Abstract: We propose a new segmentation and grouping framework for road map inference from GPS traces. We first present a progressive Density-Based Spatial Clustering of Application with Noise (DBSCAN) algorithm with an orientation constraint to partition the whole point set of the traces into clusters that represent road segments. A new point cluster grouping algorithm, according to the topolo...

In this paper an extension to the learning rule of the Self-Organizing Map (SOM) namely the Free Projection SOM (FP-SOM) is presented in order to enhance the SOM projection. The general idea of the FPSOM is to mirror the movement of weight vectors during the training process allowing their images on the map grid to move more freely between the junctions. The result of the extended training algo...

Lemma 2.2. It suffices to find disjoint L,R ∈ V such that they are (1) Large in Ω(n), or more formally stated, |L||R| ≥ α(n). (2) ∆-separated for ∆ = Ω( 1 logn) Let us define what ∆-separated means so that we can formalize this notion of “farness”. Recall that a distance from a vertex i to a set S is defined as d(i, S) = minj∈S d(i, j) (distance to the closest point in the set) and a distance f...

Finding the closest or farthest line segment (line) from a point are fundamental proximity problems. Given a set S of n points in the plane and another point q, we present optimal O(n logn) time, O(n) space algorithms for finding the closest and farthest line segments (lines) from q among those spanned by the points in S. We further show how to apply our techniques to find the minimum (maximum)...

BACKGROUND AIMS Maternal undernutrition programs metabolic adaptations which are ultimately detrimental to adult. L-tryptophan supplementation was given to manipulate the long-term sequelae of early-life programming by undernutrition and explore whether cultured cells retain circadian clock dysregulation. METHODS Male rat pups from mothers fed on low protein (8%, LP) or control (18%, CP) diet...

We find a priori and a posteriori error estimates of the best proximity point for the Picard iteration associated to a cyclic contraction map, which is defined on a uniformly convex Banach space with modulus of convexity of power type.

Self-Organizing Maps are a prominent tool for exploratory analysis and visualization of high-dimensional data. We propose a novel method for visualizing the cluster structure and coherent regions of the Self-Organizing Map that can be displayed as a vector field on top of the map lattice. Concepts of neighborhood and proximity on the map is exploited to obtain a representation where arrows poin...