fdars (version 0.3.3)

matrix.profile: Matrix Profile for Motif Discovery and Period Detection

Description

Computes the Matrix Profile using the STOMP (Scalable Time series Ordered-search Matrix Profile) algorithm. The Matrix Profile stores the z-normalized Euclidean distance between each subsequence and its nearest neighbor, enabling efficient motif discovery and period detection for non-sinusoidal patterns.

Usage

matrix.profile(fdataobj, subsequence_length = NULL, exclusion_zone = 0.5)

Value

A list of class "matrix_profile_result" with components:

profile

Numeric vector of minimum z-normalized distances at each position

profile_index

Integer vector of nearest neighbor indices (1-based)

subsequence_length

Subsequence length used

detected_periods

Candidate periods detected from arc analysis (top 5)

arc_counts

Arc counts at each index distance (for diagnostics)

primary_period

Most prominent detected period

confidence

Confidence score (0-1) based on arc prominence

Arguments

fdataobj

An fdata object.

subsequence_length

Length of subsequences to compare. If NULL, automatically determined as approximately 1/4 of series length.

exclusion_zone

Fraction of subsequence length to exclude around each position to prevent trivial self-matches. Default: 0.5.

Details

The Matrix Profile algorithm (Yeh et al., 2016; Zhu et al., 2016) is particularly suited for:

• Non-sinusoidal repeating patterns (unlike FFT/spectral methods)

• Motif discovery (finding repeated subsequences)

• Anomaly detection (subsequences with no good match)

The STOMP variant uses O(n^2) time complexity but is highly cache-efficient. For very long series (>10000 points), consider downsampling.

Period detection is based on "arc analysis": counting how often the nearest neighbor is a fixed distance away. Peaks in arc counts indicate periodicity.

References

Yeh, C. C. M., et al. (2016). Matrix profile I: All pairs similarity joins for time series: A unifying view that includes motifs, discords and shapelets. ICDM 2016.

Zhu, Y., et al. (2016). Matrix profile II: Exploiting a novel algorithm and GPUs to break the one hundred million barrier for time series motifs and joins. ICDM 2016.

See Also

estimate.period, sazed, lomb.scargle

Examples

# Periodic sawtooth wave (non-sinusoidal)
t <- seq(0, 10, length.out = 200)
period <- 2
X <- matrix((t %% period) / period, nrow = 1)
fd <- fdata(X, argvals = t)

# Compute Matrix Profile
result <- matrix.profile(fd, subsequence_length = 30)
print(result)
plot(result)

# Sine wave for comparison
X_sine <- matrix(sin(2 * pi * t / period), nrow = 1)
fd_sine <- fdata(X_sine, argvals = t)
result_sine <- matrix.profile(fd_sine, subsequence_length = 30)