A framework for estimating complex probability density structures in data streams.

Probability density function estimation is a fundamental component in several stream mining tasks such as outlier detection and classification. The nonparametric adaptive kernel density estimate (AKDE) provides a robust and asymptotically consistent estimate for an arbitrary distribution. However, its extensive computational requirements make it difficult to apply this technique to the stream environment. This paper tackles the issue of developing efficient and asymptotically consistent AKDE over data streams while heeding the stringent constraints imposed by the stream environment. We propose the concept of local regions to effectively synopsize local density features, design a suite of algorithms to maintain the AKDE under a time-based sliding window, and analyze the estimates' asymptotic consistency and computational costs. In addition, extensive experiments were conducted with real-world and synthetic data sets to demonstrate the effectiveness and efficiency of our approach.