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M-Score (Mode-Range Normalization)

Source: R/norm_mode_range.R
norm_mode_range.Rd

Unlike Z-Score or Min-Max, the M-Score algorithm identifies the "Mode Range" (the most frequent value range) and maps it to 0. This effectively suppresses the noise of daily routine (e.g., stable step counts) and amplifies anomalies (e.g., frailty or sudden activity).

It maps:

  • Mode Range: \([k_L, k_R] \to 0\) (Baseline/Routine)

  • Left Tail: \([min, k_L) \to [-1, 0)\) (Decline/Frailty)

  • Right Tail: \((k_R, max] \to (0, 1]\) (Surge/Hyperactivity)

Usage

norm_mode_range(x, tau = 0.8, digits = 0)

Arguments

x

A numeric vector.

tau

A numeric value (0 to 1). The threshold ratio for defining the mode plateau. Bins with freq >= tau * max_freq are considered part of the routine. Default is 0.8.

digits

Integer or NULL. If not NULL, values are rounded to this many decimal places solely for identifying the mode. This makes the algorithm robust against sensor noise (e.g., 1.0001 vs 1.0002). Default is 0 (rounds to integer), which is ideal for step counts or heart rates. Set to NULL to disable rounding.

Value

A numeric vector in the range [-1, 1].

Details

A robust normalization method designed for longitudinal behavioral data with a "routine plateau". Also known as Mode-Range Normalization (MRN).

References

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

Examples

# Scenario 1: Integer data (Standard)
steps <- c(3000, 3000, 200, 5000)
norm_mode_range(steps)
#> [1]  0  0 -1  1

# Scenario 2: Noisy Sensor Data (Floating point)
# Without 'digits', these would be seen as different values.
# With digits=1, they are grouped into the same mode.
sensor_data <- c(9.81, 9.82, 9.80, 2.5, 15.0)
norm_mode_range(sensor_data, digits = 1)
#> [1]  0  0  0 -1  1