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57
Manifold Learning using Robust Graph Laplacian for Interactive Image Search
"... Interactive image search or relevance feedback is the process which helps a user refining his query and finding difficult target categories. This consists in partially labeling a very small fraction of an image database and iteratively refining a decision rule using both the labeled and unlabeled da ..."
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Interactive image search or relevance feedback is the process which helps a user refining his query and finding difficult target categories. This consists in partially labeling a very small fraction of an image database and iteratively refining a decision rule using both the labeled and unlabeled data. Training of this decision rule is referred to as transductive learning. Our work is an original approach for relevance feedback based on Graph Laplacian. We introduce a new Graph Laplacian which makes it possible to robustly learn the embedding, of the manifold enclosing the dataset, via a diffusion map. Our approach is three-folds: it allows us (i) to integrate all the unlabeled images in the decision process (ii) to robustly capture the topology of the image set and (iii) to perform the search process inside the manifold. Relevance feedback experiments were conducted on simple databases including Olivetti and Swedish as well as challenging and large scale databases including Corel. Comparisons show clear and consistent gain, of our graph Laplacian method, with respect to state-of-the art relevance feedback approaches. 1.
Discriminatively Regularized Least-Squares Classification
"... Over the past decades, regularization theory is widely applied in various areas of machine learning to derive a large family of novel algorithms. Traditionally, regularization focuses on smoothing only, and does not fully utilize the underlying discriminative knowledge which is vital for classificat ..."
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Over the past decades, regularization theory is widely applied in various areas of machine learning to derive a large family of novel algorithms. Traditionally, regularization focuses on smoothing only, and does not fully utilize the underlying discriminative knowledge which is vital for classification. In this paper, we propose a novel regularization algorithm in the least-squares sense, called Discriminatively Regularized Least-Squares Classification (DRLSC) method, which is specifically designed for classification. Inspired by several new geometrically motivated methods, DRLSC directly embeds the discriminative information as well as the local geometry of the samples into the regularization term so that it can explore as much underlying knowledge inside the samples as possible and aim to maximize the margins between the samples of different classes in each local area. Furthermore, by embedding equality type constraints in the formulation, the solutions of DRLSC can follow from solving a set of linear equations and the framework naturally contains multi-class problems. Experiments on both toy and real-world problems demonstrate that DRLSC is often superior in classification performance to the classical regularization algorithms, including Regularization Networks, Support Vector Machines and some of the recent studied Manifold Regularization techniques.
Multi-agent behaviour segmentation via spectral clustering
- in Proceedings of the AAAI-2007, PAIR Workshop
, 2007
"... We examine the application of spectral clustering for breaking up the behaviour of a multi-agent system in space and time into smaller, independent elements. We extend the clustering into the temporal domain and pro-pose a novel similarity measure, which is shown to possess desirable temporal proper ..."
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Cited by 4 (1 self)
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We examine the application of spectral clustering for breaking up the behaviour of a multi-agent system in space and time into smaller, independent elements. We extend the clustering into the temporal domain and pro-pose a novel similarity measure, which is shown to possess desirable temporal properties when clustering multi-agent behaviour. We also propose a technique to add knowledge about events of multi-agent interaction with different importance. We apply spectral clustering with this measure for analysing behaviour in a strategic game.
Preimage as karcher mean using diffusion maps: Application to shape and image denoising
- In: Proceedings of International Conference on Scale Space and Variational Methods in Computer Vision. LNCS
, 2009
"... Abstract. In the context of shape and image modeling by manifold learning, we focus on the problem of denoising. A set of shapes or images being known through given samples, we capture its structure thanks to the Diffusion Maps method. Denoising a new element classically boils down to the key-proble ..."
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Abstract. In the context of shape and image modeling by manifold learning, we focus on the problem of denoising. A set of shapes or images being known through given samples, we capture its structure thanks to the Diffusion Maps method. Denoising a new element classically boils down to the key-problem of pre-image determination, i.e.recovering a point, given its embedding. We pro-pose to model the underlying manifold as the set of Karcher means of close sam-ple points. This non-linear interpolation is particularly well-adapted to the case of shapes and images. We define the pre-image as such an interpolation having the targeted embedding. Results on synthetic 2D shapes and on real 2D images and 3D shapes are presented and demonstrate the superiority of our pre-image method compared to several state-of-the-art techniques in shape and image de-noising based on statistical learning techniques. 1
A Theoretical Analysis of Joint Manifolds
, 2009
"... The emergence of low-cost sensor architectures for diverse modalities has made it possible to deploy sensor arrays that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these sensors acquire very high-dimensional data such as audio signal ..."
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The emergence of low-cost sensor architectures for diverse modalities has made it possible to deploy sensor arrays that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these sensors acquire very high-dimensional data such as audio signals, images, and video. To cope with such high-dimensional data, we typically rely on low-dimensional models. Manifold models provide a particularly powerful model that captures the structure of high-dimensional data when it is governed by a low-dimensional set of parameters. However, these models do not typically take into account dependencies among multiple sensors. We thus propose a new joint manifold framework for data ensembles that exploits such dependencies. We show that simple algorithms can exploit the joint manifold structure to improve their performance on standard signal processing applications. Additionally, recent results concerning dimensionality reduction for manifolds enable us to formulate a network-scalable data compression scheme that uses random projections of the sensed data. This scheme efficiently fuses the data from all sensors through the addition of such projections, regardless of the data modalities and dimensions. 1
GRAPH LAPLACIAN FOR INTERACTIVE IMAGE RETRIEVAL
"... Interactive image search or relevance feedback is the process which helps a user refining his query and finding difficult target categories. This consists in a step-by-step labeling of a very small fraction of an image database and iteratively refining a decision rule using both the labeled and unla ..."
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Cited by 3 (2 self)
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Interactive image search or relevance feedback is the process which helps a user refining his query and finding difficult target categories. This consists in a step-by-step labeling of a very small fraction of an image database and iteratively refining a decision rule using both the labeled and unlabeled data. Training of this decision rule is referred to as transductive learning. Our work is an original approach for relevance feedback based on Graph Laplacian. We introduce a new Graph Laplacian which makes it possible to robustly learn the embedding of the manifold enclosing the dataset via a diffusion map. Our approach is two-folds: it allows us (i) to integrate all the unlabeled images in the decision process and (ii) to robustly capture the topology of the image set. Relevance feedback experiments were conducted on simple databases including Olivetti and Swedish as well as challenging and large scale databases including Corel. Comparisons show clear and consistent gain of our graph Laplacian method with respect to state-of-the art relevance feedback approaches.
Audio-visual group recognition using diffusion maps
- IEEE Transactions on Signal Processing
, 2009
"... Abstract—Data fusion is a natural and common approach to recovering the state of physical systems. But the dissimilar appearance of different sensors remains a fundamental obstacle. We propose a unified embedding scheme for multisensory data, based on the spectral diffusion framework, which addresse ..."
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Abstract—Data fusion is a natural and common approach to recovering the state of physical systems. But the dissimilar appearance of different sensors remains a fundamental obstacle. We propose a unified embedding scheme for multisensory data, based on the spectral diffusion framework, which addresses this issue. Our scheme is purely data-driven and assumes no a priori statistical or deterministic models of the data sources. To extract the underlying structure, we first embed separately each input channel; the resultant structures are then combined in diffusion coordinates. In particular, as different sensors sample similar phenomena with different sampling densities, we apply the density invariant Laplace–Beltrami embedding. This is a fundamental issue in multisensor acquisition and processing, overlooked in prior approaches. We extend previous work on group recognition and suggest a novel approach to the selection of diffusion coor-dinates. To verify our approach, we demonstrate performance improvements in audio/visual speech recognition. Index Terms—Dimensionality reduction, multisensor, sensor fu-sion, speech recognition, Laplacian eigenmaps. I.
A GEOMETRIC FRAMEWORK FOR TRANSFER LEARNING USING MANIFOLD ALIGNMENT
, 2010
"... I would like to thank my thesis advisor, Sridhar Mahadevan. Sridhar has been such a wonderful advisor, and every aspect of this thesis has benefitted from his guidance and support throughout my graduate studies. I also like to thank Sridhar for giving me the flexibility to explore many different ide ..."
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I would like to thank my thesis advisor, Sridhar Mahadevan. Sridhar has been such a wonderful advisor, and every aspect of this thesis has benefitted from his guidance and support throughout my graduate studies. I also like to thank Sridhar for giving me the flexibility to explore many different ideas and research topics. I am appreciative of the support offered by my other thesis committee members, Andrew McCallum, Erik Learned-Miller, and Weibo Gong. Andrew helped me on CRF, MALLET and topic modeling. Erik helped me on computer vision. Weibo has many brilliant ideas on how brains work. I got a lot of inspirations from him. I am grateful for many other professors and staff members, who helped me along. Andy Barto offered me many insightful comments and advice on my research. David Kulp and Oliver Brock helped me on bioinformatics. Stephen Scott brought me to this country, taught me machine learning/bioinformatics and offers me constant support. Vadim Gladyshev helped me on biochemistry. Mauro Maggioni helped me on diffusion wavelets. I also thank Gwyn Mitchell and Leanne Leclerc for their help with my questions over the years. I am deeply thankful to my Master thesis advisor, Zhuzhi Yuan and other teachers in Nankai University for guiding my development as
High-Dimensional Pattern Recognition using Low-Dimensional Embedding and Earth Mover’s Distance
"... We propose an algorithm that combines existing techniques in a novel way to do classification of datasets consisting of high-dimensional data (e.g., sets of signals or images). Furthermore, our algorithm sets up a framework for application of the Earth Mover’s Distance (EMD) [1, 2] as a discriminant ..."
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We propose an algorithm that combines existing techniques in a novel way to do classification of datasets consisting of high-dimensional data (e.g., sets of signals or images). Furthermore, our algorithm sets up a framework for application of the Earth Mover’s Distance (EMD) [1, 2] as a discriminant measure between datasets. We show how to prepare a compact representation – a signature – for each dataset so that computation of EMD between datasets can be done efficiently. This signature-construction step requires the tasks of dimension reduction, automatic determination of the data’s intrinsic dimensionality, out-of-sample extension, and point clustering. We will show how to apply some existing methods (which include Laplacian eigenmaps [3, 4, 5], diffusion maps framework [6, 7, 8], and elongated K-means [9]) to perform these tasks successfully. We will also provide two examples of applications of our proposed algorithm. Key words: diffusion maps, Laplacian eigenmaps, principal component analysis, Earth Mover’s Distance, Hausdorff distance
RANK TRANSFORMATION AND MANIFOLD LEARNING FOR MULTIVARIATE MATHEMATICAL MORPHOLOGY
"... The extension of lattice based operators to multivariate images is still a challenging theme in mathematical morphology. In this paper, we propose to explicitly construct complete lattices and replace each element of a multivariate image by its rank, creating a rank image suitable for classical morp ..."
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The extension of lattice based operators to multivariate images is still a challenging theme in mathematical morphology. In this paper, we propose to explicitly construct complete lattices and replace each element of a multivariate image by its rank, creating a rank image suitable for classical morphological processing. Manifold learning is considered as the basis for the construction of a complete lattice after reducing a multivariate image to its main data by Vector Quantization. A quantitative comparison between usual ordering criteria is performed and experimental results illustrate the abilities of our proposal. 1.
