Convolution Matrix Anomaly Detection (CMAD)

CMAD is a lightweight, unsupervised framework for detecting clusters of negative spatio-temporal anomalies in sequential 2D data. It is designed for applications such as ice melt detection, environmental degradation, loss analysis, and decline-focused change detection.

CMAD operates on consecutive time steps, requires no labels, and adapts automatically to arbitrary spatial resolutions.

⚠️ Important Version Note

This version of CMAD detects clusters of negative anomalies only.

An anomalous event is identified when a spatially contiguous cluster of locations exhibits an extreme negative change between consecutive time steps that exceeds the normal (e.g., loss, decrease, melting, erosion).

Positive changes are intentionally ignored in this release.

Key Features

• ✔ Unsupervised (no training labels required)
• ✔ Works with images or generic 2D time-series arrays
• ✔ Supports arbitrary spatial dimensions (no fixed size)
• ✔ Adaptive IQR-based thresholding
• ✔ Binary anomaly masks (1 = anomaly, 0 = normal)
• ✔ CPU-only by default (GPU-ready via PyTorch)
• ✔ Suitable for large spatio-temporal datasets

Method Overview

Given a time series of 2D data
[ X = {X_1, X_2, \dots, X_T}, \quad X_t \in \mathbb{R}^{H \times W} ]

CMAD performs:

1. Temporal differencing [ D_t = X_{t+1} - X_t ]

2. 2×2 convolution with stride-2 downsampling

   • Captures localized spatial changes while reducing resolution

3. Second-stage 2×2 pooling

   • Aggregates local neighborhoods to emphasize spatially coherent patterns

4. Adaptive IQR-based thresholding

   • Per-cell thresholds learned from training data

5. Back-projection

   • Detected anomalous regions are mapped back to the original spatial resolution using back projection strategy

6. Negative-only cluster filtering

   • A region is marked anomalous only if:
     • It exceeds the adaptive threshold and
     • The temporal difference is negative
     • The signal forms a spatially contiguous cluster

Demo Code

from cmad import CMAD
import numpy as np

X_train = np.random.randn(30, 64, 64)
X_test  = np.random.randn(10, 64, 64)


#Demo Code for CPU
cmad = CMAD(device="cpu")
cmad.fit_from_array(X_train)

anomaly_masks = cmad.predict_from_array(X_test)
print(anomaly_masks.shape)  # (T-1, H, W)


## Demo Code for GPU (cuda)
cmad = CMAD(device="cuda")
cmad.fit_from_array(X_train)
anomaly_masks = cmad.predict_from_array(X_test)

## Demo Code for Apple Silicon (MPS)
cmad = CMAD(device="mps")
cmad.fit_from_array(X_train)
anomaly_masks = cmad.predict_from_array(X_test)

Synthetic Demo Example

import numpy as np
import matplotlib.pyplot as plt
from cmad import CMAD

T, H, W = 20, 50, 50
X = np.random.randn(T, H, W)

# Inject negative anomaly
X[10:, 20:25, 20:25] -= 5

X_train = X[:15]
X_test = X[15:]

cmad = CMAD(device="cpu")
cmad.fit_from_array(X_train)

anomaly_masks = cmad.predict_from_array(X_test)

accumulated = anomaly_masks.sum(axis=0)
plt.imshow(accumulated, cmap="hot")
plt.colorbar()
plt.title("Accumulated Negative Anomalies")
plt.show()

Installation

pip install cmad

Citation

If you use CMAD in your research, please cite the following paper:

@inproceedings{devnath2024cmad,
  author    = {Maloy Kumar Devnath and Sudip Chakraborty and Vandana P. Janeja},
  title     = {CMAD: Advancing Understanding of Geospatial Clusters of Anomalous Melt Events in Sea Ice Extent},
  booktitle = {Proceedings of the 32nd ACM SIGSPATIAL Conference},
  year      = {2024},
  publisher = {ACM},
  doi       = {10.1145/3678717.3691280}
}

Full Reference

Maloy Kumar Devnath, Sudip Chakraborty, and Vandana P. Janeja. 2024.
CMAD: Advancing Understanding of Geospatial Clusters of Anomalous Melt Events in Sea Ice Extent.
Proceedings of the 32nd ACM International Conference on Advances in Geographic Information Systems (SIGSPATIAL ’24).
ACM. https://doi.org/10.1145/3678717.3691280