Our current understanding of how emotions are expressed in speech is still very limited. Part of the difficulty has been the lack of understanding of the underlying mechanisms. Here we report the findings of a somewhat unconventional investigation of emotional speech. Instead of looking for direct acoustic correlates of multiple emotions, we tested a specific theory, the size code hypothesis of emotional speech, about two emotions – anger and happiness. According to the hypothesis, anger and happiness are conveyed in speech by exaggerating or understating the body size of the speaker. In two studies consisting of six experiments, we synthesized vowels with a three-dimensional articulatory synthesizer with parameter manipulations derived from the size code hypothesis, and asked Thai listeners to judge the body size and emotion of the speaker. Vowels synthesized with a longer vocal tract and lower F0 were mostly heard as from a larger person if the length and F0 differences were stationary, but from an angry person if the vocal tract was dynamically lengthened and F0 was dynamically lowered. The opposite was true for the perception of small body size and happiness. These results provide preliminary support for the size code hypothesis. They also point to potential benefits of theory-driven investigations in emotion research.

Nearest neighbor searching is the following problem: we are given a set S of n data points in a metric space, X, and are asked to preprocess these points so that, given any query point q ∈ X, the data point nearest to q can be reported quickly. Nearest neighbor searching has applications in many areas, including knowledge discovery and data mining [18], pattern recognition and classification [14,17], machine learning [13], data compression [22], multimedia databases [19], document retrieval [15], and statistics [16].There are many possible choices of the metric space. Throughout we will assume that the space is R d , real d-dimensional space, where distances are measured using any Minkowski L m distance metric. For any integer m ≥ 1, the L m -distance between points p = (p 1 , p 2 , . . . , p d ) and q = (q 1 , q 2 , . . . , q d ) in R d is defined to be the m-th root of 1≤i≤d |p i − q i | m . The L 1 , L 2 , and L ∞ metrics are the well-known Manhattan, Euclidean and max metrics, respectively.Our primary focus is on data structures that are stored in main memory. Since data sets can be large, we limit ourselves to consideration of data structures whose total space grows linearly with d and n. Among the most popular methods are those based on hierarchical decompositions of space. The seminal work in this area was by Friedman, Bentley, and Finkel [21] who showed that O(n) space and O(log n) query time are achievable for fixed dimensional spaces in the expected case for data distributions of bounded density through the use of kd-trees. There have been numerous variations on this theme. However, all known methods suffer from the fact that as dimension increases, either running time or space increase exponentially with dimension.The difficulty of obtaining algorithms that are efficient in the worst case with respect to both space and query time suggests the alternative problem of finding approximate nearest neighbors. Consider a set S of data points in R d and a query point q ∈ R d . Given ǫ > 0, we say that a point p ∈ S is a (1 + ǫ)-approximate nearest neighbor of q if dist(p, q) ≤ (1 + ǫ)dist(p * , q), ⋆ The support of the National Science Foundation under grant CCR-9712379 is gratefully acknowledged.

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