**1. Introduction**

Falls are one of the leading causes of death among the elderly [1]. Every year, 28% to 35% of the elderly fall at least once and this rate increases with age [2]. Falls can have severe physical, psychological and even social consequences. They can also heavily affect the independent quality of living. They can result in bruises and swellings, as well as fractures and traumas [3]. A significant risk is the *long-lie*. This happens when an elderly person remains on the ground for a long duration without being able to call for help. It is associated with death within the next few months following the accident [4]. It also affects the elderly's self-confidence who may develop the *fear of falling*' syndrome. It leads to anxiety when performing Activities of Daily Living (ADLs) and can lead to subsequent falls [1].

Therefore, the elderly must continuously be monitored to ensure their safety. Families organize visits but these can be inconvenient and even insufficient. Hiring caregivers or

**Citation:** Zurbuchen, N.; Wilde, A.; Bruegger, P. A Machine Learning Multi-Class Approach for Fall Detection Systems Based on Wearable Sensors with a Study on Sampling Rates Selection. *Sensors* **2021**, *21*, 938. https://doi.org/10.3390/s21030938

Academic Editor: Klaus Moessner Received: 22 December 2020 Accepted: 26 January 2021 Published: 30 January 2021

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moving into nursing homes are sometimes not affordable options. Recent progresses in technology have enabled the development of Assisted-Living Systems (ALSs) [5]. They can assist the elderly and provide a safer environment through constant monitoring while relieving caregivers' workload. However, ALSs create other challenges such as privacy concerns and acceptability issues that need to be addressed [6].

Fall Detection Systems (FDSs) are part of ALSs. Their goals are to identify falls and notify caregivers so that they can intervene as fast as possible. However, fall recognition is challenging from a computational perspective. Falls can be defined as "the rapid changes from the upright/sitting position to the reclining or almost lengthened position, but it is not a controlled movement" [7]. There is a higher acceleration during falls. Another challenge is that falls can happen in innumerable scenarios. They may occur anywhere at any time [3]. Their starting and ending body posture as well as their direction (e.g., forward, backward) may vary [1]. Hence, FDSs must cover the whole living area. Their reliability must be high while minimizing false alarms, all the while respecting the elderly's privacy.

This paper is an extension of our work accepted at the ICAIIC 2020 [8]. This paper has three research questions:

RQ1: *What is the difference in performance across various types of Machine Learning (ML) algorithms in a FDS?*

To answer this, we developed a reliable FDS by the mean of wearable sensors (accelerometer and gyroscope) and ML algorithms. The goal is to compare lazy, eager and ensemble learning algorithms and assess their results. We implemented five algorithms and tested them in the same setup.

RQ2: *What is the effect of the sensors' sampling rate on the fall detection?*

To study this, we analyzed the influence of the sensors' sampling rate on the detection. We filtered the data in order to reduce the number of samples measured per second. We then experimented on the filtered data with five ML algorithms. This research question extends our previous work [8].

RQ3: *What is the difference in performance across various types of ML algorithms by adopting a multi-class approach for identifying phases of a fall?*

We experimented a different fall detection approach where falls are split into three phases. These are: the period before the fall happens (pre-fall), the fall itself (impact) and after the fall happened (post-fall). This research question extends our previous work [8].

The rest of this paper is organized as follows. In Section 2, we discuss existing FDSs and highlight their distinctive features. Section 3 covers the employed methodology. Section 4 presents and discusses the obtained results. Finally, we conclude with a comment on future work in Section 5.
