Kernel clustering-based discriminant analysis

Ma, Bo; Qu, Huiyang; Wong, Hau-San

doi:10.1016/j.patcog.2006.05.033

Cited by 34 publications

(14 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These techniques can be extended to nonlinear methods by means of kernelization [19,2]. Another principled way to extend dimensionality reducing data visualization to auxiliary information is offered by an adaptation of the underlying metric.…”

Section: Introductionmentioning

confidence: 99%

Parametric nonlinear dimensionality reduction using kernel t-SNE

2015

View full text Add to dashboard Cite

Novel non-parametric dimensionality reduction techniques such as t-distributed stochastic neighbor embedding (t-SNE) lead to a powerful and flexible visualization of high-dimensional data. One drawback of non-parametric techniques is their lack of an explicit out-of-sample extension. In this contribution, we propose an efficient extension of t-SNE to a parametric framework, kernel t-SNE, which preserves the flexibility of basic t-SNE, but enables explicit out-of-sample extensions. We test the ability of kernel t-SNE in comparison to standard t-SNE for benchmark data sets, in particular addressing the generalization ability of the mapping for novel data. In the context of large data sets, this procedure enables us to train a mapping for a fixed size subset only, mapping all data afterwards in linear time. We demonstrate that this technique yields satisfactory results also for large data sets provided missing information due to the small size of the subset is accounted for by auxiliary information such as class labels, which can be integrated into kernel t-SNE based on the Fisher information.

show abstract

Section: Introductionmentioning

confidence: 99%

Parametric nonlinear dimensionality reduction using kernel t-SNE

2015

View full text Add to dashboard Cite

show abstract

“…The main idea is to firstly map the data from the initial space to a high-dimensional Hilbert space, where they might be linearly separable and then use a linear subspace method. This approach results to the kernelized versions of the linear techniques, that have already been developed, i.e., Kernel Principal Component Analysis (KPCA) [23], Kernel Discriminant Analysis (KDA) [24], Kernel Clustering Discriminant Analysis (KCDA) [25], Kernel Subclass Discriminant Analysis (KSDA) [26], etc.…”

Section: Related Workmentioning

confidence: 99%

Subclass Marginal Fisher Analysis

Maronidis

Tefas

Pitas

2015

2015 IEEE Symposium Series on Computational Intelligence

View full text Add to dashboard Cite

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Abstract-Subspace learning techniques have been extensively used for dimensionality reduction (DR) in many pattern classification problem domains. Recently, Discriminant Analysis (DA) methods, which use subclass information for the discrimination between the data classes, have attracted much attention. As DA methods are strongly dependent on the underlying distribution of the data, techniques whose functionality is based on neighbourhood information among the data samples have emerged. For instance, based on the Graph Embedding (GE) framework, which is a platform for developing novel DR methods, Marginal Fisher Analysis (MFA) has been proposed. Although MFA surpasses the above distribution limitations, it fails to model potential subclass structure that might lie within the several classes of the data. In this paper, motivated by the need to alleviate the above shortcomings, we propose a novel DR technique, called Subclass Marginal Fisher Analysis (SMFA), which combines the strength of subclass DA methods with the versatility of MFA. The new method is built by extending the GE framework so as to include subclass information. Through a series of experiments on various real-world datasets, it is shown that SMFA outperforms in most of the cases the state-of-the-art demonstrating the potential of exploiting subclass neighbourhood information in the DR process.

show abstract

“…A variety of different discriminative DR techniques has been proposed, such as Fisher's linear discriminant analysis (LDA), partial least squares regression (PLS), informed projections [7], global linear transformations of the metric [14,4], or kernelization of such approaches [25,2]. A general idea which we will use in our approach is to locally modify the metric [28,12] by defining a Riemannian manifold which takes into account auxiliary information of the data and which measures the effect of data dimensions in the feature space on this auxiliary information.…”

Section: Discriminative Dimensionality Reduction Based On the Fisher mentioning

confidence: 99%

Using Discriminative Dimensionality Reduction to Visualize Classifiers

Schulz

Gisbrecht

Hammer

2014

Neural Process Lett

View full text Add to dashboard Cite

Albeit automated classifiers offer a standard tool in many application areas, there exists hardly a generic possibility to directly inspect their behavior, which goes beyond the mere classification of (sets of) data points. In this contribution, we propose a general framework how to visualize a given classifier and its behavior as concerns a given data set in two dimensions. More specifically, we use modern nonlinear dimensionality reduction (DR) techniques to project a given set of data points and their relation to the classification decision boundaries. Furthermore, since data are usually intrinsically more than two-dimensional and hence cannot be projected to two dimensions without information loss, we propose to use discriminative DR methods which shape the projection according to given class labeling as is the case for a classification setting. With a given data set, this framework can be used to visualize any trained classifier which provides a probability or certainty of the classification together with the predicted class label.We demonstrate the suitability of the framework in the context of different dimensionality reduction techniques, in the context of different attention foci as concerns the visualization, and as concerns different classifiers which should be visualized.

show abstract

Kernel clustering-based discriminant analysis

Cited by 34 publications

References 4 publications

Parametric nonlinear dimensionality reduction using kernel t-SNE

Parametric nonlinear dimensionality reduction using kernel t-SNE

Subclass Marginal Fisher Analysis

Using Discriminative Dimensionality Reduction to Visualize Classifiers

Contact Info

Product

Resources

About