M Tech Dissertations

Permanent URI for this collectionhttp://ir.daiict.ac.in/handle/123456789/3

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Subject: search.filters.subject.Fractals

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    Financial time series analysis and prediction using Chaos theory, HHT and SVR.
    (Dhirubhai Ambani Institute of Information and Communication Technology, 2013) Zaki, Mohammadi; Patil, Hemant A.
    Stock market prediction is a very complex and therefore well studied area of economics and applied mathematics. The stock market prediction is often termed as a non-solvable problem precisely because as cited many times by various authors that the probability of correct prediction is no less than the probability of success of a fair coin toss. In this thesis, we exploit the presence of chaos in stock market data; in particular, we use the Bombay Stock Exchange data for explanation, along with results of using different datasets of different countries, and use a novel de-noising algorithm, based on the Hilbert-Huang Transform (HHT), and apply it to the - Support Vector Regression (SVR) for prediction of the pre-processed time series data. We compare the results with the existing techniques based on wavelet denoising. The purpose of this thesis is two-fold. Firstly, it deals with the verification of Takens’ embedding theorem as applied to chaotic time series data and its denoising and prediction. The work provides an experimental proof that indeed prediction of financial time series is possible via machine learning. On the other hand, it also gives a brief review of the existing techniques in various areas of data analysis and prediction so that the algorithm used can be fully justified. The algorithm presented here achieves an error of less than 1.5 % which is an improvement on the other previously existing techniques.
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    Fractal based approach for image segmentation
    (Dhirubhai Ambani Institute of Information and Communication Technology, 2004) Londhe, Tushar; Banerjee, Asim
    In this thesis, we have proposed an algorithm for image segmentation, using the fractal codes. The basic idea behind this algorithm is to use fractal codes for the image segmentation. This method uses compressed codes instead of the gray levels of the image. Therefore it is cost effective in the sense of storage space and time as no decoding is performed before using the segmentation algorithm. Moreover, the proposed scheme can directly use on the images accessed from the image database where images are kept in fractal-compressed code.
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    Fractal based approach for face recognition
    (Dhirubhai Ambani Institute of Information and Communication Technology, 2004) Athale, Suprita; Mitra, Suman K.
    An automated face recognition system is proposed in this dissertation. The system efficiently recognizes a candidate (test) image using the interdependence of the pixel that arises from the fractal compression of the image. The interdependence of the pixels is inherent within the fractal code in the form of chain of pixels. The mechanism of capturing these chains from the fractal codes is called pixel chaining. The present face recognition system tries to match pixel chains of the candidate image with that of the images present in the database. The work domain of the system is fractal codes but not the images. This leads to an advantage towards handling large database of face images.

    The system performance is found to be very satisfactory with the recognition rate of 98.4%. A minor improvement in the performance of the system over a few existing methods has been observed.

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    On wavelets and fractal modulation
    (Dhirubhai Ambani Institute of Information and Communication Technology, 2004) Mehta, Shalin; Sinha, Virendra P.
    The thesis considers a communication problem - that of communicating over a channel having simultaneously unknown bandwidth and unknown duration. As a solution to this problem, the thesis looks into a modulation scheme - Fractal Modulation - proposed by Gregory Wornell and Alan Oppenheim. Wornell and Oppenheim have observed that requirements of reliable communication over such a channel can be met using ‘scale-diversity’ (transmitting the information at multiple time-scales). To achieve this scale-diversity, they have proposed the use of a particular class of self similar signals, called bihomogeneous signals. They have developed an inner product space representation of bihomogeneous signals. This representation stems from dyadic orhthonormal wavelet based expansion of bihomogeneous signals. Apart from providing very natural and convenient framework of signal representation, these wavelet based expansions lead to efficient algorithms for analysis and synthesis of these signals. This thesis critically analyzes links between important concepts of the general communication problem, the bihomogeneous signal model and wavelet based signal-processing methods. In the process, we have been able to achieve an understanding of the role of bihomogeneous signals and wavelet-based signal processing techniques in providing elegant and efficient solution to this unconventional problem. During the course of the thesis, we could implement and simulate the transmitter part of the complete communication system (transmitter, channel model and receiver). MATLAB was used for this purpose. The thesis presents implementation and simulation of algorithms for synthesizing channel waveform for Fractal Modulation scheme. The results of the simulation corroborate those expected from theoretical treatment.