Sensory Evaluation of Odor Approximation Using Nmf with Kullback-Leibler Divergence and Itakura-Saito Divergence in Mass Spectrum Space
Authors: Prasetyawan Dani , Nakamoto Takamichi 
Published: May 2020

Introduction

The odor reproduction is achieved by approximating mass spectra of various odors by blending a set of odor components. These reproduced odors should be as close to the target odor as possible. The fidelity of odor reproduction should be as in the same manner as reproducing colors. Since no primary odors have been found, thus finding an appropriate set of odor components to perform odor reproduction is essential. The odor components should be kept as small as possible whereas it should cover a wide range of odors. In the present study, we performed a sensory evaluation of odors approximated with Kullback-Leibler and Itakura-Saito divergences on mass spectrum space.

Method

In our previous study, the non-negative matrix factorization (NMF) method was used to extract basis vector corresponding to odor components [1], [2]. NMF was performed to analyze the mass spectrum data space of essential oils as shown in Figure 1. Non-negativity property of NMF is useful in exploring odor components. We created a mass spectrum database of 185 essential oils originating from plants. Mass spectrum data were gathered at mass to charge (m/z) region from 50 to 250. Region below 50 was discarded because we diluted the samples with ethanol (molecular weight of 46). An example of essential oils' mass spectra that we gathered is shown in Figure 2.
NMF with two different cost functions were performed in odor component exploration. Kullback-Leibler divergence (NMF-KL) and Itakura-Saito divergence (NMF-IS) were performed for the odor component exploration. IS divergence can extract small peaks in the high m/z region, with much contribution to human perception [3]. Those small peaks are ignored or degraded when using KL divergences [4]. Thus NMF-IS can enhance the approximation accuracy of the small peaks in high m/z area which might have a contribution to human olfaction.
Non-negative least squares methods were performed to approximate the recipe for odor approximation. Non-negative least squares methods were applied twice. First one was used to obtain the recipe to approximate odor components explored by NMF and the second one to obtain the recipe to approximate the target odor based on odor components. Non-negative least squares with IS divergence based on optimization algorithm was applied to the result of NMF-IS, whereas normal non-negative least squares were applied to the result of NMF-KL.

Results and Discussions

The previous study revealed that 30 odor components worked well in approximating odor. We evaluated NMF-IS and NMF-KL only using 10 odor components. Although 10 odor components were insufficient for obtaining good approximation accuracy, the difference between the two methods became large. We extracted odor components from essential oils based on the recipe approximated by first non-negative least squares method.
We approximated 6 target odors (clove bud, ylang-ylang, orange, origanum, mint) by using both NMF-IS and NMF-KL methods. Duo trio sensory test was performed to evaluate the approximated odors. A comparison of the original target odor and approximated odor mass spectrum are shown in Figure 3. The peaks locations were actually reproduced in spite of certain errors in magnitude even if we used only 10 odor components. A subject was asked to pick up either of the two approximated odor (one based on NMF-IS and another one based on NMF-KL) closer to the target one. We evaluated the Z score to the results of sensory tests (Table 1, P<0.05). The Z score of “+2” means the approximated odor by NMF-IS is significantly closer to the target odor whereas the Z score of “-2” means the approximated odor by NMF-KL is significantly closer to the target odor. The Z score of between +2 and -2 means none of approximated odor from both NMFs is closer to the target odor [5]. Three of the approximated odors (orange, mint, and ylang-ylang) by NMF-IS were closer to the target odor than that by NMF-KL. One approximated odor (cypress) by NMF-KL was closer to the target odor than that by NMF-IS. There was no significant closeness for the rest of two odors (clove bud and origanum). Overall, the sensory test reveals that approximated odors by NMF-IS were closer to the target odor than the odor approximated by NMF-KL. The Approximation quality based upon IS divergence was better than that based upon KL divergence.

References:

[1] T. Nakamoto, M. Ohno, and Y. Nihei, Odor Approximation Using Mass Spectrometry, IEEE Sens. J. 12 (2012), 3225–3231; doi: 10.1109/JSEN.2012.2190506
[2] D. D. Lee and H. S. Seung, Learning the parts of objects by non-negative matrix factorization, Nature. 401 (1999), 788–791 ; doi: 10.1038/44565
[3] D. Prasetyawan and T. Nakamoto, Comparison of NMF with Kullback-Leibler Divergence and Itakura-Saito Divergence for Odor Approximation, Proc. of the ISOEN. 18 (2019); doi: 10.1109/ISOEN.2019.8823186
[4] C. Févotte, N. Bertin, and J.-L. Durrieu, Nonnegative Matrix Factorization with the Itakura-Saito Divergence: With Application to Music Analysis, Neural Comput. 21 (2009), 793–830; doi: 10.1162/neco.2008.04-08-771
[5] Gail Vance Civille, B. Thomas Carr, Sensory Evaluation Techniques, CRC Press. (2015); ISBN: 9781482216905

Figure 1