prepkit: Robust preprocessing for Digital Health

Full Documentation & Tutorials: https://gonrui.github.io/prepkit/

"When Z-Score fails, use M-Score."

prepkit is a comprehensive R package designed for the preprocessing of longitudinal behavioral data, with a specific focus on gerontology, digital health, and sensor analytics.

Its flagship feature is the M-Score (Mode-Range Normalization), a novel algorithm designed to detect anomalies in data characterized by "habitual plateaus" (e.g., daily step counts, heart rate), where traditional methods like Z-Score or Min-Max scaling often fail due to skewed distributions and high-frequency routine noise.

📦 Installation

prepkit is rigorously tested on Linux, macOS, and Windows, with compatibility verified up to R 4.5 (development version).

Install the stable version from CRAN:

install.packages("prepkit")

You can install the development version from GitHub:

# install.packages("devtools")
devtools::install_github("Gonrui/prepkit")

🚀 Key Algorithms

Function	Algorithm / Description	Use Case
norm_mode_range	M-Score (New!)	Detects frailty/falls in elderly behavioral data by suppressing routine noise.
trans_boxcox	Robust Box-Cox	MLE-optimized power transform. Auto-handles non-positive values.
trans_yeojohnson	Yeo-Johnson	Power transform natively supporting negative values.
norm_l2	Spatial Sign	Projects data onto a unit hypersphere (L2 Norm). Ideal for high-dim clustering.
pp_plot	Density Visualizer	Instant "Before vs. After" visualization for normality checks.

📊 Quick Start: The Power of M-Score

Real-world sensor data often contains routine plateaus (e.g., an older adult consistently walking 3000 steps) and sensor noise (floating-point jitter).

M-Score handles both elegantly:

library(prepkit)

# 1. Simulate Sensor Data
# - Routine: ~3000 steps (with sensor jitter like 3000.1, 2999.9)
# - Anomaly: 200 steps (Fall/Frailty)
# - Anomaly: 6000 steps (Hyperactivity)
steps <- c(3000.1, 3000.2, 2999.8, 200.0, 3000.0, 6000.0)

# 2. Apply M-Score (with precision protection)
# The 'digits' parameter rounds values internally to identify the semantic mode,
# while preserving the precision of the anomalies.
m_scores <- norm_mode_range(steps, digits = 0)

# 3. View Results
print(data.frame(Raw = steps, M_Score = m_scores))

📐 Mathematical Foundation

The M-Score transforms data based on its Mode Interval (the routine plateau). Unlike Z-Score which penalizes stability (low variance), M-Score treats the most frequent range as the "Safe Zone" (Score = 0).

The transformation function $M(x)$ is defined as:

$$ M(x) = \begin{cases} -\frac{k_L - x}{k_L - k_{min}} & \text{if } x < k_L \quad (\text{Left Tail / Frailty}) \\ 0 & \text{if } k_L \le x \le k_R \quad (\text{Routine Plateau}) \\ \frac{x - k_R}{k_{max} - k_R} & \text{if } x > k_R \quad (\text{Right Tail / Hyper}) \end{cases} $$

Validated via symbolic computation (Wolfram Mathematica) for strict monotonicity.

📚 Citation

If you use prepkit or the M-Score algorithm in your research, please cite:

Gong, R. (2026). M-Score: A Robust Normalization Method for Detecting Anomalies in Longitudinal Behavioral Data. arXiv preprint.

📄 License

MIT © Rui Gong (Tokyo Metropolitan Institute of Gerontology)