Forest Proximities for Time Series (2410.03098v3)

Abstract: RF-GAP has recently been introduced as an improved random forest proximity measure. In this paper, we present PF-GAP, an extension of RF-GAP proximities to proximity forests, an accurate and efficient time series classification model. We use the forest proximities in connection with Multi-Dimensional Scaling to obtain vector embeddings of univariate time series, comparing the embeddings to those obtained using various time series distance measures. We also use the forest proximities alongside Local Outlier Factors to investigate the connection between misclassified points and outliers, comparing with nearest neighbor classifiers which use time series distance measures. We show that the forest proximities seem to exhibit a stronger connection between misclassified points and outliers than nearest neighbor classifiers.

• The paper introduces PF-GAP, an extension of RF-GAP that enhances time series classification using proximity forests.
• It employs Multi-Dimensional Scaling and k-means clustering to demonstrate superior inter-class separation compared to traditional distance measures.
• The study shows that PF-GAP improves outlier detection with higher F1 scores, paving the way for advanced anomaly detection applications.

Forest Proximities for Time Series

The paper "Forest Proximities for Time Series" investigates the extension of RF-GAP, a defined random forest proximity measure, to proximity forests, specifically within the domain of time series classification. This extension, termed PF-GAP, incorporates the geometric and accuracy-preserving properties of RF-GAP to handle time series data. The researchers proposed utilizing PF-GAP proximities for generating vector embeddings and for outlier detection in time series datasets.

Methodology and Evaluation

The paper introduces PF-GAP as an adaptation of RF-GAP to proximity forests, facilitating class-specific proximities that are extended to time series data. Proximity forests, providing efficient and accurate classification by exploiting diverse time series distance measures, are optimized in this investigation using PF-GAP for enhanced proximity measurement. PF-GAP's computation involves bootstrapping to introduce in-bag and out-of-bag distinctions necessary for meaningful proximity definitions.

The researchers applied Multi-Dimensional Scaling (MDS) to transform the proximity matrices into two-dimensional spaces for effective visualization. By forming a distance matrix from these proximities, the paper evaluates the separation quality in projected vector spaces. The comparison is conducted against traditional time series distance measures including DTW, DDTW, and others, underpinning the paper's argument for superior inter-class separation offered by PF-GAP.

Their experiments demonstrate through $k$-means clustering that PF-GAP-generated embeddings exhibit distinct class separation for datasets like GunPoint and ItalyPowerDemand, outperforming other distance measures. Numerical results consistently show PF-GAP achieving higher $k$-means clustering scores, confirming its effectiveness in creating clean separations between classes within the embedding space.

Outlier Detection

The paper also explores outlier detection, comparing misclassification in proximity forests to time series outliers identified via PF-GAP proximities. By quantifying outliers using modified Local Outlier Factors that leverage forest proximities, the research aligns misclassified instances with outlier categorizations more effectively than with conventional distance measures. PF-GAP consistently achieved higher F1 scores across evaluated datasets, illustrating its superior capacity for identifying outliers corroborated with classification tasks.

Implications and Future Work

PF-GAP’s introduction extends the applicability of random forest-inspired proximities to time series data, providing a new dimension in analyzing such data sets. The strong results in both embedding quality and outlier detection suggest potential advancements in visualization, anomaly detection, and other time series applications. However, dependence on the number of trees and the influence of selected hyperparameters in proximity forests present areas requiring further exploration.

Future research is recommended to explore additional applications of PF-GAP, possibly extending to time series forecasting and clustering tasks. Additionally, revisiting the forest proximities with more contemporary forests like proximity forest 2.0 might yield further insights and enhancements in computation and accuracy.

Conclusion

Overall, the paper effectively showcases the benefits of PF-GAP for time series data by securing improved embeddings and enhancing outlier detection capabilities. These proximities represent a promising toolset for the analysis of time series data, empowering further research in this vibrant area of data science.