Geometrical learning, descriptive geometry, and biomimetic pattern recognition

Studies on learning problems from geometry perspective have attracted an ever increasing attention in machine learning, leaded by achievements on information geometry. This paper proposes a different geometrical learning from the perspective of high-dimensional descriptive geometry. Geometrical properties of high-dimensional structures underlying a set of samples are learned via successive projections from the higher dimension to the lower dimension until two-dimensional Euclidean plane, under guidance of the established properties and theorems in high-dimensional descriptive geometry. Specifically, we introduce a hyper sausage like geometry shape for learning samples and provides a geometrical learning algorithm for specifying the hyper sausage shapes, which is then applied to biomimetic pattern recognition. Experimental results are presented to show that the proposed approach outperforms three types of support vector machines with either a three degree polynomial kernel or a radial basis function kernel, especially in the cases of high-dimensional samples of a finite size. (c) 2005 Elsevier B.V. All rights reserved.

Continuous speech recognition based on ICA and geometrical learning

We investigate the use of independent component analysis (ICA) for speech feature extraction in digits speech recognition systems. We observe that this may be true for recognition tasks based on Geometrical Learning with little training data. In contrast to image processing, phase information is not essential for digits speech recognition. We therefore propose a new scheme that shows how the phase sensitivity can be removed by using an analytical description of the ICA-adapted basis functions. Furthermore, since the basis functions are not shift invariant, we extend the method to include a frequency-based ICA stage that removes redundant time shift information. The digits speech recognition results show promising accuracy. Experiments show that the method based on ICA and Geometrical Learning outperforms HMM in a different number of training samples.

Continuous speech recognition based on ICA and geometrical learning

We investigate the use of independent component analysis (ICA) for speech feature extraction in digits speech recognition systems. We observe that this may be true for recognition tasks based on Geometrical Learning with little training data. In contrast to image processing, phase information is not essential for digits speech recognition. We therefore propose a new scheme that shows how the phase sensitivity can be removed by using an analytical description of the ICA-adapted basis functions. Furthermore, since the basis functions are not shift invariant, we extend the method to include a frequency-based ICA stage that removes redundant time shift information. The digits speech recognition results show promising accuracy. Experiments show that the method based on ICA and Geometrical Learning outperforms HMM in a different number of training samples.

Learning World Models in Environments with Manifest Causal Structure

This thesis examines the problem of an autonomous agent learning a causal world model of its environment. Previous approaches to learning causal world models have concentrated on environments that are too "easy" (deterministic finite state machines) or too "hard" (containing much hidden state). We describe a new domain --- environments with manifest causal structure --- for learning. In such environments the agent has an abundance of perceptions of its environment. Specifically, it perceives almost all the relevant information it needs to understand the environment. Many environments of interest have manifest causal structure and we show that an agent can learn the manifest aspects of these environments quickly using straightforward learning techniques. We present a new algorithm to learn a rule-based causal world model from observations in the environment. The learning algorithm includes (1) a low level rule-learning algorithm that converges on a good set of specific rules, (2) a concept learning algorithm that learns concepts by finding completely correlated perceptions, and (3) an algorithm that learns general rules. In addition this thesis examines the problem of finding a good expert from a sequence of experts. Each expert has an "error rate"; we wish to find an expert with a low error rate. However, each expert's error rate and the distribution of error rates are unknown. A new expert-finding algorithm is presented and an upper bound on the expected error rate of the expert is derived.

A dichotomic search algorithm for mining and learning in domain-specific logics

Ferr?, S. and King, R. D. (2004) A dichotomic search algorithm for mining and learning in domain-specific logics. Fundamenta Informaticae. IOS Press. To appear

Learning Euclidean Embeddings for Indexing and Classification

BoostMap is a recently proposed method for efficient approximate nearest neighbor retrieval in arbitrary non-Euclidean spaces with computationally expensive and possibly non-metric distance measures. Database and query objects are embedded into a Euclidean space, in which similarities can be rapidly measured using a weighted Manhattan distance. The key idea is formulating embedding construction as a machine learning task, where AdaBoost is used to combine simple, 1D embeddings into a multidimensional embedding that preserves a large amount of the proximity structure of the original space. This paper demonstrates that, using the machine learning formulation of BoostMap, we can optimize embeddings for indexing and classification, in ways that are not possible with existing alternatives for constructive embeddings, and without additional costs in retrieval time. First, we show how to construct embeddings that are query-sensitive, in the sense that they yield a different distance measure for different queries, so as to improve nearest neighbor retrieval accuracy for each query. Second, we show how to optimize embeddings for nearest neighbor classification tasks, by tuning them to approximate a parameter space distance measure, instead of the original feature-based distance measure.

Learning a Family of Detectors

Object detection and recognition are important problems in computer vision. The challenges of these problems come from the presence of noise, background clutter, large within class variations of the object class and limited training data. In addition, the computational complexity in the recognition process is also a concern in practice. In this thesis, we propose one approach to handle the problem of detecting an object class that exhibits large within-class variations, and a second approach to speed up the classification processes. In the first approach, we show that foreground-background classification (detection) and within-class classification of the foreground class (pose estimation) can be jointly solved with using a multiplicative form of two kernel functions. One kernel measures similarity for foreground-background classification. The other kernel accounts for latent factors that control within-class variation and implicitly enables feature sharing among foreground training samples. For applications where explicit parameterization of the within-class states is unavailable, a nonparametric formulation of the kernel can be constructed with a proper foreground distance/similarity measure. Detector training is accomplished via standard Support Vector Machine learning. The resulting detectors are tuned to specific variations in the foreground class. They also serve to evaluate hypotheses of the foreground state. When the image masks for foreground objects are provided in training, the detectors can also produce object segmentation. Methods for generating a representative sample set of detectors are proposed that can enable efficient detection and tracking. In addition, because individual detectors verify hypotheses of foreground state, they can also be incorporated in a tracking-by-detection frame work to recover foreground state in image sequences. To run the detectors efficiently at the online stage, an input-sensitive speedup strategy is proposed to select the most relevant detectors quickly. The proposed approach is tested on data sets of human hands, vehicles and human faces. On all data sets, the proposed approach achieves improved detection accuracy over the best competing approaches. In the second part of the thesis, we formulate a filter-and-refine scheme to speed up recognition processes. The binary outputs of the weak classifiers in a boosted detector are used to identify a small number of candidate foreground state hypotheses quickly via Hamming distance or weighted Hamming distance. The approach is evaluated in three applications: face recognition on the face recognition grand challenge version 2 data set, hand shape detection and parameter estimation on a hand data set, and vehicle detection and estimation of the view angle on a multi-pose vehicle data set. On all data sets, our approach is at least five times faster than simply evaluating all foreground state hypotheses with virtually no loss in classification accuracy.

Learning Embeddings for Indexing, Retrieval, and Classification, with Applications to Object and Shape Recognition in Image Databases

Nearest neighbor retrieval is the task of identifying, given a database of objects and a query object, the objects in the database that are the most similar to the query. Retrieving nearest neighbors is a necessary component of many practical applications, in fields as diverse as computer vision, pattern recognition, multimedia databases, bioinformatics, and computer networks. At the same time, finding nearest neighbors accurately and efficiently can be challenging, especially when the database contains a large number of objects, and when the underlying distance measure is computationally expensive. This thesis proposes new methods for improving the efficiency and accuracy of nearest neighbor retrieval and classification in spaces with computationally expensive distance measures. The proposed methods are domain-independent, and can be applied in arbitrary spaces, including non-Euclidean and non-metric spaces. In this thesis particular emphasis is given to computer vision applications related to object and shape recognition, where expensive non-Euclidean distance measures are often needed to achieve high accuracy. The first contribution of this thesis is the BoostMap algorithm for embedding arbitrary spaces into a vector space with a computationally efficient distance measure. Using this approach, an approximate set of nearest neighbors can be retrieved efficiently - often orders of magnitude faster than retrieval using the exact distance measure in the original space. The BoostMap algorithm has two key distinguishing features with respect to existing embedding methods. First, embedding construction explicitly maximizes the amount of nearest neighbor information preserved by the embedding. Second, embedding construction is treated as a machine learning problem, in contrast to existing methods that are based on geometric considerations. The second contribution is a method for constructing query-sensitive distance measures for the purposes of nearest neighbor retrieval and classification. In high-dimensional spaces, query-sensitive distance measures allow for automatic selection of the dimensions that are the most informative for each specific query object. It is shown theoretically and experimentally that query-sensitivity increases the modeling power of embeddings, allowing embeddings to capture a larger amount of the nearest neighbor structure of the original space. The third contribution is a method for speeding up nearest neighbor classification by combining multiple embedding-based nearest neighbor classifiers in a cascade. In a cascade, computationally efficient classifiers are used to quickly classify easy cases, and classifiers that are more computationally expensive and also more accurate are only applied to objects that are harder to classify. An interesting property of the proposed cascade method is that, under certain conditions, classification time actually decreases as the size of the database increases, a behavior that is in stark contrast to the behavior of typical nearest neighbor classification systems. The proposed methods are evaluated experimentally in several different applications: hand shape recognition, off-line character recognition, online character recognition, and efficient retrieval of time series. In all datasets, the proposed methods lead to significant improvements in accuracy and efficiency compared to existing state-of-the-art methods. In some datasets, the general-purpose methods introduced in this thesis even outperform domain-specific methods that have been custom-designed for such datasets.

A Neural Network Architecture for Autonomous Learning, Recognition, and Prediction in a Nonstationary World

In a constantly changing world, humans are adapted to alternate routinely between attending to familiar objects and testing hypotheses about novel ones. We can rapidly learn to recognize and narne novel objects without unselectively disrupting our memories of familiar ones. We can notice fine details that differentiate nearly identical objects and generalize across broad classes of dissimilar objects. This chapter describes a class of self-organizing neural network architectures--called ARTMAP-- that are capable of fast, yet stable, on-line recognition learning, hypothesis testing, and naming in response to an arbitrary stream of input patterns (Carpenter, Grossberg, Markuzon, Reynolds, and Rosen, 1992; Carpenter, Grossberg, and Reynolds, 1991). The intrinsic stability of ARTMAP allows the system to learn incrementally for an unlimited period of time. System stability properties can be traced to the structure of its learned memories, which encode clusters of attended features into its recognition categories, rather than slow averages of category inputs. The level of detail in the learned attentional focus is determined moment-by-moment, depending on predictive success: an error due to over-generalization automatically focuses attention on additional input details enough of which are learned in a new recognition category so that the predictive error will not be repeated. An ARTMAP system creates an evolving map between a variable number of learned categories that compress one feature space (e.g., visual features) to learned categories of another feature space (e.g., auditory features). Input vectors can be either binary or analog. Computational properties of the networks enable them to perform significantly better in benchmark studies than alternative machine learning, genetic algorithm, or neural network models. Some of the critical problems that challenge and constrain any such autonomous learning system will next be illustrated. Design principles that work together to solve these problems are then outlined. These principles are realized in the ARTMAP architecture, which is specified as an algorithm. Finally, ARTMAP dynamics are illustrated by means of a series of benchmark simulations.

Fast Learning VIEWNET Architectures for Recognizing 3-D Objects from Multiple 2-D Views

The recognition of 3-D objects from sequences of their 2-D views is modeled by a family of self-organizing neural architectures, called VIEWNET, that use View Information Encoded With NETworks. VIEWNET incorporates a preprocessor that generates a compressed but 2-D invariant representation of an image, a supervised incremental learning system that classifies the preprocessed representations into 2-D view categories whose outputs arc combined into 3-D invariant object categories, and a working memory that makes a 3-D object prediction by accumulating evidence from 3-D object category nodes as multiple 2-D views are experienced. The simplest VIEWNET achieves high recognition scores without the need to explicitly code the temporal order of 2-D views in working memory. Working memories are also discussed that save memory resources by implicitly coding temporal order in terms of the relative activity of 2-D view category nodes, rather than as explicit 2-D view transitions. Variants of the VIEWNET architecture may also be used for scene understanding by using a preprocessor and classifier that can determine both What objects are in a scene and Where they are located. The present VIEWNET preprocessor includes the CORT-X 2 filter, which discounts the illuminant, regularizes and completes figural boundaries, and suppresses image noise. This boundary segmentation is rendered invariant under 2-D translation, rotation, and dilation by use of a log-polar transform. The invariant spectra undergo Gaussian coarse coding to further reduce noise and 3-D foreshortening effects, and to increase generalization. These compressed codes are input into the classifier, a supervised learning system based on the fuzzy ARTMAP algorithm. Fuzzy ARTMAP learns 2-D view categories that are invariant under 2-D image translation, rotation, and dilation as well as 3-D image transformations that do not cause a predictive error. Evidence from sequence of 2-D view categories converges at 3-D object nodes that generate a response invariant under changes of 2-D view. These 3-D object nodes input to a working memory that accumulates evidence over time to improve object recognition. ln the simplest working memory, each occurrence (nonoccurrence) of a 2-D view category increases (decreases) the corresponding node's activity in working memory. The maximally active node is used to predict the 3-D object. Recognition is studied with noisy and clean image using slow and fast learning. Slow learning at the fuzzy ARTMAP map field is adapted to learn the conditional probability of the 3-D object given the selected 2-D view category. VIEWNET is demonstrated on an MIT Lincoln Laboratory database of l28x128 2-D views of aircraft with and without additive noise. A recognition rate of up to 90% is achieved with one 2-D view and of up to 98.5% correct with three 2-D views. The properties of 2-D view and 3-D object category nodes are compared with those of cells in monkey inferotemporal cortex.

Communications inspired linear discriminant analysis

We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label. By harnessing a recent theoretical result on the gradient of mutual information, the above optimization problem can be solved directly using gradient descent, without requiring simplification of the objective function. Theoretical analysis and empirical comparison are made between the proposed method and two closely related methods, and comparisons are also made with a method in which Rényi entropy is used to define the mutual information (in this case the gradient may be computed simply, under a special parameter setting). Relative to these alternative approaches, the proposed method achieves promising results on real datasets. Copyright 2012 by the author(s)/owner(s).

A heterosynaptic learning rule for neural networks

In this article we intoduce a novel stochastic Hebb-like learning rule for neural networks that is neurobiologically motivated. This learning rule combines features of unsupervised (Hebbian) and supervised (reinforcement) learning and is stochastic with respect to the selection of the time points when a synapse is modified. Moreover, the learning rule does not only affect the synapse between pre- and postsynaptic neuron, which is called homosynaptic plasticity, but effects also further remote synapses of the pre-and postsynaptic neuron. This more complex form of synaptic plasticity has recently come under investigations in neurobiology and is called heterosynaptic plasticity. We demonstrate that this learning rule is useful in training neural networks by learning parity functions including the exclusive-or (XOR) mapping in a multilayer feed-forward network. We find, that our stochastic learning rule works well, even in the presence of noise. Importantly, the mean leaxning time increases with the number of patterns to be learned polynomially, indicating efficient learning.

Incremental learning from stream data

Recent years have witnessed an incredibly increasing interest in the topic of incremental learning. Unlike conventional machine learning situations, data flow targeted by incremental learning becomes available continuously over time. Accordingly, it is desirable to be able to abandon the traditional assumption of the availability of representative training data during the training period to develop decision boundaries. Under scenarios of continuous data flow, the challenge is how to transform the vast amount of stream raw data into information and knowledge representation, and accumulate experience over time to support future decision-making process. In this paper, we propose a general adaptive incremental learning framework named ADAIN that is capable of learning from continuous raw data, accumulating experience over time, and using such knowledge to improve future learning and prediction performance. Detailed system level architecture and design strategies are presented in this paper. Simulation results over several real-world data sets are used to validate the effectiveness of this method.