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Abstract. Locally Linear Embedding (LLE) has recently been proposed as a method for dimensional reduction of high-dimensional nonlinear data sets. In LLE each data point is reconstructed from a linear combination of its n nearest neighbors, which are typically found using the Euclidean Distance. We propose an extension of LLE which consists in performing the search for the neighbors with respect to the geodesic distance (ISOLLE). In this study we show that the usage of this metric can lead to a more accurate preservation of the data structure. The proposed approach is validated on both real-world and synthetic data.

Absbucf-Locally Linear Embedding (LLE) has recently been proposed as a powerful algorithm for unsupervised learning and dimensional data reduction. For a first time we apply LLE to a problem of medical data analysis. Magnetic resonance imaging (MRI) is considered as an essential imaging modality in the detection and classification oi breast cancer. In dynamic contrast enhanced MRI (DCE-MRI) the data set of each patient is composed of a sequence oi images and each data point .in the image is associated with one time-series feature vector. Our results show that LLE is capable of revealing the heterogeneity of malignant tumors from the data strnctnre of DCEMRI signals. -Malignant ekcterisrie LO t l t> t l tr II ta

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