A Metric Approach to Isolated Word Recognition

Some of the best known approaches to Isolated Word Recognition (IWR) are based on the Dynamic Time Warping (DTW) distance function. However, because this distance function is not defined w.r.t. an inner product, the recognition decisions in these approaches must be made with nonparametric classification algorithms like the k-nearest-neighbor search method. Although such methods can achieve a high degree of accuracy when sufficient numbers of training samples are present, they require significantly more memory and processing time than vector based approaches which can exploit the geometry of the representation space to model the decision regions much more efficiently. In this thesis, we show how a new metric approach to pattern recognition can be used to construct an efficient vector representation of speech patterns which geometrically preserves the DTW interdistances. This approach, which was first conceived by Goldfarb (10] as a way of unifying the classical structural and vector based methods of pattern recognition, achieves its efficiency by mapping the distance information from an abstract metric space into a low dimensional pseudo-Euclidean vector space,. Once this is done, the decision regions of each class can be modeled efficiently using various parametric classification methods like those based on Multi-Layered Perceptrons (MLP). In our case, the metric space will be defined by a standard DTW distance function and a set of isolated word samples. This metric space will then be mapped into the vector space in two stages. In the first stage, we use the Goldfarb embedding algorithm to incrementally construct a vector representation w.r.t. the leading principal axes. From this process, the intrinsic dimension of the metric space will be analyzed. Our studies will show that the intrinsic dimension of the DTW metric space is closely related to the number classes in the metric space rather then the number of training samples. Furthermore, the convergence to the intrinsic dimension appears to happen at an exponential rate. Once a low dimensional representation is determined, we will use the second stage to construct a more efficient mapping function from the metric space to the vector space. This will be done with a projection formula which uses a set of original input speech samples to act as basis samples in the low dimensional vector space. Obtaining a projection this way is mathematically possible because there is a well-defined relationship between the DTW distance in the metric space and inner products in the pseudo-Euclidean vector space. The basis samples will be selected with a greedy search algorithm that exploits the statistical properties of the vector representation computed by the embedding algorithm. In our implementation of this approach, using a MLP to analyze the decision regions and testing with monosyllabic digits form the the TI 20 word database, we were able to achieve recognition accuracy of 98.63 on speaker-independent test samples. This score was comparable to the results of the brute-force nearest-neighbor classifier in the DTW metric space; however, our results were obtained using only 16 basis samples in the classifier instead of 320 training samples. Consequently, we were able to reduced the total number of distance computations by nearly 95%, and the total memory requirements by nearly 90%.

Advisor: Sevcik, Ken