Wavelet transform in similarity paradigm

[INS-R9802] Searching for similarity in time series finds still broader applications in data mining. However, due to the very broad spectrum of data involved, there is no possibility of defining one single notion of similarity suitable to serve all applications. We present a powerful framework based on wavelet decomposition, which allows designing and implementing a variety of criteria for the evaluation of similarity between time series. As an example, two main classes of similarity measures are considered. One is the global, statistical similarity which uses the wavelet transform derived Hurst exponent to classify time series according to their global scaling properties. The second measure estimates similarity locally using the scale-position bifurcation representation derived from the wavelet transform modulus maxima representation of the time series. A variety of generic or custom designed matching criteria can be incorporated into the detail similarity measure. We demonstrate the ability of the technique to deal with the presence of scaling, translation and polynomial bias and we also test sensitivity to the addition of random noise. Other criteria can be designed and this flexibility can be built into the data mining system to allow for specific user requirements.#[INS-R9815] For the majority of data mining applications, there are no models of data which would facilitate the tasks of comparing records of time series, thus leaving one with `noise' as the only description. We propose a generic approach to comparing noise time series using the largest deviations from consistent statistical behaviour. For this purpose we use a powerful framework based on wavelet decomposition, which allows filtering polynomial bias, while capturing the essential singular behaviour. In particular we are able to reveal scale-wise ranking of singular events including their scale-free characteristic: the Hölder exponent. We use such characteristics to design a compact representation of the time series suitable for direct comparison, e.g. evaluation of the correlation product. We demonstrate that the distance between such representations closely corresponds to the subjective feeling of similarity between the time series. In order to test the validity of subjective criteria, we test the records of currency exchanges, finding convincing levels of (local) correlation

Wavelet transform in similarity paradigm II

For the majority of data mining applications, there are no models of data which would facilitate the tasks of comparing records of time series, thus leaving one with `noise' as the only description. We propose a generic approach to comparing noise time series using the largest deviations from consistent statistical behaviour. For this purpose we use a powerful framework based on wavelet decomposition, which allows filtering polynomial bias, while capturing the essential singular behaviour. In particular we are able to reveal scale-wise ranking of singular events including their scale-free characteristic: the H"older exponent. We use such characteristics to design a compact representation of the time series suitable for direct comparison, e.g. evaluation of the correlation product. We demonstrate that the distance between such representations closely corresponds to the subjective feeling of similarity between the time series. In order to test the validity of subjective criteria, we test the records of currency exchanges, finding convincing levels of (local) correlation

Toward reduction of artifacts in fused images

Most fusion satellite image methodologies at pixel-level introduce false spatial details, i.e.artifacts, in the resulting fusedimages. In many cases, these artifacts appears because image fusion methods do not consider the differences in roughness or textural characteristics between different land covers. They only consider the digital values associated with single pixels. This effect increases as the spatial resolution image increases. To minimize this problem, we propose a new paradigm based on local measurements of the fractal dimension (FD). Fractal dimension maps (FDMs) are generated for each of the source images (panchromatic and each band of the multi-spectral images) with the box-counting algorithm and by applying a windowing process. The average of source image FDMs, previously indexed between 0 and 1, has been used for discrimination of different land covers present in satellite images. This paradigm has been applied through the fusion methodology based on the discrete wavelet transform (DWT), using the à trous algorithm (WAT). Two different scenes registered by optical sensors on board FORMOSAT-2 and IKONOS satellites were used to study the behaviour of the proposed methodology. The implementation of this approach, using the WAT method, allows adapting the fusion process to the roughness and shape of the regions present in the image to be fused. This improves the quality of the fusedimages and their classification results when compared with the original WAT metho

Dynamic similarity promotes interpersonal coordination in joint-action

Human movement has been studied for decades and dynamic laws of motion that are common to all humans have been derived. Yet, every individual moves differently from everyone else (faster/slower, harder/smoother etc). We propose here an index of such variability, namely an individual motor signature (IMS) able to capture the subtle differences in the way each of us moves. We show that the IMS of a person is time-invariant and that it significantly differs from those of other individuals. This allows us to quantify the dynamic similarity, a measure of rapport between dynamics of different individuals' movements, and demonstrate that it facilitates coordination during interaction. We use our measure to confirm a key prediction of the theory of similarity that coordination between two individuals performing a joint-action task is higher if their motions share similar dynamic features. Furthermore, we use a virtual avatar driven by an interactive cognitive architecture based on feedback control theory to explore the effects of different kinematic features of the avatar motion on the coordination with human players

A Self-Organized-Criticality model consistent with statistical properties of edge turbulence in a fusion plasma

The statistical properties of the intermittent signal generated by a recent model for self-organized-criticality (SOC) are examined. A successful comparison is made with previously published results of the equivalent quantities measured in the electrostatic turbulence at the edge of a fusion plasma. This result re-establishes SOC as a potential paradigm for transport in magnetic fusion devices, overriding shortcomings pointed out in earlier works [E. Spada, et al, Phys. Rev. Lett. 86, 3032 (2001); V. Antoni, et al, Phys. Rev. Lett. 87, 045001 (2001)].Comment: 4 pages, 4 figure