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1,353
Face recognition using laplacianfaces
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2005
"... Abstract—We propose an appearancebased face recognition method called the Laplacianface approach. By using Locality Preserving Projections (LPP), the face images are mapped into a face subspace for analysis. Different from Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) wh ..."
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Cited by 188 (21 self)
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Abstract—We propose an appearancebased face recognition method called the Laplacianface approach. By using Locality Preserving Projections (LPP), the face images are mapped into a face subspace for analysis. Different from Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) which effectively see only the Euclidean structure of face space, LPP finds an embedding that preserves local information, and obtains a face subspace that best detects the essential face manifold structure. The Laplacianfaces are the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the face manifold. In this way, the unwanted variations resulting from changes in lighting, facial expression, and pose may be eliminated or reduced. Theoretical analysis shows that PCA, LDA, and LPP can be obtained from different graph models. We compare the proposed Laplacianface approach with Eigenface and Fisherface methods on three different face data sets. Experimental results suggest that the proposed Laplacianface approach provides a better representation and achieves lower error rates in face recognition. Index Terms—Face recognition, principal component analysis, linear discriminant analysis, locality preserving projections, face manifold, subspace learning. 1
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 184 (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.
Charting a Manifold
 Advances in Neural Information Processing Systems 15
, 2003
"... this paper we use m i ( j ) N ( j ; i , s ), with the scale parameter s specifying the expected size of a neighborhood on the manifold in sample space. A reasonable choice is s = r/2, so that 2erf(2) > 99.5% of the density of m i ( j ) is contained in the area around y i where the manifold is e ..."
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Cited by 162 (7 self)
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this paper we use m i ( j ) N ( j ; i , s ), with the scale parameter s specifying the expected size of a neighborhood on the manifold in sample space. A reasonable choice is s = r/2, so that 2erf(2) > 99.5% of the density of m i ( j ) is contained in the area around y i where the manifold is expected to be locally linear. With uniform p i and i , m i ( j ) and fixed, the MAP estimates of the GMM covariances are S i = m i ( j ) (y j i )(y j i ) # + ( j i )( j i ) # +S j m i ( j ) . (3) Note that each covariance S i is dependent on all other S j . The MAP estimators for all covariances can be arranged into a set of fully constrained linear equations and solved exactly for their mutually optimal values. This key step brings nonlocal information about the manifold's shape into the local description of each neighborhood, ensuring that adjoining neighborhoods have similar covariances and small angles between their respective subspaces. Even if a local subset of data points are dense in a direction perpendicular to the manifold, the prior encourages the local chart to orient parallel to the manifold as part of a globally optimal solution, protecting against a pathology noted in [8]. Equation (3) is easily adapted to give a reduced number of charts and/or charts centered on local centroids. 4 Connecting the charts We now build a connection for set of charts specified as an arbitrary nondegenerate GMM. A GMM gives a soft partitioning of the dataset into neighborhoods of mean k and covariance S k . The optimal variancepreserving lowdimensional coordinate system for each neighborhood derives from its weighted principal component analysis, which is exactly specified by the eigenvectors of its covariance matrix: Eigendecompose V k L k V # k S k with...
Unsupervised Learning of Image Manifolds by Semidefinite Programming
, 2004
"... Can we detect low dimensional structure in high dimensional data sets of images and video? The problem of dimensionality reduction arises often in computer vision and pattern recognition. In this paper, we propose a new solution to this problem based on semidefinite programming. Our algorithm can be ..."
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Cited by 162 (9 self)
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Can we detect low dimensional structure in high dimensional data sets of images and video? The problem of dimensionality reduction arises often in computer vision and pattern recognition. In this paper, we propose a new solution to this problem based on semidefinite programming. Our algorithm can be used to analyze high dimensional data that lies on or near a low dimensional manifold. It overcomes certain limitations of previous work in manifold learning, such as Isomap and locally linear embedding. We illustrate the algorithm on easily visualized examples of curves and surfaces, as well as on actual images of faces, handwritten digits, and solid objects.
Trainable Videorealistic Speech Animation
 PROCEEDINGS OF SIGGRAPH 2002, SAN ANTONIO TEXAS
, 2002
"... We describe how to create with machine learning techniques a generative, videorealistic, speech animation module. A human subject is first recorded using a videocamera as he/she utters a predetermined speech corpus. After processing the corpus automatically, a visual speech module is learned from th ..."
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Cited by 156 (5 self)
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We describe how to create with machine learning techniques a generative, videorealistic, speech animation module. A human subject is first recorded using a videocamera as he/she utters a predetermined speech corpus. After processing the corpus automatically, a visual speech module is learned from the data that is capable of synthesizing the human subject's mouth uttering entirely novel utterances that were not recorded in the original video. The synthesized utterance is recomposited onto a background sequence which contains natural head and eye movement. The final output is videorealistic in the sense that it looks like a video camera recording of the subject. At run time, the input to the system can be either real audio sequences or synthetic audio produced by a texttospeech system, as long as they have been phonetically aligned. The two key
Bounded geometries, fractals, and lowdistortion embeddings
"... The doubling constant of a metric space (X; d) is thesmallest value * such that every ball in X can be covered by * balls of half the radius. The doubling dimension of X isthen defined as dim(X) = log2 *. A metric (or sequence ofmetrics) is called doubling precisely when its doubling dimension is ..."
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Cited by 154 (31 self)
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The doubling constant of a metric space (X; d) is thesmallest value * such that every ball in X can be covered by * balls of half the radius. The doubling dimension of X isthen defined as dim(X) = log2 *. A metric (or sequence ofmetrics) is called doubling precisely when its doubling dimension is bounded. This is a robust class of metric spaceswhich contains many families of metrics that occur in applied settings.We give tight bounds for embedding doubling metrics into (lowdimensional) normed spaces. We consider bothgeneral doubling metrics, as well as more restricted families such as those arising from trees, from graphs excludinga fixed minor, and from snowflaked metrics. Our techniques include decomposition theorems for doubling metrics, andan analysis of a fractal in the plane due to Laakso [21]. Finally, we discuss some applications and point out a centralopen question regarding dimensionality reduction in L2.
Finding Nearest Neighbors in Growthrestricted Metrics
 In 34th Annual ACM Symposium on the Theory of Computing
, 2002
"... Most research on nearest neighbor algorithms in the literature has been focused on the Euclidean case. In many practical search problems however, the underlying metric is nonEuclidean. Nearest neighbor algorithms for general metric spaces are quite weak, which motivates a search for other classes o ..."
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Cited by 150 (0 self)
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Most research on nearest neighbor algorithms in the literature has been focused on the Euclidean case. In many practical search problems however, the underlying metric is nonEuclidean. Nearest neighbor algorithms for general metric spaces are quite weak, which motivates a search for other classes of metric spaces that can be tractably searched.
A DataDriven Reflectance Model
 ACM TRANSACTIONS ON GRAPHICS
, 2003
"... We present a generative model for isotropic bidirectional reflectance distribution functions (BRDFs) based on acquired reflectance data. Instead of using analytical reflectance models, we represent each BRDF as a dense set of measurements. This allows us to interpolate and extrapolate in the space o ..."
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Cited by 143 (6 self)
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We present a generative model for isotropic bidirectional reflectance distribution functions (BRDFs) based on acquired reflectance data. Instead of using analytical reflectance models, we represent each BRDF as a dense set of measurements. This allows us to interpolate and extrapolate in the space of acquired BRDFs to create new BRDFs. We treat each acquired BRDF as a single highdimensional vector taken from a space of all possible BRDFs. We apply both linear (subspace) and nonlinear (manifold) dimensionality reduction tools in an effort to discover a lowerdimensional representation that characterizes our measurements. We let users define perceptually meaningful parametrization directions to navigate in the reduceddimension BRDF space. On the lowdimensional manifold, movement along these directions produces novel but valid BRDFs.
Locating the Nodes  Cooperative localization in wireless sensor networks
, 2005
"... Accurate and lowcost sensor localization is a critical requirement for the deployment of wireless sensor networks in a wide variety of applications. Lowpower wireless sensors may be many hops away from any other sensors with a priori location information. In cooperative localization, sensors work ..."
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Cited by 142 (12 self)
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Accurate and lowcost sensor localization is a critical requirement for the deployment of wireless sensor networks in a wide variety of applications. Lowpower wireless sensors may be many hops away from any other sensors with a priori location information. In cooperative localization, sensors work together in a peertopeer manner to make measurements and then form a map of the network. Various application requirements (such as scalability, energy efficiency, and accuracy) will influence the design of sensor localization systems. In this article, we describe measurementbased statistical models useful to describe timeofarrival (TOA), angleofarrival (AOA), and receivedsignalstrength (RSS) measurements in wireless sensor networks. Wideband and ultrawideband (UWB) measurements, and RF and acoustic media are also discussed. Using the models, we show how to calculate a CramérRao bound (CRB) on the location estimation precision possible for a given set of measurements. This is a useful tool to help system designers and researchers select measurement technologies and evaluate localization algorithms. We also briefly survey a large and growing body of sensor localization algorithms. This article is intended to emphasize the basic statistical signal processing background necessary to understand the stateoftheart and to make progress in the new and largely open areas of sensor network localization research.
Cover trees for nearest neighbor
 In Proceedings of the 23rd international conference on Machine learning
, 2006
"... ABSTRACT. We present a tree data structure for fast nearest neighbor operations in generalpoint metric spaces. The data structure requires space regardless of the metric’s structure. If the point set has an expansion constant � in the sense of Karger and Ruhl [KR02], the data structure can be const ..."
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Cited by 139 (0 self)
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ABSTRACT. We present a tree data structure for fast nearest neighbor operations in generalpoint metric spaces. The data structure requires space regardless of the metric’s structure. If the point set has an expansion constant � in the sense of Karger and Ruhl [KR02], the data structure can be constructed in � time. Nearest neighbor queries obeying the expansion bound require � time. In addition, the nearest neighbor of points can be queried in time. We experimentally test the algorithm showing speedups over the brute force search varying between 1 and 2000 on natural machine learning datasets. 1.