Assessing scale-wise similarity of curves with a thick pen: As illustrated through comparisons of spectral irradiance.

Forest canopies create dynamic light environments in their understorey, where spectral composition changes among patterns of shade and sunflecks, and through the seasons with canopy phenology and sun angle. Plants use spectral composition as a cue to adjust their growth strategy for optimal resource use. Quantifying the ever-changing nature of the understorey light environment is technically challenging with respect to data collection. Thus, to capture the simultaneous variation occurring in multiple regions of the solar spectrum, we recorded spectral irradiance from forest understoreys over the wavelength range 300-800 nm using an array spectroradiometer. It is also methodologically challenging to analyze solar spectra because of their multi-scale nature and multivariate lay-out. To compare spectra, we therefore used a novel method termed thick pen transform (TPT), which is simple and visually interpretable. This enabled us to show that sunlight position in the forest understorey (i.e., shade, semi-shade, or sunfleck) was the most important factor in determining shape similarity of spectral irradiance. Likewise, the contributions of stand identity and time of year could be distinguished. Spectra from sunflecks were consistently the most similar, irrespective of differences in global irradiance. On average, the degree of cross-dependence increased with increasing scale, sometimes shifting from negative (dissimilar) to positive (similar) values. We conclude that the interplay of sunlight position, stand identity, and date cannot be ignored when quantifying and comparing spectral composition in forest understoreys. Technological advances mean that array spectroradiometers, which can record spectra contiguously over very short time intervals, are being widely adopted, not only to measure irradiance under pollution, clouds, atmospheric changes, and in biological systems, but also spectral changes at small scales in the photonics industry. We consider that TPT is an applicable method for spectral analysis in any field and can be a useful tool to analyze large datasets in general.

Classification of genomic sequences via wavelet variance and a self-organizing map with an application to mitochondrial DNA.

We present a new methodology for discriminating genomic symbolic sequences, which combines wavelet analysis and a self-organizing map algorithm. Wavelets are used to extract variation across various scales in the oligonucleotide patterns of a sequence. The variation is quantified by the estimated wavelet variance, which yields a feature vector. Feature vectors obtained from many genomic sequences, possibly of different lengths, are then classified with a nonparametric self-organizing map scheme. When applied to nearly 200 entire mitochondrial DNA sequences, or their fragments, the method predicts species taxonomic group membership very well, and allows the results to be visualized. When only thousands of nucleotides are available, wavelet-based feature vectors of short oligonucleotide patterns are more efficient in discrimination than frequency-based feature vectors of long patterns. This new data analysis strategy could be extended to numeric genomic data. The routines needed to perform the computations are readily available in two packages of software R.