1 Spectral clustering and dimensionality reduction applied to Content based image retrieval with hybrid Descriptors. K. Houari University Larbi Ben M’hidi, Oum El Bouaghi, Algéria hk_houari@yahoo.fr M. K. Kholladi University Mentouri of Constantine, Algeria, Director of MISC Laboratory kholladi@yahoo.fr Y. Chahir University of Caen, France, Team of research on Image Processing, GREYC, URA CNRS 6072, campus II chahir@info.unicaen.fr Abstract – The topic of research exposed in this paper concerns Content Based image retrieval in a heterogeneous high database. The increase of storage capacities and the evolution of compression techniques have generated an explosion of the digital information quantity. Their computerization opens a vast field of applications. In this setting we are interested more especially in the problem of the dimensionality reduction and spectral clustering of a heterogeneous database of images in order to image retrieval by the content. Our new gait described in this paper consists to:  In first phase the description of the database images by a hybrid descriptor which are Interest SIFT points combined with texture descriptor given by the application of Wavelet transform. The descriptor is multi-dimensional, robust and invariant to changes and scales.  In second phase the representation of the database images as a convex graph.  In third phase the reduction of the space of representation by the application of an unsupervised spectral classification (The Spectral training uses information contained in the eigenvectors of the normalized matrix of transition to detect structures in data.) That will provide us classes of images that has shortcoming the Eigen-values calculated on the matrix of symmetry. As last phase, we use the Nyström theory that will permit us, not to recalculate the all Eigen-values, but only the lasts one. Keywords: image retrieval, Sift, clustering, texture, Nyström. I. Introduction Algorithms of spectral classification for the unsupervised analysis of data offer a very effective tool for the exploration of the data structure. Methods of Clustering [1, 2] have been used in various contexts and such disciplines 'dated mining', research of documents, image segmentation and classification of objects. The objective of clustering methods is the classification of objects on the basis of the criteria of similarity or chosen dissimilarity where groups (or classes) are a set of similar objects. The Crucial aspect in the classification is the representation of models and the distance of similarity. Every model is usually represented by a set of descriptors of the studied system. It is important to note that a good choice of model representation can increase performances of the classification. The choice of the set of descriptors depends on the system. The system of representation being fixed, it is possible to choose the suitable similarity measure between models or objects. The most popular measure of dissimilarity for a metric representation is the distance, as Euclidian distance. [3]. Techniques of Clustering can be divided globally in two categories: