### DisTools examples: Spectra

Some exercises are defined on the basis of spectral data. It is assumed that readers are familiar with PRTools and will consult the following pages where needed:

- PRTools User Guide, See at the bottom of the page for a TOC
- Introduction to DisTools
- Dissimilarity Representation Course
- The following packages should be in the Matlab path: PRTools, DisTools, PRDisData

Spectra arise in many pattern recognition application areas like remote sensing, chemometrics, seismics and speech. Spectra behave very similar to histograms as they can be considered as counts (of, for instance fotons) on a set of pre-defined wavelengths. Spectra are even more simple than one-dimensional images, as the latter are usually shift invariant, while spectra are naturally aligned by the frequencies.

Like the use of pixels in images the number of wavelength used for defining a spectrum or the number of bins used for a histogram may on one side yield a better, more complete description of the objects while many pattern recognition procedures suffer from a higher dimensionality. The dissimilarity representation may just profit from a higher sampling rate as it may result in a more accurate dissimilarity, while the dimensionality remains constant (equal to the size of the representation set). In comparison with images, distances between spectra are better defined due to the natural aligment of spectra.

Depending on the application various distance measures are studied. The routine `specproxm`

offers measures based on on L1, L2, the original spectra, cumulative spectra and derivatives. The routines `specdata`

gives access to a set of data examples, among others, from chemometrics and remote sensing.

`dismeas = {'L1','L2','C1','C2','D1','D2'}; % define distance measures`

`S =`

`specdata`

('tecator'); % load a spectral dataset

`E = zeros(1,6); % space for LOO 1NN errors`

`for j=1:6`

`D = S*`

`specproxm`

(S,`dismeas`

{j},1); % compute dissimilarity matrices

`E(j) =`

`nne`

(D); % determine 1NN error

`end`

`disp(E) % display`

#### Exercise

Analyze one or more spectral dataset offered by specdata.

- Plot a number of spectra. Are there class differences visible?
- Study scatterplots based on pcam and fisherm.
- Determine some learning curves for 1NN and at least one other classifier.
- Compare these learning curves with those found for a dissimilarity approach based on the above mentioned distance measures. Make your own choice for the representation set.
- In an advanced study smaller representation sets may be compared with a feature representation found by resampled spectra.

**elements:**
datasets
datafiles
cells and doubles
mappings
classifiers
mapping types.

**operations:**
datasets
datafiles
cells and doubles
mappings
classifiers
stacked
parallel
sequential
dyadic.

**user commands:**
datasets
representation
classifiers
evaluation
clustering
examples
support routines.

**introductory examples:**
Introduction
Scatterplots
Datasets
Datafiles
Mappings
Classifiers
Evaluation
Learning curves
Feature curves
Dimension reduction
Combining classifiers
Dissimilarities.

**advanced examples**.