Above are papers related to the following paper: [Paper_ID] Paper #2702. 	[Title] In  Fast Non-Linear Dimension Reduction [Abstract] We present a fast algorithm for non-linear dimension reduction. The algorithm builds a local linear model of the data by merging PCA with clustering based on a new distortion measure. Experiments with speech and image data indicate that the local linear algorithm produces encodings with lower distortion than those built by five layer auto-associative networks. The local linear algorithm is also more than an order of magnitude faster to train. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #395553. 	[Title] Mixtures of Probabilistic Principal Component Analysers [Abstract] Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a combination of local linear PCA projections. However, conventional PCA does not correspond to a probability density, and so there is no unique way to combine PCA models. Previous attempts to formulate mixture models for PCA have therefore to some extent been ad hoc. In this paper, PCA is formulated within a maximum-likelihood framework, based on a specific form of Gaussian latent variable model. This leads to a well-defined mixture model for probabilistic principal component analysers, whose parameters can be determined using an EM algorithm. We discuss the advantages of this model in the context of clustering, density modelling and local dimensionality reduction, and we demonstrate its application to image compression and handwritten digit recognition. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #949217. 	[Title] Comparison of Neural and Statistical Classifiers| Theory and Practice [Abstract] Research Reports A13 January 1996 Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #400356. 	[Title] Factor Analysis Using Delta-Rule Wake-Sleep Learning [Abstract] Technical Report No. 9607, Department of Statistics, University of Toronto We describe a linear network that models correlations between real-valued visible variables using one or more real-valued hidden variables a factor analysis model. This model can be seen as a linear version of the Helmholtz machine, and its parameters can be learned using the wake-sleep method, in which learning of the primary generative model is assisted by a recognition model, whose role is to fill in the values of hidden variables based on the values of visible variables. The generative and recognition models are jointly learned in wake and sleep phases, using just the delta rule. This learning procedure is comparable in simplicity to Oja's version of Hebbian learning, which produces a somewhat different representation of correlations in terms of principal components. We argue that the simplicity of wake-sleep learning makes factor analysis a plau sible alternative to Hebbian learning as a model of activity-dependent cortical plasticity. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1153861. 	[Title] Data Mining for Association Rules with Unsupervised Neural Networks [Abstract] results for Gaussian mixture models and factor analysis are discussed. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1120777. 	[Title] Modelling the Manifolds of Images of Handwritten Digits [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #4330. 	[Title] Hierarchical Mixtures of Experts and the EM Algorithm [Abstract] We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM's). Learning is treated as a maximum likelihood problem; in particular, we present an Expectation-Maximization (EM) algorithm for adjusting the parameters of the architecture. We also develop an on-line learning algorithm in which the parameters are updated incrementally. Comparative simulation results are presented in the robot dynamics domain. This report describes research done at the Dept. of Brain and Cognitive Sciences, the Center for Biological and Computational Learning, and the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for CBCL is provided in part by a grant from the NSF (ASC-9217041). Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Dept. of Defense. The authors were supported by a grant from the McDonnell-Pew Foundation, by a grant from ATR Human Information Processing Research Laboratories, by a grant from Siemens Corporation, by by grant IRI-9013991 from the National Science Foundation, by grant N00014-90-J-1942 from the Office of Naval Research, and by NSF grant ECS-9216531 to support an Initiative in Intelligent Control at MIT. Michael I. Jordan is a NSF Presidential Young Investigator. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12330. 	[Title] Recognizing Handwritten Digits Using Mixtures of Linear Models [Abstract] We construct a mixture of locally linear generative models of a collection of pixel-based images of digits, and use them for recognition. Different models of a given digit are used to capture different styles of writing, and new images are classified by evaluating their log-likelihoods under each model. We use an EM-based algorithm in which the M-step is computationally straightforward principal components analysis (PCA). Incorporating tangent-plane information [12] about expected local deformations only requires adding tangent vectors into the sample covariance matrices for the PCA, and it demonstrably improves performance. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #684972. 	[Title] Probabilistic Principal Component Analysis [Abstract] Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum-likelihood estimation of parameters in a latent variable model closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace iteratively, and discuss the advantages conveyed by the definition of a probability density function for PCA. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1152490. 	[Title] Data Mining for Association Rules with Unsupervised Neural Networks [Abstract] results for Gaussian mixture models and factor analysis are discussed. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #156977. 	[Title] The EM Algorithm for Mixtures of Factor Analyzers [Abstract] Technical Report CRG-TR-96-1 May 21, 1996 (revised Feb 27, 1997) Abstract Factor analysis, a statistical method for modeling the covariance structure of high dimensional data using a small number of latent variables, can be extended by allowing different local factor models in different regions of the input space. This results in a model which concurrently performs clustering and dimensionality reduction, and can be thought of as a reduced dimension mixture of Gaussians. We present an exact Expectation-Maximization algorithm for fitting the parameters of this mixture of factor analyzers. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1135122. 	[Title] Quicknet on MultiSpert: Fast Parallel Neural Network Training [Abstract] The MultiSpert parallel system is a straight-forward extension of the Spert workstation accelerator, which is predominantly used in speech recognition research at ICSI. In order to deliver high performance for Artificial Neural Network training without requiring changes to the user interfaces, the exisiting Quicknet ANN library was modified to run on MultiSpert. In this report, we present the algorithms used in the parallelization of the Quicknet code and analyse their communication and computation requirements. The resulting performance model yields a better understanding of system speed-ups and potential bottlenecks. Experimental results from actual training runs validate the model and demonstrate the achieved performance levels. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #107569. 	[Title] Using generative models for handwritten digit recognition [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #72056. 	[Title] MBP on T0: mixing floating- and fixed-point formats in BP learning [Abstract] We examine the efficient implementation of back prop type algorithms on T0 [4], a vector processor with a fixed point engine, designed for neural network simulation. A matrix formulation of back prop, Matrix Back Prop [1], has been shown to be very efficient on some RISCs [2]. Using Matrix Back Prop, we achieve an asymptotically optimal performance on T0 (about 0.8 GOPS) for both forward and backward phases, which is not possible with the standard on-line method. Since high efficiency is futile if convergence is poor (due to the use of fixed point arithmetic), we use a mixture of fixed and floating point operations. The key observation is that the precision of fixed point is sufficient for good convergence, if the range is appropriately chosen. Though the most expensive computations are implemented in fixed point, we achieve a rate of convergence that is comparable to the floating point version. The time taken for conversion between fixed and floating point is also shown to be reasonable. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #684986. 	[Title] A Hierarchical Latent Variable Model for Data Visualization [Abstract] Visualization has proven to be a powerful and widely-applicable tool for the analysis and interpretation of multi-variate data. Most visualization algorithms aim to find a projection from the data space down to a two-dimensional visualization space. However, for complex data sets living in a high-dimensional space it is unlikely that a single two-dimensional projection can reveal all of the interesting structure. We therefore introduce a hierarchical visualization algorithm which allows the complete data set to be visualized at the top level, with clusters and sub-clusters of data points visualized at deeper levels. The algorithm is based on a hierarchical mixture of latent variable models, whose parameters are estimated using the expectation-maximization algorithm. We demonstrate the principle of the approach on a toy data set, and we then apply the algorithm to the visualization of a synthetic data set in 12 dimensions obtained from a simulation of multi-phase flows in oil pipelines, and to data in 36 dimensions derived from satellite images. A Matlab software implementation of the algorithm is publicly available from the world-wide web. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #395547. 	[Title] EM Algorithms for PCA and SPCA [Abstract] I present an expectation-maximization (EM) algorithm for principal component analysis (PCA). The algorithm allows a few eigenvectors and eigenvalues to be extracted from large collections of high dimensional data. It is computationally very efficient in space and time. It also naturally accommodates missing information. I also introduce a new variant of PCA called sensible principal component analysis (SPCA) which defines a proper density model in the data space. Learning for SPCA is also done with an EM algorithm. I report results on synthetic and real data showing that these EM algorithms correctly and efficiently find the leading eigenvectors of the covariance of datasets in a few iterations using up to hundreds of thousands of datapoints in thousands of dimensions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #213279. 	[Title] Constraint Tangent Distance for On-line Character Recognition [Abstract] In on-line character recognition we can observe two kinds of intra-class variations: small geometric deformations and completely different writing styles. We propose a new approach to deal with these problems by defining an extension of tangent distance [9], well known in off-line character recognition. The system has been implemented with a k-nearest neighbor classifier and a so called diabolo classifier [6] respectively. Both classifiers are invariant under transformations like rotation, scale or slope and can deal with variations in stroke order and writing direction. Results are presented for our digit database with more than 200 writers. Please summarise all the given information.

Paper #2702 has the title `In  Fast Non-Linear Dimension Reduction  
` and the abstract `We present a fast algorithm for non-linear dimension reduction. The algorithm builds a local linear model of the data by merging PCA with clustering based on a new distortion measure. Experiments with speech and image data indicate that the local linear algorithm produces encodings with lower distortion than those built by five layer auto-associative networks. The local linear algorithm is also more than an order of magnitude faster to train.
`.
Question: Which category should Paper #2702 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #2702 has the title `In  Fast Non-Linear Dimension Reduction  
` and the abstract `We present a fast algorithm for non-linear dimension reduction. The algorithm builds a local linear model of the data by merging PCA with clustering based on a new distortion measure. Experiments with speech and image data indicate that the local linear algorithm produces encodings with lower distortion than those built by five layer auto-associative networks. The local linear algorithm is also more than an order of magnitude faster to train.
`.
Question: Which category should Paper #2702 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