One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a low-dimensional manifold embedded in a high-dimensional space. Drawing on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for representing the high-dimensional data. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality-preserving properties and a natural connection to clustering. Some potential applications and illustrative examples are discussed.

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Laplacian Eigenmaps for dimensionality reduction and data representation

"Sniffin' Sticks" is a test of nasal chemosensory function that is based on pen-like odor dispensing devices, introduced some 10 years ago by Kobal and co-workers. It consists of tests for odor threshold, discrimination, and identification. Previous work established its test-retest reliability and validity. Results of the test are presented as "TDI score", the sum of results obtained for threshold, discrimination, and identification measures. While normative data have been established they are based on a relatively small number of subjects, especially with regard to subjects older than 55 years where data from only 30 healthy subjects have been used. The present study aimed to remedy this situation. Now data are available from 3,282 subjects as compared to data from 738 subjects published previously. Disregarding sex-related differences, the TDI score at the tenth percentile was 24.9 in subjects younger than 15 years, 30.3 for ages from 16 to 35 years, 27.3 for ages from 36 to 55 years, and 19.6 for subjects older than 55 years. Because the tenth percentile has been defined to separate hyposmia from normosmia, these data can be used as a guide to estimate individual olfactory ability in relation to subject's age. Absolute hyposmia was defined as the tenth percentile score of 16-35 year old subjects. Other than previous reports the present norms are also sex-differentiated with women outperforming men in the three olfactory tests. Further, the present data suggest specific changes of individual olfactory functions in relation to age, with odor thresholds declining most dramatically compared to odor discrimination and odor identification.

Normative data for the "Sniffin' Sticks" including tests of odor identification, odor discrimination, and olfactory thresholds: an upgrade based on a group of more than 3,000 subjects.

Indoor air quality and health

Our knowledge of the molecular basis of odorant reception in insects has grown exponentially over the past decade. Odorant receptors (ORs) from moths, fruit flies, mosquitoes, and the honey bees have been deorphanized, odorant-degrading enzymes (ODEs) have been isolated, and the functions of odorant-binding proteins (OBPs) have been unveiled. OBPs contribute to the sensitivity of the olfactory system by transporting odorants through the sensillar lymph, but there are competing hypotheses on how they act at the end of the journey. A few ODEs that have been demonstrated to degrade odorants rapidly may act in signal inactivation alone or in combination with other molecular traps. Although ORs in Drosophila melanogaster respond to multiple odorants and seem to work in combinatorial code involving both periphery and antennal lobes, reception of sex pheromones by moth ORs suggests that their labeled lines rely heavily on selectivity at the periphery.

Odorant Reception in Insects: Roles of Receptors, Binding Proteins, and Degrading Enzymes

Dissociation of neural representation of intensity and affective valuation in human gustation.

The Labeled Magnitude Scale (LMS) is a semantic scale of perceptual intensity characterized by a quasi-logarithmic spacing of its verbal labels. The LMS had previously been shown to yield psychophysical functions equivalent to magnitude estimation (ME) when gustatory, thermal and nociceptive stimuli were presented and rated together, and the upper bound of the LMS was defined as the 'strongest imaginable oral sensation'. The present study compared the LMS to ME within the more limited contexts of taste and smell. In Experiment 1, subjects used both methods to rate either taste intensity produced by sucrose and NaC1 or odor intensity produced by acetic acid and phenyl ethyl alcohol, with the upper bound of the LMS defined as either the 'strongest imaginable taste' or the 'strongest imaginable odor'. The LMS produced psychophysical functions equivalent to those produced by ME. In, Experiment 2 a new group of subjects used both methods to rate the intensity of three different taste qualities, with the upper bound of the LMS defined as the 'strongest imaginable [sweetness, saltiness, or bitterness]'. In all three cases the LMS produced steeper functions than did ME. Experiment 3 tested the hypothesis that the LMS yields data comparable to ME only when the perceptual domain under study includes painful sensations. This hypothesis was supported when the LMS again produced steeper functions that ME after subjects had been explicitly instructed to omit painful sensations (e.g. the 'burn' of hot peppers) from the concept of 'strongest imaginable taste'. We conclude that the LMS can be used to scale sensations of taste and smell when they are broadly defined, but that it should be modified for use in scaling specific taste (and probably odor) qualities. The implications of these results for theoretical issues related to ME, category-ratio scales and the size of the perceptual range in different sensory modalities are discussed.

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Evaluating the ‘Labeled Magnitude Scale’ for Measuring Sensations of Taste and Smell

Central neural integration of sensory input from different modalities is a prerequisite for many types of perception and behavior. One of the best examples of such an integrative process may be flavor perception, whereby activation in two peripherally distinct neural systems, olfaction and gustation, combines to give rise to a unified oral sensation. Here we used a psychophysical method to show cross-modal summation of subthreshold concentrations of selected gustatory and olfactory stimuli, thus demonstrating that central neural integration of taste and smell inputs generates a representation of flavor perception.

The merging of the senses: integration of subthreshold taste and smell

Recent studies that have compared CT or MRI images of an individual's nasal anatomy and measures of their olfactory sensitivity have found a correlation between specific anatomical areas and performance on olfactory assessments. Using computational fluid dynamics (CFD) techniques, we have developed a method to quickly (<few days) convert nasal CT scans from an individual patient into an anatomically accurate 3-D numerical nasal model that can be used to predict airflow and odorant transport, which may ultimately determine olfactory sensitivity. The 3-D model can be also be rapidly modified to depict various anatomical deviations, such as polyps and their removal, that may alter nasal airflow and impair olfactory ability. To evaluate the degree to which variations in critical nasal areas such as the olfactory slit and nasal valve can alter airflow and odorant transport, inspiratory and expiratory airflow with odorants were simulated using numerical finite volume methods. Results suggest that anatomical changes in the olfactory region (upper meatus below the cribriform plate) and the nasal valve region will strongly affect airflow patterns and odorant transport through the olfactory region, with subsequent effects on olfactory function. The ability to model odorant transport through individualized models of the nasal passages holds promise for relating anatomical deviations to generalized or selective disturbances in olfactory perception and may provide important guidance for treatments for nasal-sinus disease, occupational rhinitis and surgical interventions that seek to optimize airflow and improve deficient olfactory function.

Effect of Anatomy on Human Nasal Air Flow and Odorant Transport Patterns: Implications for Olfaction

Sensory adaptation allows organisms to reach behavioral equilibrium with the ambient environment and respond primarily to changes in stimulation. Given its functional significance, it is not surprising that adaptation in the olfactory system exhibits many of the same characteristics as adaptation in other sensory systems, including vision. Repeated or prolonged exposure to an odorant typically leads to stimulus-specific decreases in olfactory sensitivity to that odorant, but sensitivity recovers over time in the absence of further exposure. Psychophysical analysis shows that olfactory adaptation results in elevations in odor thresholds and in reduced responsiveness to suprathreshold stimulation. Further, the magnitude of the decrease and the time course of adaptation and recovery are dependent on the concentration of the odor and on the duration of exposure. It is generally agreed that olfactory adaptation can occur at multiple levels in the olfactory system and can involve both peripheral (receptor level) and more central (post-receptor) components. Evidence for peripheral and central involvement comes from studies showing that monorhinal stimulation results in adaptation in both the ipsilateral and contralateral nostril, although the degree of adaptation in the ipsilateral nostril is more profound and recovery is slower. Additional evidence for central involvement comes from studies that have found relatively small decreases in peripheral response following repeated stimulation despite substantial reductions in perceived intensity. Most psychophysical studies of adaptation, however, have not differentiated the peripheral and central processes. Although relatively few in number, studies of the parametric features of olfactory adaptation in both vertebrate (e.g. rat) and invertebrate (e.g. Drosophila, Caenorhabditis elegans) animal models appear to replicate the findings in psychophysical studies of adult humans. Despite the broad overall similarity of olfactory adaptation to adaptation in other sensory systems, olfactory adaptation exhibits some unique features. Adaptation in olfaction has been shown to be very long-lasting in some cases and may be modulated by the contribution of pre-neural events and physico-chemical properties of the odorant molecules that govern diffusion to receptor sites and post-receptor clearance.

Psychophysical and Behavioral Characteristics of Olfactory Adaptation

Induction of olfactory sensitivity in humans was first illustrated when men and women who were initially unable to smell the volatile steroid androstenone (5α-androst-16-en-3-one) developed that ability after repeated, brief exposures1. Because this finding has not been replicated with other compounds in humans, it has been assumed that olfactory induction is a narrowly constrained phenomenon, occurring only in individuals with specific anosmias, perhaps only to androstenone (compare ref. 2). Here we show that induction of enhanced olfactory sensitivity seems to be a more general phenomenon, with marked changes in olfactory acuity occurring during repeated test exposures to several odorants among people with average baseline sensitivity to these compounds. This increased sensitivity (averaging five orders of magnitude) was observed only among females of reproductive age. These observations provide convincing evidence that female olfactory acuity to a variety of odorants can vastly improve with repeated test exposures. They also suggest a sensory basis for the anecdotal observation of greater olfactory sensitivities among females and raise the possibility that the olfactory-induction process may be associated with female reproductive behaviors such as pair bonding and kin recognition.

Pamela Dalton

Papers

Evaluating the ‘Labeled Magnitude Scale’ for Measuring Sensations of Taste and Smell

The merging of the senses: integration of subthreshold taste and smell

Effect of Anatomy on Human Nasal Air Flow and Odorant Transport Patterns: Implications for Olfaction

Psychophysical and Behavioral Characteristics of Olfactory Adaptation

Gender-specific induction of enhanced sensitivity to odors.