20,299 research outputs found
Scale-Based Monotonicity Analysis in Qualitative Modelling with Flat Segments
Qualitative models are often more suitable than classical quantitative models in tasks such as Model-based Diagnosis (MBD), explaining system behavior, and designing novel devices from first principles. Monotonicity is an important feature to leverage when constructing qualitative models. Detecting monotonic pieces robustly and efficiently from sensor or simulation data remains an open problem. This paper presents scale-based monotonicity: the notion that monotonicity can be defined relative to a scale. Real-valued functions defined on a finite set of reals e.g. sensor data or simulation results, can be partitioned into quasi-monotonic segments, i.e. segments monotonic with respect to a scale, in linear time. A novel segmentation algorithm is introduced along with a scale-based definition of "flatness"
An Optimal Linear Time Algorithm for Quasi-Monotonic Segmentation
Monotonicity is a simple yet significant qualitative characteristic. We
consider the problem of segmenting a sequence in up to K segments. We want
segments to be as monotonic as possible and to alternate signs. We propose a
quality metric for this problem using the l_inf norm, and we present an optimal
linear time algorithm based on novel formalism. Moreover, given a
precomputation in time O(n log n) consisting of a labeling of all extrema, we
compute any optimal segmentation in constant time. We compare experimentally
its performance to two piecewise linear segmentation heuristics (top-down and
bottom-up). We show that our algorithm is faster and more accurate.
Applications include pattern recognition and qualitative modeling.Comment: This is the extended version of our ICDM'05 paper (arXiv:cs/0702142
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