Combining Data Mining and Visualization: UMAP on ROPE

This research explores data mining techniques for time-series data, focusing on enhancing the performance and interpretability of transformer models through Rotary positioning embedding (RoPE) and probabilistic sparse attention (ProbSparse). RoPE incorporates positional data into the query and key components of transformers, ensuring that each data point's relevance within a sequence is effectively captured. In this setup, the query represents the question each token poses to the rest, while the key holds information that other tokens need to determine relevance. By embedding positional information into these components, RoPE helps maintain the temporal structure of time-series data, even when ProbSparse attention selects fewer data points. By concentrating on a selected subset of significant data points, the ProbSparse attention mechanism reduces its computational demand from <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O(N^{2})$</tex> to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O(N\log N)$</tex>, making it highly efficient for handling extensive datasets. However, this reduction can risk losing essential sequential information, which RoPE compensates for, preserving temporal relationships and the overall order. To assess this method, dimensionality reduction techniques like UMAP, PaCMAP, and t-SNE were utilized to transform high-dimensional data into lower-dimensional representations, offering insights into both model performance and the underlying data patterns. Results show that RoPE effectively retains shape characteristics and temporal dependencies in time-series data, balancing efficiency and accuracy. Furthermore, these findings can enhance IoT-based systems by providing a robust approach to handle real-time, large-scale sensor data efficiently.