# Variable Selection Using Adaptive Band Clustering and Physarum Network
## 1 Introduction  
Spectroscopy has been widely used for quantitative analysis of complex samples in various fields, such as petrochemical, pharmaceutical, agricultural, food, and biological sectors. It is a non-invasive and efficient analytic technology that can be deployed in on-line analysis. To predict the concentration of one or more samples, a mathematical model has to be built to relate the spectrum (spectra) of the sample (samples) with the concentration. A common problem in spectroscopy is that the large number of spectral variables makes the prediction unreliable and complicates the prediction model. To reduce the dimensionality of the spectral date, projection methods [1], variable selection methods [2], or a combination of both [3; 4; 5] are used. The projection methods, such as principle component analysis [6], partial least square (PLS) [7; 8; 9], discrete cosine transform [10], etc., change the high dimensional spectral data into low dimension space. The variable selection methods, such as the genetic algorithm (GA) [11; 12; 13], interval partial least square [2], etc. select a subset of variables to replace the original whole variable. Considering the high correlation between adjacent spectral variables (wavelengths) due to the characteristics of the spectrograph, [PERSON] et al. [14] transformed the variable selection problem into a path finding problem, i.e., the whole spectrum was divided into many sub-spectral bands. Each sub-spectral band was regarded as a node in a maze, every wavelength inside the sub-spectral band provided a route to its neighbor node; the shortest route (least correlation) was found by using a physarum network (PN) [15; 16; 17; 18; 19], and, thus, one wavelength from each sub-spectral band was selected, and the selected wavelengths had the least correlation. The PN is a mathematical model simulating the foraging process of plasmodium in a maze. This model has been proven to be able to compute the shortest path in the maze [15], and, thus, finds applications in many other fields, such as network design [16], sensornetwork [17], and supply chain network [19]. The PN can be used together with other variable selection methods to further reduce the dimensionality, i.e., it has been found that the PN-GA-PLS can achieve similar prediction performance with that of GA-PLS but uses much less wavelength. The PN-GA-PLS algorithm is a sequential combination of PN, GA, and PLS. It uses PN to select one wavelength from each sub-spectral band, and then inputs these wavelengths into GA for further selection, during which the PLS acts as the evaluation function for guiding the selection. A comprehensive description of PN-GA-PLS can be found in [14]. In PN-GA-PLS, the whole spectrum is equally divided into M sub-spectral bands, each of which has P wavelengths. Many sets of M and P are tried, the final M and P are determined if they gave a minimum prediction error. This dividing criteria in the PN-GA-PLS has one limitation in that the whole spectrum has to be equally divided, which only considers the characteristics of spectrometer. If the spectral features of the samples are also taken into account, the spectrum can be divided according to the correlation of spectral response at each wavelength, i.e., a sub-spectral band can include more wavelengths if the wavelengths within the band have high correlation with each other. To solve the limitation of the PN-GA-PLS and make the spectrum division scheme automatic and adaptive to the spectral features, in this paper, we transformed the spectrum division problem into a clustering problem, and solved the problem by using an adaptive band clustering method or affinity propagation algorithm (AP). The main contribution of our work is three fold. The first contribution is that we considered the spectral features of the probed samples for building a new spectrum division scheme.