Samples were collected during a prospection in a cassava field in the north of the National Polytechnic Institute Felix Houphouet-Boigny (INP-HB) Yamoussoukro/Ivory Coast. All the leaves were practically infected by the African cassava mosaic. We selected three leaves of cassava plants:

- A healthy leaf as a reference;

- An infected leaf in which the limb has been deformed;

- An infected leaf in which there has been a color change on its interface.

The data acquisition system has been described in [8] [9] . The classical luminous sources have been removed and replaced for all modes, by a set of 13 LEDs, ranging from 375 nm to 940 nm. This enables the spectral coverage of this region with a mean step of 40 nm. The initial mechanical oculars are substituted by a monochrome camera CMOS 12-bit (2592 × 1944, Guppy-503B, Vision Allied Technology, with a sensor of MT9P031 micron/Aptina), with a pixel size of 2.2 μm × 2.2 μm, which is used to acquire images. The system acquires automatically a total of 39 spectral images; 13 images by mode), for the same scene using a data acquisition card (NI-DAQ) coupled to a computer, which controls the intensities of current for fine adjustments. In this work, we visualized the leaves naturally infected by the African cassava mosaic with three modes, transmission, reflection and scattering, because they better reveal the presence of substances in the cell. The thirteen luminous sources are sufficient to study the optical properties of biological cells [10] . We get images of leaves infected by ACMV and their spectra of transmission, reflection and scattering (see results below).

The images that we treated are of three dimensions, characterized by two spaces: the image space that accounts on the spatial dimension and spectral space representing the spectral dimension. The regions of interest correspond to the images of cassava leaves. In these regions, the objects, which are analyzed and should be characterized, are the naturally stressed leaves by ACMV. In image space, each of those objects is characterized by a repartition of intensities of the pixels representing them; objects are observed following 13 channels. If N is the number of channels corresponding to spectral bands, each pixel observed along the N channels will be represented by a vector X belonging to a sub vector space of dimension N. The objective of this work requires that the X vectors are identified and grouped into M classes corresponding to different symptoms caused by ACMV present in the leaf. The data analysis method can be summarized by the flow chart below (see Figure 1).

We have images of 75 cassava leaves (25 healthy leaves, 25 leaves with deformed limb, 25 light-green and dark green leaves). The microscopic image shows a difference in transmission mode, reflection and scattering (see Figure 2).

The spectral signatures of healthy and infected cassava leaves by the African cassava mosaic in the three modes have redundancies of information (Figure 3). To reduce this redundancy by keeping the maximum of information, we will apply the method of principal component analysis [11] . By applying PCA we have condensed the data for each vector X into new groups so that they don’t present any correlation between them and are ordered in terms of the percentage of variance brought by each component. Thus, the first principal component contains information related to the maximum variance, the second contains information related to the following variance. The process is repeated up to the n^th principal component. The loss of information decreases from one stage to the next. So we obtain the principal component with. We have:

These averages are used to calculate covariance and correlations between variables and.

: Represents proper vectors associated with proper values calculated from the polynomial of the matrix of covariance S:

However, the quality of the estimates, which led PCA, depends on the choice of the number of components retained to reconstruct the data, or the dimension of the subspace representation. So we have from the Eboulis criterion [12] , which is a graph presenting the decreasing of the proper values reducing the number of dimen- sionality. The principal consists to search for if there is an “elbow” in the graph for each mode and keep only the proper values up to this elbow (Figure 4) for the selection of principal components. According to the Eboulis graph:

- Components 1and 2 can better describe our data in transmission and scattering mode;

- The components 2 and 3 also better describe our data in reflection mode;

- The projection of transmission, reflection and scattering mode in two dimensional pace of these principal components retained gives us the graphs in Figure 5.

Two or three classes are formed according to these projections in the three geometries. Healthy cassava leaves form a class, but the two leaves naturally infected by the African cassava mosaic seem to form a class together or two classes if the infected leaves are considered in the same class.

The results of our principal component analysis are difficult to interpret physically because certain points have a great dispersion compared to elements of their class [13] . So we made recourse to two cluster analysis methods: Ascending Hierarchical Classification and K-means classification. Both methods were applied to the data after the PCA. Graphs of Figure 6 gave the results after application of the Ascending Hierarchical Classifi- cation (AHC) and the K-means method.

The result of this classification method we give three distinct elements in transmission, reflection and scat- tering namely blue (healthy leaf), green (limb of a deformed leaf), red (bright-green and dark-green leaf). We have proposed another method (Ascending Hierarchical Classification or AHC) to verify the performances of K-means. After applying AHC, we have:

- A class in transmission mode;

- Three distinct classes in reflection mode;

- Two classes in diffusion mode (see the representation graphs in Figure 7).

The objective to verify the spectral characterization of our samples using the hierarchical cluster method was not attained. The collected samples were distinguishable with the naked eye. We just wanted to check that with a statistical approach to study their photosynthetic effect with the technique of optical spectroscopy. We can say that the K-means method is an ideal technique in our study. Finally, we get three distinct classes (graphs in Figure 8) after the analysis of the optical spectra means.