Self-organized Clustering System for Unsupervised Distribution Shift Detection

Core Concepts

A self-organizing clustering system that can efficiently monitor and detect distribution changes in high-dimensional data streams without any assumptions about the data distribution.

Abstract

The proposed framework addresses the problem of distribution shift detection in high-dimensional data streams. The key highlights are:

It develops a bio-inspired self-organizing clustering system to assess distribution changes in data streams, which can be applied in unsupervised contexts.

It investigates the use of Self-Organizing Maps (SOMs) and Scale-Invariant Maps (SIMs) for dimensionality reduction, exploring the statistical aspects of the latent space.

By construction, the framework generates a univariate signal that can be reasonably assumed to be Gaussian, enabling efficient computation of the Kullback-Leibler divergence to quantify distribution changes.

The framework first applies a non-linear projection of the high-dimensional input data using a topology-preserving mapping (SOM or SIM). It then creates a distance matrix capturing the geometric relationships between the projected points and the representative neurons. This distance matrix is further embedded using statistical summaries, with the mean function being the focus in this work.
The resulting univariate signal is monitored for distribution changes using the Kullback-Leibler divergence between consecutive chunks of data. A simple decision rule based on outlier detection is used to identify significant distribution shifts.
The empirical evaluation on synthetic and real-world datasets, including MNIST with adversarial samples, gas sensor measurements, and ozone data, demonstrates the potential of the proposed approach in efficiently detecting distribution shifts in high-dimensional data streams.

Stats

The mean function of the distance matrix captures sufficient information to distinguish between the original MNIST samples and the adversarial MNIST samples.

Quotes

None

Key Insights Distilled From

A Self-Organizing Clustering System for Unsupervised Distribution Shift Detection

by Seba... at arxiv.org 04-26-2024

https://arxiv.org/pdf/2404.16656.pdf

Deeper Inquiries

How can the proposed framework be extended to handle more complex types of distribution shifts, such as gradual or incremental shifts

To extend the proposed framework to handle more complex types of distribution shifts, such as gradual or incremental shifts, several modifications and enhancements can be considered:

Adaptive Learning Rates: Implementing adaptive learning rates in the self-organizing clustering process can help the framework adjust to gradual shifts in the data distribution. By dynamically changing the learning rates based on the rate of change in the data, the framework can better capture gradual shifts.

Dynamic Window Sizes: Introducing dynamic window sizes for monitoring the distribution shifts can enable the framework to detect incremental changes over time. By adjusting the window size based on the rate of change, the framework can effectively track incremental shifts in the data distribution.

Incorporating Time Series Analysis: Utilizing time series analysis techniques can enhance the framework's ability to detect gradual and incremental shifts. By analyzing the temporal patterns in the data stream, the framework can identify subtle changes in the distribution over time.

Ensemble Methods: Implementing ensemble methods that combine multiple models trained on different segments of the data stream can improve the framework's robustness to various types of distribution shifts. By aggregating the outputs of multiple models, the framework can provide more reliable detection of complex shifts.

What other statistical summaries of the distance matrix could be explored to further improve the robustness and sensitivity of the distribution shift detection

To further improve the robustness and sensitivity of the distribution shift detection, the framework can explore the following statistical summaries of the distance matrix:

Higher Order Moments: In addition to the mean function, incorporating higher-order moments such as variance, skewness, and kurtosis can provide a more comprehensive representation of the distribution in the latent space. By considering a wider range of statistical moments, the framework can capture more nuanced patterns in the data distribution.

Quantile-Based Summaries: Utilizing quantile-based summaries of the distance matrix can offer insights into the distribution's tail behavior and extreme values. By analyzing quantiles such as median, quartiles, and percentiles, the framework can detect outliers and anomalies that may indicate distribution shifts.

Entropy Measures: Calculating entropy measures of the distance matrix can quantify the uncertainty and complexity of the distribution in the latent space. By incorporating entropy-based metrics, the framework can capture the information content and variability of the data distribution, enhancing the detection of subtle shifts.

Correlation Analysis: Exploring the correlation structure within the distance matrix can reveal relationships between different dimensions in the latent space. By analyzing correlations between distance values, the framework can identify patterns and dependencies that may indicate distribution shifts.

Can the framework be adapted to incorporate domain knowledge or side information to enhance the distribution shift detection capabilities

To incorporate domain knowledge or side information into the framework for enhancing distribution shift detection capabilities, the following strategies can be implemented:

Feature Engineering: Integrate domain-specific features or engineered attributes that capture relevant information about the data distribution. By incorporating domain knowledge into the feature representation, the framework can improve its ability to detect shifts based on meaningful domain-specific characteristics.

Anomaly Detection Techniques: Utilize anomaly detection algorithms that leverage domain knowledge to identify unusual patterns or outliers in the data stream. By incorporating domain-specific anomaly detection methods, the framework can focus on detecting shifts that are relevant to the specific domain context.

Expert Rules: Incorporate expert-defined rules or heuristics that reflect domain-specific insights about expected data behavior. By encoding expert knowledge into the detection process, the framework can prioritize certain types of shifts or patterns that are deemed critical based on domain expertise.

Contextual Information: Integrate contextual information or metadata associated with the data stream to provide additional context for the distribution shift detection. By considering contextual factors such as time of day, seasonality, or external events, the framework can adapt its detection strategy based on the broader context of the data.