Stable local feature detection and representation is a fundamental component of many image registration and object recognition algorithms. Mikolajczyk and Schmid [14] recently evaluated a variety of approaches and identified the SIFT [11] algorithm as being the most resistant to common image deformations. This paper examines (and improves upon) the local image descriptor used by SIFT. Like SIFT, our descriptors encode the salient aspects of the image gradient in the feature point's neighborhood; however, instead of using SIFT's smoothed weighted histograms, we apply Principal Components Analysis (PCA) to the normalized gradient patch. Our experiments demonstrate that the PCAbased local descriptors are more distinctive, more robust to image deformations, and more compact than the standard SIFT representation. We also present results showing that using these descriptors in an image retrieval application results in increased accuracy and faster matching.

Accrue Software, Inc. Clustering is a division of data into groups of similar objects. Representing the data by fewer clusters necessarily loses certain fine details, but achieves simplification. It models data by its clusters. Data modeling puts clustering in a historical perspective rooted in mathematics, statistics, and numerical analysis. From a machine learning perspective clusters correspond to hidden patterns, the search for clusters is unsupervised learning, and the resulting system represents a data concept. From a practical perspective clustering plays an outstanding role in data mining applications such as scientific data exploration, information retrieval and text mining, spatial database applications, Web analysis, CRM, marketing, medical diagnostics, computational biology, and many others. Clustering is the subject of active research in several fields such as statistics, pattern recognition, and machine learning. This survey focuses on clustering in data mining. Data mining adds to clustering the complications of very large datasets with very many attributes of different types. This imposes unique

Standard value function approaches to finding policies for Partially Observable Markov Decision Processes (POMDPs) are intractable for large models. This intractability of these algorithms is due to a great extent to their generating an optimal policy over the entire belief space. However, in real POMDP problems most belief states are highly unlikely, and there is a highly structured, low-dimensional manifold of plausible beliefs embedded in the high-dimensional belief space.

Standard value function approaches to finding policies for Partially Observable Markov Decision Processes (POMDPs) are generally considered to be intractable for large models. The intractability of these algorithms is to a large extent a consequence of computing an exact, optimal policy over the entire belief space. However, in real-world POMDP problems, computing the optimal policy for the full belief space is often unnecessary for good control even for problems with complicated policy classes. The beliefs experienced by the controller often lie near a structured, low-dimensional manifold embedded in the high-dimensional belief space. Finding a good approximation to the optimal value function for only this manifold can be much easier than computing the full value function. We introduce a new method for solving large-scale POMDPs by reducing the dimensionality of the belief space. We use Exponential family Principal Components Analysis (Collins, Dasgupta, & Schapire, 2002) to represent sparse, high-dimensional belief spaces using low-dimensional sets of learned features of the belief state. We then plan only in terms of the low-dimensional belief features. By planning in this low-dimensional space, we can find policies for POMDP models that are orders of magnitude larger than models that can be handled by conventional techniques. We demonstrate the use of this algorithm on a synthetic problem and on mobile robot navigation tasks. 1.

Abstract—Over the past few decades, a large family of algorithms—supervised or unsupervised; stemming from statistics or geometry theory—has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called Marginal Fisher Analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional Linear Discriminant Analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions. Index Terms—Dimensionality reduction, manifold learning, subspace learning, graph embedding framework. 1

We present recent work on integration of visual information (automatic lip-reading) with acoustic speech for better overall speech recognition. A Multi-State Time Delay Neural Network performs the recognition of spelled letter sequences taking advantage of lip images from a standard camera. The problems addressed include efficient but effective representation of the visual information and optimum manner of combining the two modalities when rendering a decision. We show results for several alternatives to direct gray level image as the visual evidence. These are: Principal Components, Linear Discriminants, and DFT coefficients. Dimensionality of the input is decreased by a factor of 12 while maintaining recognition rates. Combination of the visual and acoustic information is performed at three different levels of abstraction. Results suggest that integration of higher order input features works best. On a continuous spelling task, visual-alone recognition of 45-55%, when combined with a...

A motion-based, correspondence-free technique for human gait recognition in monocular video is presented. We contend that the planar dynamics of a walking person are encoded in a 2D plot consisting of the pairwise image similarities of the sequence of images of the person, and that gait recognition can be achieved via standard pattern classification of these plots. We use background modelling to track the person for a number of frames and extract a sequence of segmented images of the person. The self-similarity plot is computed via correlation of each pair of images in this sequence. For recognition, the method applies Principal Component Analysis to reduce the dimensionality of the plots, then uses the k-nearest neighbor rule in this reduced space to classify an unknown person. This method is robust to tracking and segmentation errors, and to variation in clothing and background. It is also invariant to small changes in camera viewpoint and walking speed. The method is tested on outdoor sequences of 44 people with 4 sequences of each taken on two different days, and achieves a classification rate of 77%. It is also tested on indoor sequences of 7 people walking on a treadmill, taken from 8 different viewpoints and on 7 different days. A classification rate of 78% is obtained for near-fronto-parallel views, and 65% on average over all view.

In the last decades, a large family of algorithms ─ supervised or unsupervised; stemming from statistic or geometry theory─have been proposed to provide different solutions to the problem of dimensionality reduction. In this paper, beyond the different motivations of these algorithms, we propose a general framework, graph embedding along with its linearization and kernelization, which in theory reveals the underlying objective shared by most previous algorithms. It presents a unified perspective to understand these algorithms; that is, each algorithm can be considered as the direct graph embedding or its linear/kernel extension of some specific graph characterizing certain statistic or geometry property of a data set. Furthermore, this framework is a general platform to develop new algorithm for dimensionality reduction. To this end, we propose a new supervised algorithm, Marginal Fisher Analysis (MFA), for dimensionality reduction by designing two graphs that characterize the intra-class compactness and interclass separability, respectively. MFA measures the intra-class compactness with the distance between each data point and its neighboring points of the same class, and measures the inter-class separability with the class margins; thus it overcomes the limitations of traditional Linear Discriminant Analysis algorithm in terms of data distribution assumptions and available projection directions. The toy problem on artificial data and the real face recognition experiments both show the superiority of our proposed MFA in comparison to LDA. 1.

A robust principal component analysis can be easily performed by computing the eigenvalues and eigenvectors of a robust estimator of the covariance or correlation matrix. In this paper we derive the influence functions and the corresponding asymptotic variances for these robust estimators of eigenvalues and eigenvectors. The behavior of several of these estimators is investigated by a simulation study. Finally, the use of empirical influence functions is illustrated by a real data example.

In this paper we introduce a new method for robust principal component analysis. Classical PCA is based on the empirical covariance matrix of the data and hence it is highly sensitive to outlying observations. In the past, two robust approaches have been developed. The first is based on the eigenvectors of a robust scatter matrix such as the MCD or an S-estimator, and is limited to relatively low-dimensional data. The second approach is based on projection pursuit and can handle high-dimensional data. Here, we propose the ROBPCA approach which combines projection pursuit ideas with robust scatter matrix estimation. It yields more accurate estimates at non-contaminated data sets and more robust estimates at contaminated data. ROBPCA can be computed fast, and is able to detect exact fit situations. As a byproduct, ROBPCA produces a diagnostic plot which displays and classifies the outliers. The algorithm is applied to several data sets from chemometrics and engineering.