David R. Hardoon

Canonical Correlation Analysis: An Overview with Application to Learning Methods

We present a general method using kernel canonical correlation analysis to learn a semantic representation to web images and their associated text. The semantic space provides a common representation and enables a comparison between the text and images. In the experiments, we look at two approaches of retrieving images based on only their content from a text query. We compare orthogonalization approaches against a standard cross-representation retrieval technique known as the generalized vector space model.

Sparse canonical correlation analysis

We present a novel method for solving Canonical Correlation Analysis (CCA) in a sparse convex framework using a least squares approach. The presented method focuses on the scenario when one is interested in (or limited to) a primal representation for the first view while having a dual representation for the second view. Sparse CCA (SCCA) minimises the number of features used in both the primal and dual projections while maximising the correlation between the two views. The method is compared to alternative sparse solutions as well as demonstrated on paired corpuses for mate-retrieval. We are able to observe, in the mate-retrieval, that when the number of the original features is large SCCA outperforms Kernel CCA (KCCA), learning the common semantic space from a sparse set of features.

Unsupervised analysis of fMRI data using kernel canonical correlation.

We introduce a new unsupervised fMRI analysis method based on kernel canonical correlation analysis which differs from the class of supervised learning methods (e.g., the support vector machine) that are increasingly being employed in fMRI data analysis. Whereas SVM associates properties of the imaging data with simple specific categorical labels (e.g., -1, 1 indicating experimental conditions 1 and 2), KCCA replaces these simple labels with a label vector for each stimulus containing details of the features of that stimulus. We have compared KCCA and SVM analyses of an fMRI data set involving responses to emotionally salient stimuli. This involved first training the algorithm (SVM, KCCA) on a subset of fMRI data and the corresponding labels/label vectors (of pleasant and unpleasant), then testing the algorithms on data withheld from the original training phase. The classification accuracies of SVM and KCCA proved to be very similar. However, the most important result arising form this study is the KCCA is able to extract some regions that SVM also identifies as the most important in task discrimination and these are located manly in the visual cortex. The results of the KCCA were achieved blind to the categorical task labels. Instead, the stimulus category is effectively derived from the vector of image features.

Convergence analysis of kernel Canonical Correlation Analysis: theory and practice

Canonical Correlation Analysis is a technique for finding pairs of basis vectors that maximise the correlation of a set of paired variables, these pairs can be considered as two views of the same object. This paper provides a convergence analysis of Canonical Correlation Analysis by defining a pattern function that captures the degree to which the features from the two views are similar. We analyse the convergence using Rademacher complexity, hence deriving the error bound for new data. The analysis provides further justification for the regularisation of kernel Canonical Correlation Analysis and is corroborated by experiments on real world data.

A correlation approach for automatic image annotation

The automatic annotation of images presents a particularly complex problem for machine learning researchers. In this work we experiment with semantic models and multi-class learning for the automatic annotation of query images. We represent the images using scale invariant transformation descriptors in order to account for similar objects appearing at slightly different scales and transformations. The resulting descriptors are utilised as visual terms for each image. We first aim to annotate query images by retrieving images that are similar to the query image. This approach uses the analogy that similar images would be annotated similarly as well. We then propose an image annotation method that learns a direct mapping from image descriptors to keywords. We compare the semantic based methods of Latent Semantic Indexing and Kernel Canonical Correlation Analysis (KCCA), as well as using a recently proposed vector label based learning method known as Maximum Margin Robot.

Can eyes reveal interest? Implicit queries from gaze patterns

We study a new research problem, where an implicit information retrieval query is inferred from eye movements measured when the user is reading, and used to retrieve new documents. In the training phase, the user’s interest is known, and we learn a mapping from how the user looks at a term to the role of the term in the implicit query. Assuming the mapping is universal, that is, the same for all queries in a given domain, we can use it to construct queries even for new topics for which no learning data is available. We constructed a controlled experimental setting to show that when the system has no prior information as to what the user is searching, the eye movements help significantly in the search. This is the case in a proactive search, for instance, where the system monitors the reading behaviour of the user in a new topic. In contrast, during a search or reading session where the set of inspected documents is biased towards being relevant, a stronger strategy is to search for content-wise similar documents than to use the eye movements.

Constructing nonlinear discriminants from multiple data views

There are many situations in which we have more than one view of a single data source, or in which we have multiple sources of data that are aligned. We would like to be able to build classifiers which incorporate these to enhance classification performance. Kernel Fisher Discriminant Analysis (KFDA) can be formulated as a convex optimisation problem, which we extend to the Multiview setting (MFDA) and introduce a sparse version (SMFDA). We show that our formulations are justified from both probabilistic and learning theory perspectives. We then extend the optimisation problem to account for directions unique to each view (PMFDA). We show experimental validation on a toy dataset, and then give experimental results on a brain imaging dataset and part of the PASCAL 2007 VOC challenge dataset.

Compressed Sampling for pulse Doppler radar

This paper presents a study of how the Analogue to Digital Converter (ADC) sampling rate in a digital radar can be reduced-without reduction in waveform bandwidth-through the use of Compressed Sampling (CS). Real radar data is used to show that through use of chirp or Gabor dictionaries and Basis Pursuit (BP) the ADC sampling frequency can be reduced by a factor of 128, to under 1 mega sample per second, while the waveform bandwidth remains 40 MHz. The error on the reconstructed fast-time samples is small enough that accurate range-profiles and range-frequency surfaces can be produced.

Decomposing the tensor kernel support vector machine for neuroscience data with structured labels

The tensor kernel has been used across the machine learning literature for a number of purposes and applications, due to its ability to incorporate samples from multiple sources into a joint kernel defined feature space. Despite these uses, there have been no attempts made towards investigating the resulting tensor weight in respect to the contribution of the individual tensor sources. Motivated by the increase in the current availability of Neuroscience data, specifically for two-source analyses, we propose a novel approach for decomposing the resulting tensor weight into its two components without accessing the feature space. We demonstrate our method and give experimental results on paired fMRI image-stimuli data.

Correlation-based multivariate analysis of genetic influence on brain volume

Considerable research effort has focused on achieving a better understanding of the genetic correlates of individual differences in volumetric and morphological brain measures. The importance of these efforts is underlined by evidence suggesting that brain changes in a number of neuropsychiatric disorders are at least partly genetic in origin. The currently used methods to study these relationships are mostly based on single-genotype univariate analysis techniques. These methods are limited as multiple genes are likely to interact with each other in their influences on brain structure and function. In this paper we present a feasibility study where we show that by using kernel correlation analysis, with a new genotypes representation, it is possible to analyse the relative associations of several genetic polymorphisms with brain structure. The implementation of the method is demonstrated on genetic and structural magnetic resonance imaging (MRI) data acquired from a group of 16 healthy subjects by showing the multivariate genetic influence on grey and white matter.