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757
Independent Factor Analysis
 Neural Computation
, 1999
"... We introduce the independent factor analysis (IFA) method for recovering independent hidden sources from their observed mixtures. IFA generalizes and unifies ordinary factor analysis (FA), principal component analysis (PCA), and independent component analysis (ICA), and can handle not only square no ..."
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Cited by 222 (9 self)
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We introduce the independent factor analysis (IFA) method for recovering independent hidden sources from their observed mixtures. IFA generalizes and unifies ordinary factor analysis (FA), principal component analysis (PCA), and independent component analysis (ICA), and can handle not only square noiseless mixing, but also the general case where the number of mixtures differs from the number of sources and the data are noisy. IFA is a twostep procedure. In the first step, the source densities, mixing matrix and noise covariance are estimated from the observed data by maximum likelihood. For this purpose we present an expectationmaximization (EM) algorithm, which performs unsupervised learning of an associated probabilistic model of the mixing situation. Each source in our model is described by a mixture of Gaussians, thus all the probabilistic calculations can be performed analytically. In the second step, the sources are reconstructed from the observed data by an optimal nonlinear ...
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
, 2007
"... A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combinato ..."
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Cited by 207 (31 self)
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A fullrank matrix A ∈ IR n×m with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries: can it ever be unique? If so, when? As optimization of sparsity is combinatorial in nature, are there efficient methods for finding the sparsest solution? These questions have been answered positively and constructively in recent years, exposing a wide variety of surprising phenomena; in particular, the existence of easilyverifiable conditions under which optimallysparse solutions can be found by concrete, effective computational methods. Such theoretical results inspire a bold perspective on some important practical problems in signal and image processing. Several wellknown signal and image processing problems can be cast as demanding solutions of undetermined systems of equations. Such problems have previously seemed, to many, intractable. There is considerable evidence that these problems often have sparse solutions. Hence, advances in finding sparse solutions to underdetermined systems energizes research on such signal and image processing problems – to striking effect. In this paper we review the theoretical results on sparse solutions of linear systems, empirical
Robust object recognition with cortexlike mechanisms
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 2007
"... Abstract—We introduce a new general framework for the recognition of complex visual scenes, which is motivated by biology: We describe a hierarchical system that closely follows the organization of visual cortex and builds an increasingly complex and invariant feature representation by alternating b ..."
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Cited by 206 (36 self)
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Abstract—We introduce a new general framework for the recognition of complex visual scenes, which is motivated by biology: We describe a hierarchical system that closely follows the organization of visual cortex and builds an increasingly complex and invariant feature representation by alternating between a template matching and a maximum pooling operation. We demonstrate the strength of the approach on a range of recognition tasks: From invariant single object recognition in clutter to multiclass categorization problems and complex scene understanding tasks that rely on the recognition of both shapebased as well as texturebased objects. Given the biological constraints that the system had to satisfy, the approach performs surprisingly well: It has the capability of learning from only a few training examples and competes with stateoftheart systems. We also discuss the existence of a universal, redundant dictionary of features that could handle the recognition of most object categories. In addition to its relevance for computer vision, the success of this approach suggests a plausibility proof for a class of feedforward models of object recognition in cortex.
An equivalence between sparse approximation and Support Vector Machines
 A.I. Memo 1606, MIT Arti cial Intelligence Laboratory
, 1997
"... This publication can be retrieved by anonymous ftp to publications.ai.mit.edu. The pathname for this publication is: aipublications/15001999/AIM1606.ps.Z This paper shows a relationship between two di erent approximation techniques: the Support Vector Machines (SVM), proposed by V.Vapnik (1995), ..."
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Cited by 205 (7 self)
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This publication can be retrieved by anonymous ftp to publications.ai.mit.edu. The pathname for this publication is: aipublications/15001999/AIM1606.ps.Z This paper shows a relationship between two di erent approximation techniques: the Support Vector Machines (SVM), proposed by V.Vapnik (1995), and a sparse approximation scheme that resembles the Basis Pursuit DeNoising algorithm (Chen, 1995 � Chen, Donoho and Saunders, 1995). SVM is a technique which can be derived from the Structural Risk Minimization Principle (Vapnik, 1982) and can be used to estimate the parameters of several di erent approximation schemes, including Radial Basis Functions, algebraic/trigonometric polynomials, Bsplines, and some forms of Multilayer Perceptrons. Basis Pursuit DeNoising is a sparse approximation technique, in which a function is reconstructed by using a small number of basis functions chosen from a large set (the dictionary). We show that, if the data are noiseless, the modi ed version of Basis Pursuit DeNoising proposed in this paper is equivalent to SVM in the following sense: if applied to the same data set the two techniques give the same solution, which is obtained by solving the same quadratic programming problem. In the appendix we also present a derivation of the SVM technique in the framework of regularization theory, rather than statistical learning theory, establishing a connection between SVM, sparse approximation and regularization theory.
Efficient sparse coding algorithms
 In NIPS
, 2007
"... Sparse coding provides a class of algorithms for finding succinct representations of stimuli; given only unlabeled input data, it discovers basis functions that capture higherlevel features in the data. However, finding sparse codes remains a very difficult computational problem. In this paper, we ..."
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Cited by 205 (12 self)
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Sparse coding provides a class of algorithms for finding succinct representations of stimuli; given only unlabeled input data, it discovers basis functions that capture higherlevel features in the data. However, finding sparse codes remains a very difficult computational problem. In this paper, we present efficient sparse coding algorithms that are based on iteratively solving two convex optimization problems: an L1regularized least squares problem and an L2constrained least squares problem. We propose novel algorithms to solve both of these optimization problems. Our algorithms result in a significant speedup for sparse coding, allowing us to learn larger sparse codes than possible with previously described algorithms. We apply these algorithms to natural images and demonstrate that the inferred sparse codes exhibit endstopping and nonclassical receptive field surround suppression and, therefore, may provide a partial explanation for these two phenomena in V1 neurons. 1
Blind Source Separation by Sparse Decomposition in a Signal Dictionary
, 2000
"... Introduction In blind source separation an Nchannel sensor signal x(t) arises from M unknown scalar source signals s i (t), linearly mixed together by an unknown N M matrix A, and possibly corrupted by additive noise (t) x(t) = As(t) + (t) (1.1) We wish to estimate the mixing matrix A and the M ..."
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Cited by 194 (31 self)
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Introduction In blind source separation an Nchannel sensor signal x(t) arises from M unknown scalar source signals s i (t), linearly mixed together by an unknown N M matrix A, and possibly corrupted by additive noise (t) x(t) = As(t) + (t) (1.1) We wish to estimate the mixing matrix A and the Mdimensional source signal s(t). Many natural signals can be sparsely represented in a proper signal dictionary s i (t) = K X k=1 C ik ' k (t) (1.2) The scalar functions ' k
Face recognition by independent component analysis
 IEEE Transactions on Neural Networks
, 2002
"... Abstract—A number of current face recognition algorithms use face representations found by unsupervised statistical methods. Typically these methods find a set of basis images and represent faces as a linear combination of those images. Principal component analysis (PCA) is a popular example of such ..."
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Cited by 192 (4 self)
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Abstract—A number of current face recognition algorithms use face representations found by unsupervised statistical methods. Typically these methods find a set of basis images and represent faces as a linear combination of those images. Principal component analysis (PCA) is a popular example of such methods. The basis images found by PCA depend only on pairwise relationships between pixels in the image database. In a task such as face recognition, in which important information may be contained in the highorder relationships among pixels, it seems reasonable to expect that better basis images may be found by methods sensitive to these highorder statistics. Independent component analysis (ICA), a generalization of PCA, is one such method. We used a version of ICA derived from the principle of optimal information transfer through sigmoidal neurons. ICA was performed on face images in the FERET database under two different architectures, one which treated the images as random variables and the pixels as outcomes, and a second which treated the pixels as random variables and the images as outcomes. The first architecture found spatially local basis images for the faces. The second architecture produced a factorial face code. Both ICA representations were superior to representations based on PCA for recognizing faces across days and changes in expression. A classifier that combined the two ICA representations gave the best performance. Index Terms—Eigenfaces, face recognition, independent component analysis (ICA), principal component analysis (PCA), unsupervised learning. I.
Deriving Intrinsic Images from Image Sequences
, 2001
"... Intrinsic images are a useful midlevel description of scenes proposed by Barrow and Tenebaum [1]. An image is decomposed into two images: a reflectance image and an illumination image. Finding such a decomposition remains a difficult problem in computer vision. Here we focus on a slightly easier pro ..."
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Cited by 191 (5 self)
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Intrinsic images are a useful midlevel description of scenes proposed by Barrow and Tenebaum [1]. An image is decomposed into two images: a reflectance image and an illumination image. Finding such a decomposition remains a difficult problem in computer vision. Here we focus on a slightly easier problem: given a sequence of T images where the reflectance is constant and the illumination changes, can we recover T illumination images and a single reflectance image? We show that this problem is still illposed and suggest approaching it as a maximumlikelihood estimation problem. Following recent work on the statistics of natural images, we use a prior that assumes that illumination images will give rise to sparse filter outputs. We show that this leads to a simple, novel algorithm for recovering reflectance images. We illustrate the algorithm's performance on real and synthetic image sequences.
Selftaught learning: Transfer learning from unlabeled data
 Proceedings of the Twentyfourth International Conference on Machine Learning
, 2007
"... We present a new machine learning framework called “selftaught learning ” for using unlabeled data in supervised classification tasks. We do not assume that the unlabeled data follows the same class labels or generative distribution as the labeled data. Thus, we would like to use a large number of ..."
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Cited by 186 (20 self)
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We present a new machine learning framework called “selftaught learning ” for using unlabeled data in supervised classification tasks. We do not assume that the unlabeled data follows the same class labels or generative distribution as the labeled data. Thus, we would like to use a large number of unlabeled images (or audio samples, or text documents) randomly downloaded from the Internet to improve performance on a given image (or audio, or text) classification task. Such unlabeled data is significantly easier to obtain than in typical semisupervised or transfer learning settings, making selftaught learning widely applicable to many practical learning problems. We describe an approach to selftaught learning that uses sparse coding to construct higherlevel features using the unlabeled data. These features form a succinct input representation and significantly improve classification performance. When using an SVM for classification, we further show how a Fisher kernel can be learned for this representation. 1.
Image and depth from a conventional camera with a coded aperture
 ACM Trans. Graph
"... Figure 1: Left: Image captured using our coded aperture. Center: Top, closeup of captured image. Bottom, closeup of recovered sharp image. Right: Recovered depth map with color indicating depth from camera (cm) (in this this case, without user intervention). A conventional camera captures blurred ve ..."
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Cited by 184 (19 self)
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Figure 1: Left: Image captured using our coded aperture. Center: Top, closeup of captured image. Bottom, closeup of recovered sharp image. Right: Recovered depth map with color indicating depth from camera (cm) (in this this case, without user intervention). A conventional camera captures blurred versions of scene information away from the plane of focus. Camera systems have been proposed that allow for recording allfocus images, or for extracting depth, but to record both simultaneously has required more extensive hardware and reduced spatial resolution. We propose a simple modification to a conventional camera that allows for the simultaneous recovery of both (a) high resolution image information and (b) depth information adequate for semiautomatic extraction of a layered depth representation of the image. Our modification is to insert a patterned occluder within the aperture of the camera lens, creating a coded aperture. We introduce a criterion for depth discriminability which we use to design the preferred aperture pattern. Using a statistical model of images, we can recover both depth information and an allfocus image from single photographs taken with the modified camera. A layered depth map is then extracted, requiring userdrawn strokes to clarify layer assignments in some cases. The resulting sharp image and layered depth map can be combined for various photographic applications, including automatic scene segmentation, postexposure refocusing, or rerendering of the scene from an alternate viewpoint.