Online clustering, in an evolving high dimensional data is an amazing challenge for data mining applications. Although, many clustering strategies have been proposed, it is still an exciting task since the published algorithms fail to do well with high dimensional datasets, finding arbitrary shaped clusters and handling outliers. Knowing fractal characteristics of dataset can help abstract the ...

This paper presents a method for fast encoding of still images based on iterated function systems (IFSs). The major disadvantage of this coding approach, usually referred to as fractal coding, is the high computational effort of the encoding process compared to e.g. the JPEG algorithm [1]. This is mainly due to the costly “full search” of the transform parameters within a fractal codebook. We t...

Fluctuations in the concentration of Brownian particles in one and two dimensions, or any reasonable measurement of the concentration such as in fluorescence correlation spectroscopy, is shown to be a stochastic fractal with a long tail. Being singular at omega = 0, the power spectrum of the fluctuation S(omega) approximately omega-1/2 for diffusion in one dimension, approximately log omega in ...

We study a simplified stochastic model for the vascularization of a growing tumor, incorporating the formation of new blood vessels at the tumor periphery as well as their regression in the tumor center. The resulting morphology of the tumor vasculature differs drastically from the original one. We demonstrate that the probabilistic vessel collapse has to be correlated with the blood shear forc...

We introduce stochastic Discrete Laplacian Growth and consider its deterministic continuous version. These are reminiscent respectively to well-known Diffusion Limited Aggregation and Hele-Shaw free boundary problem for the interface propagation. We study correlation between stability of deterministic free-boundary problem and macroscopic fractal growth in the corresponding discrete problem. It...

We present an algorithm for fast stochastic gradient descent that uses a nonlinear adaptive momentum scheme to optimize the late time convergence rate. The algorithm makes eeective use of curvature information, requires only O(n) storage and computation, and delivers convergence rates close to the theoretical optimum. We demonstrate the technique on linear and large nonlinear back-prop networks...

We investigate the question, " how does time flow? " and show that time may change by inversions as well. We discuss its implications to a simple class of linear systems. Instead of introducing any unphysical behaviour, inversions can lead to a new multi-time scale evolutionary path for the linear system exhibiting late time stochastic fluctuations. We explain how stochastic behaviour is inject...

In this paper, a procedure for retrieval of forest parameters is developed using the recently developed fractalbased coherent scattering model (FCSM) and a stochastic optimization algorithm. Since the fractal scattering model is computationally extensive, first a simplified empirical model with high fidelity for a desired forest stand is constructed using FCSM. Inputs to the empirical model are...

Fractal geometry has been used to describe natural and built environments, but has yet to be studied in navigational research. In order to establish a relationship between the fractal dimension (D) of a natural environment and humans' ability to navigate such spaces, we conducted two experiments using virtual environments that simulate the fractal properties of nature. In Experiment 1, particip...

A new method for fractal image compression is proposed using genetic algorithm (GA) with an elitist model. The self transformation property of images is assumed and exploited in the fractal image compression technique. The technique described utilizes the GA, which greatly decreases the search space for finding the self similarities in the given image. This article presents theory, implementati...