Two variations on Fisher's linear discriminant for pattern recognition

Cooke, Tristrom

doi:10.1109/34.982904

Cited by 73 publications

(26 citation statements)

References 6 publications

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“…Recently, enhanced methods have been proposed to improve learning performances when feature dimension is high compared to the training set size and reach non linear solutions [15][16][17][18]. Linear discriminant techniques aims at finding a discriminant vector w (also called Fisher vector) which maximize the Fisher criterion: …”

Section: Proposed Ridgelet Featuresmentioning

confidence: 99%

Global semantic classification of scenes using ridgelet transform

2004

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In recent years, new harmonic analysis tools providing sparse representation in high dimension space have been proposed. In particular, ridgelets and curvelets bases are similar to the sparse components of naturally occurring image data derived empirically by computational neuroscience researchers. Ridgelets take the form of basis elements which exhibit very high directional sensitivity and are highly anisotropic. The ridgelet transform have been shown to provide a sparse representation for smooth objects with straight edges. Independently, for the purpose of scene description, the shape of the Fourier energy spectra has been used as an efficient way to provide a "holistic" description of the scene picture and its semantic category. Similarly, we focus on a simple binary semantic classification (artificial vs. natural) based on various ridgelet features. The learning stage is performed on a large image database using different state of the art Linear Discriminant techniques. Classification results are compared with those resulting from the Gabor representation. Additionally, ridgelet representation provides us with a way to accurately reconstruct the original signal. Using this synthesis step, we filter the ridgelet coefficients with the discriminant vector. The resulting image identifies the elements within the scene contributing to the different perceptual dimensions.

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Section: Proposed Ridgelet Featuresmentioning

confidence: 99%

Global semantic classification of scenes using ridgelet transform

2004

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“…Generally speaking, SVM performs well than KFD. However, Chakrabarti et al [88] and Cooke [89] have proved the equivalence between SVM and FLD on support vectors classification. Typically, two parts are necessary in tracking-by-detection approach: a) the generation of samples and labeled; b) update the classifier.…”

Section: Kernel Fisher Discriminantmentioning

confidence: 99%

“…Subspace features have been widely used in tracking for many years [89], [90], [91], [92], [93] due to its low-dimensional representation on the appearance of tracking target. Under the requirements of online and real-time applications, incremental subspace learning has been proposed recently [94].…”

Section: Kernel Subspace Learningmentioning

confidence: 99%

Review on Kernel based Target Tracking for Autonomous Driving

Wang

Yue

Dong

et al. 2016

Journal of Information Processing

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Significant progress has been made in the field of autonomous driving during the past decades. However, fully autonomous driving in urban traffic is still extremely difficult in the near future. Visual tracking of vehicles or pedestrians is an essential part of autonomous driving. Among these tracking methods, kernel-based object tracking is an effective means of tracking in video sequences. This paper reviews the kernel theory adopted in target tracking of autonomous driving and makes a qualitative and quantitative comparison among several well-known kernel based methods. The theoretical and experimental analysis allow us to conclude that the kernel based online subspace learning algorithm achieves a good trade-off between the stability and real-time processing for target tracking in the practical application environments of autonomous driving. This paper reports on the result of evaluating the performances of five algorithms by using seven video sequences.

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“…The most popularly used method is the Fisher's linear discriminant [7] of the data points in the node. This discriminant minimizes the ratio of the intra-class distance to the inter-class distance.…”

Section: Computation Of Discrimination Indexmentioning

confidence: 99%

A Framework for Local Supervised Dimensionality Reduction of High Dimensional Data

Aggarwal¹

2006

Proceedings of the 2006 SIAM International Conference on Data Mining

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High dimensional data presents a challenge to the classification problem because of the difficulty in modeling the precise relationship between the large number of feature variables and the class variable. In such cases, it may be desirable to reduce the information to a small number of dimensions in order to improve the accuracy and effectiveness of the classification process. While data reduction has been a well studied problem for the unsupervised domain, the technique has not been explored quite as extensively for the supervised case. Existing techniques which try to perform dimensionality reduction are too slow for practical use in the high dimensional case. These techniques try to find global discriminants in the data. However, the behavior of the data often varies considerably with data locality and different subspaces may show better discrimination in different localities. This is an even more challenging task than the global discrimination problem because of the additional issue of data localization. In this paper, we propose the novel idea of supervised subspace sampling in order to create a reduced representation of the data for classification applications in an efficient and effective way. The method exploits the natural distribution of the different classes in order to sample the best subspaces for class discrimination. Because of its sampling approach, the procedure is extremely fast and scales almost linearly both with data set size and dimensionality.

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Two variations on Fisher's linear discriminant for pattern recognition

Cited by 73 publications

References 6 publications

Global semantic classification of scenes using ridgelet transform

Global semantic classification of scenes using ridgelet transform

Review on Kernel based Target Tracking for Autonomous Driving

A Framework for Local Supervised Dimensionality Reduction of High Dimensional Data

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