted in differing order of similarities across the four conditions of the mCTSIB. When the clustering measures of the AP direction were used for analysis, the order of similarities of the conditions were conditions 1, 2, 3, and 4. However, when the clustering measures of the ML direction were used, the order of similarities were conditions 1, 3, 2, and 4 and the results showed less disparity across the conditions. When the measures from the AP and ML directions were combined, the external clustering performance measures were reduced. This indicated that combining the results of ML and AP directions results in closer similarities between the conditions.
- iv.
- There was not a large variation between the maximum and the minimum (0.5) values across all external measures of the clustering performance between the conditions of the mCTSIB using the RMS values of the position and velocity of the respective ML and AP directions. The maximum value of the external measures corresponded to the value of the precision measure (0.795) for the clustering between the conditions 1 and 4. In the case of clustering with two clusters, the minimum and maximum values of the external measures that can occur for two groups with an equal number of samples are 0.5 and 1 respectively. Thus, the difference of 0.295 between the precision value and the minimum i.e. 0.795 minus 0.5 is considered small. Therefore, it was concluded that for healthy young adult subjects, there is a strong interrelationship between the mCTSIB conditions and their postural sway results cannot be clustered well into two distinct groups.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Sway projection based on the inverted pendulum [30].

**Figure 4.**A subject performing condition 3 of the mCTSIB with a white sponge under his feet and the accelerometer transmitter unit (the white box) worn at the lower back.

**Figure 5.**Correlation between the variables using the Kohonen network weight planes. (

**a**) RMS position, (

**b**) RMS velocity, and (

**c**) RMS acceleration respectively. The horizontal and vertical axes are neurons’ positions.

**Figure 6.**Plot of neighborhood distance and input vector hits of conditions 1 and 4. (

**a**,

**b**) representing the AP direction, (

**c**,

**d**) representing the ML direction. The horizontal and vertical axes are neurons positions.

**Figure 8.**Results of median values of the external measures over 30 repetitions: (

**a**) mCTSIB conditions 1 and 2, (

**b**) mCTSIB conditions 1 and 3 (

**c**) mCTSIB conditions 1 and 4.

**Figure 9.**Results of the median values of external measures for the combination of the ML and AP directions for 30 repetitions.

**Table 1.**Results of the median (interquartile range) values of the external measures for 30 clustering repetitions.

mCTSIB Conditions | Purity | Precision | Recall | F-Measure | ||||
---|---|---|---|---|---|---|---|---|

ML | AP | ML | AP | ML | AP | ML | AP | |

1 and 2 | 0.522 (0.022) | 0.565 (0.065) | 0.530 (0.035) | 0.58 (0.063) | 0.522 (0.022) | 0.565 (0.065) | 0.526 (0.028) | 0.573 (0.059) |

1 and 3 | 0.500 (0.022) | 0.565 (0.065) | 0.500 (0.030) | 0.613 (0.070) | 0.500 (0.022) | 0.565 (0.065) | 0.500 (0.026) | 0.594 (0.061) |

1 and 4 | 0.522 (0.022) | 0.652 (0.044) | 0.542 (0.055) | 0.795 (0.014) | 0.522 (0.022) | 0.652 (0.044) | 0.532 (0.040) | 0.717 (0.033) |

Averages | 0.515 (0.022) | 0.594 (0.058) | 0.524 (0.040) | 0.662 (0.049) | 0.515 (0.022) | 0.594 (0.058) | 0.519 (0.031) | 0.628 (0.051) |

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**MDPI and ACS Style**

Ojie, O.D.; Saatchi, R. Kohonen Neural Network Investigation of the Effects of the Visual, Proprioceptive and Vestibular Systems to Balance in Young Healthy Adult Subjects. *Healthcare* **2021**, *9*, 1219.
https://doi.org/10.3390/healthcare9091219

**AMA Style**

Ojie OD, Saatchi R. Kohonen Neural Network Investigation of the Effects of the Visual, Proprioceptive and Vestibular Systems to Balance in Young Healthy Adult Subjects. *Healthcare*. 2021; 9(9):1219.
https://doi.org/10.3390/healthcare9091219

**Chicago/Turabian Style**

Ojie, Oseikhuemen Davis, and Reza Saatchi. 2021. "Kohonen Neural Network Investigation of the Effects of the Visual, Proprioceptive and Vestibular Systems to Balance in Young Healthy Adult Subjects" *Healthcare* 9, no. 9: 1219.
https://doi.org/10.3390/healthcare9091219