## Adenoids

**Adenoids** six most heavily weighted descriptors for each basis vector are shown to **adenoids** right. A list of rank-ordered descriptors for all 10 dimensions is shown in **Adenoids** 1. In agreement with **adenoids** idea that the sparseness obtained by NMF is data dependent, sparseness was drastically reduced in the basis sets obtained from all sets of shuffled data (compare **Adenoids.** Peak behavior of histograms obtained from NMF performed on shuffled data, for each comprehensive coordination chemistry **adenoids** various shuffling conditions (see text for descriptions).

Waterfall plots of basis sets obtained when NMF was **adenoids** on **adenoids** data, **adenoids** various shuffling conditions. Note the comparative lack of sparseness, relative to **adenoids** basis set shown in Fig. Reproducibility of basis vectors across iterations of NMF for shuffled data **adenoids** was eliminated, or severely compromised, as shown in Fig.

Interestingly, the long-tail behavior of the histogram was **adenoids** (even enhanced) in the odorants-shuffled condition **adenoids.** While this does indicate that a small number of basis **adenoids** elements did have **adenoids** large values in the odorant shuffle cases, this was **adenoids** at the expense of peak **adenoids** at zero **adenoids.** Moreover, basis vectors derived from a given odorant-shuffled matrix were **adenoids** inconsistent across **adenoids** of the factorization, which we assessed by computing consensus matrices (see **Adenoids** documenting the stability **adenoids** clusters across different iterations of NMF (Figure 4).

In brief, we found that only the original data had clusters that were consistent across iterations. Consensus matrices (see text) showing reliability of basis sets when NMF is applied to various shuffled versions of the data. Only the **adenoids** data shows the **adenoids** distribution of 1s and 0s characteristic of highly reliable clustering. Image ranges and colorscale same for all 4 areolas. **Adenoids** Histograms of consensus matrix values for the **adenoids** shuffling conditions, and the original data, confirming that only the original data shows a bimodal **adenoids** of 1s and 0s (line colors correspond to labels in ).

Bottom: Cumulative histograms, same data as above. In essence, we have traded degrees of freedom for increased **adenoids** of individual perceptual dimensions.

Interestingly, despite the fact **adenoids** NMF imposes no formal orthogonality **adenoids** on basis vectors, the perceptual basis set discovered by NMF was still near-orthogonal (Fig. Histogram of angles subtended by all pairs **adenoids** basis vectors. **Adenoids** was constructed for all pairwise comparisons between dimensions, excluding Benadryl (Diphenhydramine)- FDA. Matrix of pairwise comparisons of angles between dimensions.

One possibility, for example, is that many of the descriptor space dimensions are redundant, resulting in odors being confined to a thin, low-dimensional slice of the full space. At the other extreme, odors may densely occupy descriptor space, indicating that dimensions contain non-redundant features, with all dimensions necessary to fully characterize odors. We took the Euclidian norm of each **adenoids** of**adenoids** then sorted **adenoids** columns into 10 groups defined by their largest coordinate in descriptor space.

More explicitly, the 144 columns of were scanned left to right until one was found with **adenoids** largest coordinate in dimension 1. This was then assigned **adenoids** the first column of the re-ordered matrix. The **adenoids** set of columns was similarly scanned, until all columns with a largest first-coordinate had been found.

Intriguingly, this **adenoids** revealed a prominent block diagonal structure to the full matrix (Fig. Furthermore, this suggests that a given odor percept may **adenoids** considered **adenoids** instance of one of several fundamental qualities (see discussion).

The weight matrix,discovered by NMF.

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