Above are papers related to the following paper: [Paper_ID] Paper #370366. 	[Title] From Data Distributions to Regularization in Invariant Learning [Abstract] Ideally pattern recognition machines provide constant output when the inputs are transformed under a group G of desired invariances. These invariances can be achieved by enhancing the training data to include examples of inputs transformed by elements of G, while leaving the corresponding targets unchanged. Alternatively the cost function for training can include a regularization term that penalizes changes in the output when the input is transformed under the group. This paper relates the two approaches, showing precisely the sense in which the regularized cost function approximates the result of adding transformed (or distorted) examples to the training data. The cost function for the enhanced training set is equivalent to the sum of the original cost function plus a regularizer. For unbiased models, the regularizer reduces to the intuitively obvious choice - a term that penalizes changes in the output when the inputs are transformed under the group. For infinitesimal transformations, the coefficient of the regularization term reduces to the variance of the distortions introduced into the training data. This correspondence provides a simple bridge between the two approaches. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #641956. 	[Title] Adaptive Noise Injection for Input Variables Relevance Determination [Abstract] In this paper we consider the application of training with noise in multi-layer perceptron to input variables relevance determination. Noise injection is modified in order to penalize irrelevant features. The proposed algorithm is attractive as it requires the tuning of a single parameter. This parameter controls the penalization of the inputs together with the complexity of the model. After the presentation of the method, experimental evidences are given on simulated data sets. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1140040. 	[Title] for Projective Basis Function Networks 2m1 Global Form 2m Local Form With appropriate constant factors, [Abstract] OGI CSE Technical Report 96-006 Abstract: Smoothing regularizers for radial basis functions have been studied extensively, but no general smoothing regularizers for projective basis functions (PBFs), such as the widely-used sigmoidal PBFs, have heretofore been proposed. We derive new classes of algebraically-simple m th -order smoothing regularizers for networks of projective basis functions f (W; x) = P N fi fl + u 0 ; with general transfer functions g[]. These simple algebraic forms R(W; m) enable the direct enforcement of smoothness without the need for costly Monte Carlo integrations of S(W; m). The regularizers are tested on illustrative sample problems and compared to quadratic weight decay. The new regularizers are shown to yield better generalization errors than Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #928873. 	[Title] Face Recognition: A Hybrid Neural Network Approach [Abstract] Faces represent complex, multidimensional, meaningful visual stimuli and developing a computational model for face recognition is difficult (Turk and Pentland, 1991). We present a hybrid neural network solution which compares favorably with other methods. The system combines local image sampling, a self-organizing map neural network, and a convolutional neural network. The self-organizing map provides a quantization of the image samples into a topological space where inputs that are nearby in the original space are also nearby in the output space, thereby providing dimensionality reduction and invariance to minor changes in the image sample, and the convolutional neural network provides for partial invariance to translation, rotation, scale, and deformation. The convolutional network extracts successively larger features in a hierarchical set of layers. We present results using the Karhunen-Loeve transform in place of the self-organizing map, and a multilayer perceptron in place of the convolutional network. The Karhunen-Loeve transform performs almost as well (5.3% error versus 3.8%). The multilayer perceptron performs very poorly (40% error versus 3.8%). The method is capable of rapid classification, requires only fast, approximate normalization and preprocessing, and consistently exhibits better classification performance than the eigenfaces approach (Turk and Pentland, 1991) on the database considered as the number of images per person in the training database is varied from 1 to 5. With 5 images per person the proposed method and eigenfaces result in 3.8% and 10.5% error respectively. The recognizer provides a measure of confidence in its output and classification error approaches zero when rejecting as few as 10% of the examples. We use a database of 400 images of 40 individuals which contains quite a high degree of variability in expression, pose, and facial details. We analyze computational complexity and discuss how new classes could be added to the trained recognizer. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #906. 	[Title] Regularization Theory and Neural Networks Architectures [Abstract] We had previously shown that regularization principles lead to approximation schemes which are equivalent to networks with one layer of hidden units, called Regularization Networks. In particular, standard smoothness functionals lead to a subclass of regularization networks, the well known Radial Basis Functions approximation schemes. This paper shows that regularization networks encompass a much broader range of approximation schemes, including many of the popular general additive models and some of the neural networks. In particular, we introduce new classes of smoothness functionals that lead to different classes of basis functions. Additive splines as well as some tensor product splines can be obtained from appropriate classes of smoothness functionals. Furthermore, the same generalization that extends Radial Basis Functions (RBF) to Hyper Basis Functions (HBF) also leads from additive models to ridge approximation models, containing as special cases Breiman's hinge functions, some forms of Projection Pursuit Regression and several types of neural networks. We propose to use the term Generalized Regularization Networks for this broad class of approximation schemes that follow from an extension of regularization. In the probabilistic interpretation of regularization, the different classes of basis functions correspond to different classes of prior probabilities on the approximating function spaces, and therefore to different types of smoothness assumptions. In summary, different multilayer networks with one hidden layer, which we collectively call Generalized Regularization Networks, correspond to different classes of priors and associated smoothness functionals in a classical regularization principle. Three broad classes are a) Radial Basis Functions that can be generalized to Hyper Basis Functions, b) some tensor product splines, and c) additive splines that can be generalized to schemes of the type of ridge approximation, hinge functions and several perceptron-like neural networks with one-hidden layer. 1 This paper will appear on Neural Computation, vol. 7, pages 219-269, 1995. An earlier version of Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #24043. 	[Title] Human Face Detection in Visual Scenes [Abstract] We present a neural network-based face detection system. A retinally connected neural network examines small windows of an image, and decides whether each window contains a face. The system arbitrates between multiple networks to improve performance over a single network. We use a bootstrap algorithm for training, which adds false detections into the training set as training progresses. This eliminates the difficult task of manually selecting non-face training examples, which must be chosen to span the entire space of non-face images. Comparisons with another state-of-the-art face detection system are presented; our system has better performance in terms of detection and false-positive rates. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #25772. 	[Title] Flexible Metric Nearest Neighbor Classiflcation [Abstract] The K-nearest-neighbor decision rule assigns an object of unknown class to the plurality class among the K labeled "training" objects that are closest to it. Closeness is usually deflned in terms of a metric distance on the Euclidean space with the input measurement variables as axes. The metric chosen to deflne this distance can strongly efiect performance. An optimal choice depends on the problem at hand as characterized by the respective class distributions on the input measurement space, and within a given problem, on the location of the unknown object in that space. In this paper new types of K-nearest-neighbor procedures are described that estimate the local relevance of each input variable, or their linear combinations, for each individual point to be classifled. This information is then used to separately customize the metric used to deflne distance from that object in flnding its nearest neighbors. These procedures are a hybrid between regular K-nearest-neighbor methods and treestructured recursive partitioning techniques popular in statistics and machine learning. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131149. 	[Title] Least Absolute Shrinkage is Equivalent to Quadratic Penalization [Abstract] Adaptive ridge is a special form of ridge regression, balancing the quadratic penalization on each parameter of the model. This paper shows the equivalence between adaptive ridge and lasso (least absolute shrinkage and selection operator). This equivalence states that both procedures produce the same estimate. Least absolute shrinkage can thus be viewed as a particular quadratic penalization. From this observation, we derive an EM algorithm to compute the lasso solution. We finally present a series of applications of this type of algorithm in regres sion problems: kernel regression, additive modeling and neural net training. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #910. 	[Title] Learning networks for face analysis and synthesis [Abstract] This paper presents an overview of the face-related projects in our group. The unifying theme underlying our work is the use of example-based learning methods for both analyzing and synthesizing face images. We label the example face images (and for the problem of face detection, "near miss" faces as well) with descriptive parameters for pose, expression, identity, and face vs. non-face. Then, by using example-based learning techniques, we develop networks for performing analysis tasks such as pose and expression estimation, face recognition, and face detection in cluttered scenes. In addition to these analysis applications, we show how the example-based technique can also be used as a novel method for image synthesis that is for computer graphics. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1131150. 	[Title] Penalisation multiple adaptative un nouvel algorithme de regression, la penalisation multiple adapta-tive. Cet algorithme represente [Abstract] Chaque parametre du modele est penalise individuellement. Le reglage de ces penalisations se fait automatiquement a partir de la definition d'un hyperparametre de regularisation globale. Cet hyperparametre, qui controle la complexite du regresseur, peut ^etre estime par des techniques de reechantillonnage. Nous montrons experimentalement les performances et la stabilite de la penalisation multiple adaptative dans le cadre de la regression lineaire. Nous avons choisi des problemes pour lesquels le probleme du controle de la complexite est particulierement crucial, comme dans le cadre plus general de l'estimation fonctionnelle. Les comparaisons avec les moindres carres regularises et la selection de variables nous permettent de deduire les conditions d'application de chaque algorithme de penalisation. Lors des simulations, nous testons egalement plusieurs techniques de reechantillonnage. Ces techniques sont utilisees pour selectionner la complexite optimale des estimateurs de la fonction de regression. Nous comparons les pertes occasionnees par chacune d'entre elles lors de la selection de modeles sous-optimaux. Nous regardons egalement si elles permettent de determiner l'estimateur de la fonction de regression minimisant l'erreur en generalisation parmi les differentes methodes de penalisation en competition. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #340078. 	[Title] Evaluation of Pattern Classifiers for Fingerprint and OCR Applications [Abstract] In this paper we evaluate the classification accuracy of four statistical and three neural network classifiers for two image based pattern classification problems. These are fingerprint classification and optical character recognition (OCR) for isolated handprinted digits. The evaluation results reported here should be useful for designers of practical systems for these two important commercial applications. For the OCR problem, the Karhunen-Loeve (K-L) transform of the images is used to generate the input feature set. Similarly for the fingerprint problem, the K-L transform of the ridge directions is used to generate the input feature set. The statistical classifiers used were Euclidean minimum distance, quadratic minimum distance, normal, and k-nearest neighbor. The neural network classifiers used were multilayer perceptron, radial basis function, and probabilistic. The OCR data consisted of 7,480 digit images for training and 23,140 digit images for testing. The fingerprint data consisted of 2,000 training and 2,000 testing images. In addition to evaluation for accuracy, the multilayer perceptron and radial basis function networks were evaluated for size and generalization capability. For the evaluated datasets the best accuracy obtained for either problem was provided by the probabilistic neural network, where the minimum classification error was 2.5% for OCR and 7.2% for fingerprints. Please summarise all the given information.

Paper #370366 has the title `From Data Distributions to Regularization in Invariant Learning  
` and the abstract `Ideally pattern recognition machines provide constant output when the inputs are transformed under a group G of desired invariances. These invariances can be achieved by enhancing the training data to include examples of inputs transformed by elements of G, while leaving the corresponding targets unchanged. Alternatively the cost function for training can include a regularization term that penalizes changes in the output when the input is transformed under the group. This paper relates the two approaches, showing precisely the sense in which the regularized cost function approximates the result of adding transformed (or distorted) examples to the training data. The cost function for the enhanced training set is equivalent to the sum of the original cost function plus a regularizer. For unbiased models, the regularizer reduces to the intuitively obvious choice - a term that penalizes changes in the output when the inputs are transformed under the group. For infinitesimal transformations, the coefficient of the regularization term reduces to the variance of the distortions introduced into the training data. This correspondence provides a simple bridge between the two approaches. 
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Question: Which category should Paper #370366 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #370366 has the title `From Data Distributions to Regularization in Invariant Learning  
` and the abstract `Ideally pattern recognition machines provide constant output when the inputs are transformed under a group G of desired invariances. These invariances can be achieved by enhancing the training data to include examples of inputs transformed by elements of G, while leaving the corresponding targets unchanged. Alternatively the cost function for training can include a regularization term that penalizes changes in the output when the input is transformed under the group. This paper relates the two approaches, showing precisely the sense in which the regularized cost function approximates the result of adding transformed (or distorted) examples to the training data. The cost function for the enhanced training set is equivalent to the sum of the original cost function plus a regularizer. For unbiased models, the regularizer reduces to the intuitively obvious choice - a term that penalizes changes in the output when the inputs are transformed under the group. For infinitesimal transformations, the coefficient of the regularization term reduces to the variance of the distortions introduced into the training data. This correspondence provides a simple bridge between the two approaches. 
`.
Question: Which category should Paper #370366 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks