Modelling Key Health Indicators from Sensor Data Using Knowledge Graphs and Fuzzy Logic
Abstract
:1. Introduction
Literature Review
2. Materials and Methods
- KG Model of KHI: We construct hierarchical knowledge graphs to represent critical health indicators, including sleep patterns, excretion control, physical mobility, and social interaction. In this work, we use the term ’excretion control’ as a general category; however, in clinical practice, it is more common to refer specifically to urinary and faecal control. It is important to note that in patients with incontinence who use absorbent products, data collection through environmental sensors may present limitations that should be considered. These graphs represent indicators as nodes, with edges that define relationships with control variables derived from sensor data. This structured approach allows us to integrate clinical knowledge with quantitative data, providing a comprehensive view of health status.
- Sensor Architecture for Data Acquisition: A minimally invasive sensing architecture is implemented, combining wearable devices and ambient sensors. Wearable devices track physical activity and sleep, while ambient sensors provide indoor localisation and activity data. This integration provides a general view of daily activity patterns while prioritising user comfort and long-term adherence.
- FL modelling of Linguistic Protoforms: FL bridges the gap between sensor data and clinical language. The temporal and linguistic terms used by healthcare professionals are modelled using membership functions, which allow the system to reason with imprecise and subjective information. This approach ensures that the system’s output is clinically relevant and interpretable.
2.1. Knowledge Graph Representation of Key Health Indicators
- V is a set of nodes (vertices) that represent entities or concepts related to health indicators. These entities are not merely static data points but are imbued with linguistic meaning, facilitating human-like reasoning.
- E is a set of edges that represent the relationships between these entities. Each edge is an ordered pair where .
- L is a set of labels associated with both the nodes and edges, providing semantic context.
- Each node/entity is associated with a protoform that captures its underlying semantic structure.
- These protoforms are instantiated with specific values derived from:
- –
- Terms: Linguistic variables representing ranges or categories of health indicators (e.g. “active mobility”, “adequate sleep time”).
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- Temporal Restrictions: Time-based constraints or patterns associated with health indicators (e.g., low physical activity “while daytime”).
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- Location Restrictions: Location-based constraints or patterns associated with user activity (e.g., sleep activity levels “in the living room”).
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- Quantifiers: Linguistic terms represent relative or absolute quantities, allowing the manipulation of linguistic concepts. They can be modelled under crisp or fuzzy approaches (e.g., “adequate number of excretions”, “most of sleeping time”).
- –
- Data Streams: Composed by the data from ambient and wearable devices collected and the inferred protoforms over time.
- This connection to protoforms allows the KG to reason with the semantic meaning of health data, not just its numerical values.
- In fuzzy rules, the relationships between nodes are assigned degrees of membership, reflecting the strength or certainty to the antecedents by means of fuzzy norms (T-norms and Co-norms) to represent conjunctive and disjunctive relationships, respectively.
- By applying these operators, the KG can perform fuzzy inference, combining evidence from multiple relationships to derive conclusions about health indicators. This allows for a more robust and flexible representation of complex health patterns.
2.2. Sensor Architecture for Data Acquisition
2.3. Fuzzy Logic Modelling of Linguistic Protoforms for Sensor Data
- V designates the fuzzy data stream derived from sensor or location sources.
- T, an optional element, specifies a fuzzy temporal window (FTW) , within which the fuzzy data streams are aggregated, represented as . The projection of a fuzzy temporal window T with a fuzzy data stream is achieved through a membership function associated with the FTW, which is derived from the temporal displacement , where , measuring the interval from a present time to the preceding timestamps within the data stream. For every timestamp , we compute the combined membership degrees of the terms, considering the fuzzy temporal influence, utilising t-norm and co-norm operations:
- –
- In max–min, the norms are defined as and , which are related to existential aggregators where a single value indicates the presence of a single value of V within the fuzzy temporal window T.
- –
- In weighted average = , the norms are defined as and , which are related to the weighted impact of the term V within the fuzzy temporal window T.
- L, also optional, acts as a location filter to compute the spatial interaction in the environment [12] .
- Q, also optional, acts as a quantifier to filter and modulate the degree of aggregation of .
3. Case Study
3.1. Real-Home Deployment
- A motion sensor and a flush sensor (both Aqara) in the bathroom, providing cross-validation for presence and flush detection (see Figure 6B).
- A smart plug to monitor energy consumption (TP-Link) in the bedroom lamp (see Figure 6C). Another smart plug in the living room to monitor the use of the TV.
- The patient wore a smart watch (Amazfit Bip U Pro) (see Figure 6D) that collected physiological and activity-related data, including heart rate, step count, and sleep quality, including periods of deep, normal, and light sleep.
3.2. Fuzzy Inference in KG for Sleep Pattern Evaluation
3.2.1. Input Data Sources
3.2.2. Knowledge Graph
- +) SA: Adequate sleep time
- SA1: Most of the sleeping at night. Evaluates whether most of the sleeping time occurs during the night window and combines quantity (Q), temporality (T), and value streams (V).
- SA2: Sleeping quantity. Assesses if the total sleep time falls between 6 and 8 h per day. Fuzzy weighted by value (V) and time window (T).
- +) SB: Quality of sleep
- SB1: Sleeping is normal or deep. Measures if the majority of sleep is spent in normal or deep stages and uses value (V), quantity (Q), and temporal alignment (T)
- SB2: Sleep in the bedroom Assesses whether sleep occurs predominantly in the bedroom and relies on value (V), localisation (L), and quantity (Q).
3.2.3. Discussion and Explainability
3.3. Fuzzy Inference in KG for Excretion Control
3.3.1. Input Data Sources
3.3.2. Knowledge Graph
- +) SA: Daily excretions
- Captures regularity and frequency of bathroom visits throughout the day aggregating value (V) and time-based frequency (T) over the full day.
- Defined as healthy when the total number of inferred excretion episodes is between 3 and 5 per day.
- +) SB: Night excretions
- Evaluates bathroom visits during the night calculated using a fuzzy combination of value (V) and temporal indicator (T) restricted to night-time hours.
- Considered healthy if the number of visits ranges between 0 and 2.
- +) S1: Excretion detection
- Core detection mechanism combining: flush events, presence in the toilet, and localisation in the toilet room.
- Fuzzy temporal aggregation is applied over short intervals (2 to 4 min) to infer likely excretion episodes.
- Outputs a time-aligned indicator that feeds into both the SA and SB branches.
3.3.3. Discussion and Explainability
3.4. Fuzzy Inference in KG for Physical Mobility
3.4.1. Input Data Sources
3.4.2. Knowledge Graph
- +) SA: Physical activity
- SA1: Active mobility. Assesses whether an adequate number of steps is taken each day and combines quantity (Q), temporality (T), and step count values (V).
- SA2: Walking consecutive. Evaluates whether walking sessions include at least one sustained period of approximately 30 min. Derived from continuous step activity patterns, weighted by time (T) and value (V).
- +) SB: Most activity outdoor
- Checks whether most activity occurs outside the home environment. Using location data (L), step values (V), and quantity (Q) to infer whether physical activity occurs predominantly in outdoor settings.
- Considered relevant to prevent the sedentary routines commonly associated with indoor confinement.
- +) SB: Physical mobility
- Aggregates quantity and location using fuzzy temporal indicators. The model balances beneficial closeness with potential overdependence, providing a complete interpretation of daily caregiver engagement.
3.4.3. Discussion and Explainability
3.5. Fuzzy Inference in KG for Adequate Caregiver Interaction
3.5.1. Input Data Sources
3.5.2. Knowledge Graph
- +) SA: Closeness
- The social distance is tracked and compared against a fuzzy threshold (for example, within 1 to 2 metres for at least 30 min/day).
- Includes temporal coverage (T), quantity of interactions (Q), and value assessment (V) of proximity episodes.
- Based on the detection of caregiver presence in specific rooms (e.g., bedroom, bathroom) where autonomy is expected.
- Uses spatial location (L) and value (V) indicators to assess appropriateness of room-sharing patterns.
- Aggregates both positive (company) and negative (dependence) contributions using fuzzy temporal indicators. The model balances beneficial closeness with potential over-dependence, providing a complete interpretation of daily caregiver engagement.
3.5.3. Discussion and Explainability
3.6. Data-Driven Approaches for Modelling KHI
- Temporal windowing: We employed a sliding window approach to aggregate sensor data [39]. This method enabled the capture of both current and preceding sensor values within defined window size (WS), providing a comprehensive context for each point of time. The window size for each protoform is elaborated in further detail in Table 1.
- Protoform Defuzzification: To enable the training of supervised learning models, the expert-defined protoforms of KHI were defuzzified using alpha-cuts. This transformation converted the fuzzy linguistic descriptions into a quantifiable, typically binary, classification problem for each indicator. The precise alpha-cut values used in this stage are presented in Table 1.
- Cross-Validation Strategy: For the validation of our models, we implemented a cross-validation strategy of 2-hour-leave-out. This method ensured that the models’ performance was assessed on entirely unseen temporal blocks of data, thus providing a more reliable estimation of their generalisation capabilities.
- Model Evaluation: The performance of the selected machine learning models, specifically K-Nearest Neighbours (KNN), Support Vector Machines (SVM) and Random Forest (RF), was thoroughly evaluated. Their effectiveness was quantified using established metrics, namely accuracy (ACC) and F1 score. The detailed evaluation results for each model are summarised in Table 1.
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
AAL | Ambient Assisted Living |
FL | Fuzzy Logic |
FTW | Fuzzy Temporal Window |
KHI | Fuzzy Health Indicators |
KG | Knowledge Graph |
TLA | Three letter acronym |
UWB | Ultra-Wideband |
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Alpha-Cut | WS | Protoform | ACC | F1 Score | ||||
---|---|---|---|---|---|---|---|---|
SVM | RF | KNN | SVM | RF | KNN | |||
0.75 | 360 | C#most_sleep_night_per_day | 0.89 | 0.83 | 0.87 | 0.88 | 0.79 | 0.88 |
0.75 | 360 | C#sleep_per_day | 0.56 | 0.76 | 0.88 | 0.52 | 0.73 | 0.89 |
0.98 | 360 | C#deep_per_day | 0.98 | 0.99 | 0.97 | 0.99 | 0.99 | 0.98 |
0.71 | 360 | C#bedroom_sleep_per_day | 0.71 | 0.67 | 0.86 | 0.66 | 0.62 | 0.86 |
0.5 | 15 | C#excretion_detection | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 |
0.5 | 360 | C#agg_wc_day_adequate | 0.77 | 0.83 | 0.92 | 0.75 | 0.81 | 0.92 |
0.25 | 360 | C#agg_wc_night_adequate | 0.82 | 0.90 | 0.96 | 0.83 | 0.88 | 0.96 |
0.25 | 360 | C#active_mobility | 0.74 | 0.80 | 0.95 | 0.71 | 0.78 | 0.95 |
0.25 | 60 | C#walking30m | 0.98 | 0.96 | 0.98 | 0.97 | 0.96 | 0.98 |
0.75 | 360 | C#walk_per_day_outdoor | 0.81 | 0.81 | 0.92 | 0.79 | 0.79 | 0.92 |
0.25 | 360 | C#social_distance2_per_day | 0.65 | 0.72 | 0.90 | 0.61 | 0.70 | 0.90 |
0.25 | 360 | C#non_privacy__per_day | 0.76 | 0.84 | 0.90 | 0.74 | 0.83 | 0.86 |
AVG | 0.80 | 0.84 | 0.93 | 0.79 | 0.82 | 0.92 |
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Polo-Rodríguez, A.; López, I.V.; Diaz, R.; Rivadeneyra, A.; Gil, D.; Medina-Quero, J. Modelling Key Health Indicators from Sensor Data Using Knowledge Graphs and Fuzzy Logic. Electronics 2025, 14, 2459. https://doi.org/10.3390/electronics14122459
Polo-Rodríguez A, López IV, Diaz R, Rivadeneyra A, Gil D, Medina-Quero J. Modelling Key Health Indicators from Sensor Data Using Knowledge Graphs and Fuzzy Logic. Electronics. 2025; 14(12):2459. https://doi.org/10.3390/electronics14122459
Chicago/Turabian StylePolo-Rodríguez, Aurora, Isabel Valenzuela López, Raquel Diaz, Almudena Rivadeneyra, David Gil, and Javier Medina-Quero. 2025. "Modelling Key Health Indicators from Sensor Data Using Knowledge Graphs and Fuzzy Logic" Electronics 14, no. 12: 2459. https://doi.org/10.3390/electronics14122459
APA StylePolo-Rodríguez, A., López, I. V., Diaz, R., Rivadeneyra, A., Gil, D., & Medina-Quero, J. (2025). Modelling Key Health Indicators from Sensor Data Using Knowledge Graphs and Fuzzy Logic. Electronics, 14(12), 2459. https://doi.org/10.3390/electronics14122459