Designing a global framework for non linear dimensionality reduction

Abstract

The key tool of dimensionality reduction is that the large set of parameters or features must be summarized into a smaller set, with no or less redundancy. With the emergence of non-linear dynamic systems analysis over recent years it is clear that the conventional approaches for dimensionality reduction may be far from optimal. There are generally no techniques available, especially for finding the features corresponding to contour appearing over different muscles movement. Moreover, the available techniques considering both geometric and discriminant information simultaneously are not computationally efficient and robust. The work takes into account all of the above and few novel dimensionality reduction techniques which have been demonstrated to be more robust than conventional analysis techniques. In this thesis, a novel framework for non-linear dimensionality reduction is designed to extract non-linear features using the concept that local is non-linear. To detect non linearity, relation between the nearest neighborhood elements of the image, have been expressed in terms of Gaussian membership functions. All the elements of the image are connected with the nearest neighborhood elements with some membership degree of the Gaussian functions. It results in the formation of number of fuzzy lattices. Fuzzy lattices deform according to the various muscles movements. Three fuzzy lattices of maximum kinetic energy corresponding to these contours are sufficient to recognize any object. The technique is based on the concept that any face can be recognized by sketching just few prominent lines corresponding to contours, which are appearing over different muscles movements. The developed technique based on the concept of local non-linear relation has also been tested on real time data (power quality events) generated by interfacing Fluke 610000A with Laptop via data acquisition system. The generated events are detected and classified using the developed technique based on the concept of local non-linear relation. It extracts any change occurring in the patterns of power quality events. The proposed technique efficiently distinguishes various real time power quality events in a single cycle. Additional work is an improvement over the well known non-linear dimensionality reduction techniques such as Isomap and Local Linear Embedding. All such methods are based upon the neighborhood information and require a user base input such as constant parameter epsilon or number of nearest neighborhood, which is computational burden. In proposed work, the neighborhood graph is constructed by stacking image in third dimension using Morphmap that reduces the computational complexity. The representation of the depth has been taken into account within small area in these objects by applying the intensity attenuation function. Another work is designing a novel framework for non-linear dimensionality reduction that considers both discriminant and geometric information of data. It aims to preserve the pairwise geodesic distances between the intraclass separable pairs and to separate the interclass neighbors in the reduced embedding spaces. Based on the extracted information features, large margins between inter and intra class clusters are organized, delivering a strong interclass discriminative power. Most of the real world data applications such as fingerprint, face or signature recognition suffer from the curse of dimensionality. In order to handle this efficiently, its dimensionality needs to be reduced without much loss of information. Principal Component Analysis is one of the most common and efficient technique for linear dimensionality reduction. However, it is not optimal for classification of data as there is no class discriminatory information in Principal Component Analysis. Thus, Linear Discriminant Analysis could be used to achieve dimensionality reduction along with classification of data classes. Linear Discriminant Analysis works well for distributions which are Gaussian. If the densities are significantly non-Gaussian, Linear Discriminant Analysis may not preserve any complex structure of the data required for the classification. The Marginal Fisher Analysis overcomes this difficulty to a large extent as it uses a different criterion for classification. Furthermore, the Marginal Fisher Analysis with suitable threshold value has been introduced for improving the recognition accuracy and detection of forged signatures. A new method is proposed for designing wavelet statistically matched to the signal and is applied for data compression. It overcomes the difficulty of choosing the appropriate wavelet from a library of previously designed wavelets. The statistically matched wavelet is designed based on the characteristics of the power quality event using the concept of fractional Brownian motion. It has been found that the proposed technique is better than Daubechies wavelet in the detection of power quality events. To classify the detected events, an iterative closest point algorithm is used which classifies the detected event even in the presence of outlier points and Gaussian noise.