Probabilistic embeddings of the Fr\'echet distance

The Fr\'echet distance is a popular distance measure for curves which naturally lends itself to fundamental computational tasks, such as clustering, nearest-neighbor searching, and spherical range searching in the corresponding metric space. However, its inherent complexity poses considerable computational challenges in practice. To address this problem we study distortion of the probabilistic embedding that results from projecting the curves to a randomly chosen line. Such an embedding could be used in combination with, e.g. locality-sensitive hashing. We show that in the worst case and under reasonable assumptions, the discrete Fr\'echet distance between two polygonal curves of complexity $t$ in $\mathbb{R}^d$, where $d\in\lbrace 2,3,4,5\rbrace$, degrades by a factor linear in $t$ with constant probability. We show upper and lower bounds on the distortion. We also evaluate our findings empirically on a benchmark data set. The preliminary experimental results stand in stark contrast with our lower bounds. They indicate that highly distorted projections happen very rarely in practice, and only for strongly conditioned input curves. Keywords: Fr\'echet distance, metric embeddings, random projectionsComment: 27 pages, 11 figure

An HMM-Like Dynamic Time Warping Scheme for Automatic Speech Recognition

In the past, the kernel of automatic speech recognition (ASR) is dynamic time warping (DTW), which is feature-based template matching and belongs to the category technique of dynamic programming (DP). Although DTW is an early developed ASR technique, DTW has been popular in lots of applications. DTW is playing an important role for the known Kinect-based gesture recognition application now. This paper proposed an intelligent speech recognition system using an improved DTW approach for multimedia and home automation services. The improved DTW presented in this work, called HMM-like DTW, is essentially a hidden Markov model- (HMM-) like method where the concept of the typical HMM statistical model is brought into the design of DTW. The developed HMM-like DTW method, transforming feature-based DTW recognition into model-based DTW recognition, will be able to behave as the HMM recognition technique and therefore proposed HMM-like DTW with the HMM-like recognition model will have the capability to further perform model adaptation (also known as speaker adaptation). A series of experimental results in home automation-based multimedia access service environments demonstrated the superiority and effectiveness of the developed smart speech recognition system by HMM-like DTW

Smart Monitoring of Manufacturing Systems for Automated Decision-Making: A Multi-Method Framework

Smart monitoring plays a principal role in the intelligent automation of manufacturing systems. Advanced data collection technologies, like sensors, have been widely used to facilitate real-time data collection. Computationally efficient analysis of the operating systems, however, remains relatively underdeveloped and requires more attention. Inspired by the capabilities of signal analysis and information visualization, this study proposes a multi-method framework for the smart monitoring of manufacturing systems and intelligent decision-making. The proposed framework uses the machine signals collected by noninvasive sensors for processing. For this purpose, the signals are filtered and classified to facilitate the realization of the operational status and performance measures to advise the appropriate course of managerial actions considering the detected anomalies. Numerical experiments based on real data are used to show the practicability of the developed monitoring framework. Results are supportive of the accuracy of the method. Applications of the developed approach are worthwhile research topics to research in other manufacturing environments