The sample complexity of pattern classification with neural networks: the size of the weights is more important than the size of the network

Sample complexity results from computational learning theory, when applied to neural network learning for pattern classification problems, suggest that for good generalization performance the number of training examples should grow at least linearly with the number of adjustable parameters in the network. Results in this paper show that if a large neural network is used for a pattern classification problem and the learning algorithm finds a network with small weights that has small squared error on the training patterns, then the generalization performance depends on the size of the weights rather than the number of weights. For example, consider a two-layer feedforward network of sigmoid units, in which the sum of the magnitudes of the weights associated with each unit is bounded by A and the input dimension is n. We show that the misclassification probability is no more than a certain error estimate (that is related to squared error on the training set) plus A3 √((log n)/m) (ignoring log A and log m factors), where m is the number of training patterns. This may explain the generalization performance of neural networks, particularly when the number of training examples is considerably smaller than the number of weights. It also supports heuristics (such as weight decay and early stopping) that attempt to keep the weights small during training. The proof techniques appear to be useful for the analysis of other pattern classifiers: when the input domain is a totally bounded metric space, we use the same approach to give upper bounds on misclassification probability for classifiers with decision boundaries that are far from the training examples.

Navigating, recognizing and describing urban spaces with vision and lasers

In this paper we describe a body of work aimed at extending the reach of mobile navigation and mapping. We describe how running topological and metric mapping and pose estimation processes concurrently, using vision and laser ranging, has produced a full six-degree-of-freedom outdoor navigation system. It is capable of producing intricate three-dimensional maps over many kilometers and in real time. We consider issues concerning the intrinsic quality of the built maps and describe our progress towards adding semantic labels to maps via scene de-construction and labeling. We show how our choices of representation, inference methods and use of both topological and metric techniques naturally allow us to fuse maps built from multiple sessions with no need for manual frame alignment or data association.

The RatSLAM project : robot spatial navigation

Rats are superior to the most advanced robots when it comes to creating and exploiting spatial representations. A wild rat can have a foraging range of hundreds of meters, possibly kilometers, and yet the rodent can unerringly return to its home after each foraging mission, and return to profitable foraging locations at a later date (Davis, et al., 1948). The rat runs through undergrowth and pipes with few distal landmarks, along paths where the visual, textural, and olfactory appearance constantly change (Hardy and Taylor, 1980; Recht, 1988). Despite these challenges the rat builds, maintains, and exploits internal representations of large areas of the real world throughout its two to three year lifetime. While algorithms exist that allow robots to build maps, the questions of how to maintain those maps and how to handle change in appearance over time remain open. The robotic approach to map building has been dominated by algorithms that optimise the geometry of the map based on measurements of distances to features. In a robotic approach, measurements of distance to features are taken with range-measuring devices such as laser range finders or ultrasound sensors, and in some cases estimates of depth from visual information. The features are incorporated into the map based on previous readings of other features in view and estimates of self-motion. The algorithms explicitly model the uncertainty in measurements of range and the measurement of self-motion, and use probability theory to find optimal solutions for the geometric configuration of the map features (Dissanayake, et al., 2001; Thrun and Leonard, 2008). Some of the results from the application of these algorithms have been impressive, ranging from three-dimensional maps of large urban strucutures (Thrun and Montemerlo, 2006) to natural environments (Montemerlo, et al., 2003).

Lingodroids : studies in spatial cognition and language

The Lingodroids are a pair of mobile robots that evolve a language for places and relationships between places (based on distance and direction). Each robot in these studies has its own understanding of the layout of the world, based on its unique experiences and exploration of the environment. Despite having different internal representations of the world, the robots are able to develop a common lexicon for places, and then use simple sentences to explain and understand relationships between places even places that they could not physically experience, such as areas behind closed doors. By learning the language, the robots are able to develop representations for places that are inaccessible to them, and later, when the doors are opened, use those representations to perform goal-directed behavior.

Graph rigidity for near-coplanar structure from motion

Recent algorithms for monocular motion capture (MoCap) estimate weak-perspective camera matrices between images using a small subset of approximately-rigid points on the human body (i.e. the torso and hip). A problem with this approach, however, is that these points are often close to coplanar, causing canonical linear factorisation algorithms for rigid structure from motion (SFM) to become extremely sensitive to noise. In this paper, we propose an alternative solution to weak-perspective SFM based on a convex relaxation of graph rigidity. We demonstrate the success of our algorithm on both synthetic and real world data, allowing for much improved solutions to marker less MoCap problems on human bodies. Finally, we propose an approach to solve the two-fold ambiguity over bone direction using a k-nearest neighbour kernel density estimator.

Using incomplete online metric maps for topological exploration with the Gap Navigation Tree

This paper presents a general, global approach to the problem of robot exploration, utilizing a topological data structure to guide an underlying Simultaneous Localization and Mapping (SLAM) process. A Gap Navigation Tree (GNT) is used to motivate global target selection and occluded regions of the environment (called “gaps”) are tracked probabilistically. The process of map construction and the motion of the vehicle alters both the shape and location of these regions. The use of online mapping is shown to reduce the difficulties in implementing the GNT.

Overview of INEX 2008 Link the Wiki Track

The Link the Wiki track at INEX 2008 offered two tasks, file-to-file link discovery and anchor-to-BEP link discovery. In the former 6600 topics were used and in the latter 50 were used. Manual assessment of the anchor-to-BEP runs was performed using a tool developed for the purpose. Runs were evaluated using standard precision & recall measures such as MAP and precision / recall graphs. 10 groups participated and the approaches they took are discussed. Final evaluation results for all runs are presented.

Planning most-likely paths from overhead imagery

This paper is about planning paths from overhead imagery, the novelty of which is taking explicit account of uncertainty in terrain classification and spatial variation in terrain cost. The image is first classified using a multi-class Gaussian Process Classifier which provides probabilities of class membership at each location in the image. The probability of class membership at a particular grid location is then combined with a terrain cost evaluated at that location using a spatial Gaussian process. The resulting cost function is, in turn, passed to a planner. This allows both the uncertainty in terrain classification and spatial variations in terrain costs to be incorporated into the planned path. Because the cost of traversing a grid cell is now a probability density rather than a single scalar value, we can produce not only the most-likely shortest path between points on the map, but also sample from the cost map to produce a distribution of paths between the points. Results are shown in the form of planned paths over aerial maps, these paths are shown to vary in response to local variations in terrain cost.

Discovering the best feature extraction and selection algorithms for spontaneous facial expression recognition

Feature extraction and selection are critical processes in developing facial expression recognition (FER) systems. While many algorithms have been proposed for these processes, direct comparison between texture, geometry and their fusion, as well as between multiple selection algorithms has not been found for spontaneous FER. This paper addresses this issue by proposing a unified framework for a comparative study on the widely used texture (LBP, Gabor and SIFT) and geometric (FAP) features, using Adaboost, mRMR and SVM feature selection algorithms. Our experiments on the Feedtum and NVIE databases demonstrate the benefits of fusing geometric and texture features, where SIFT+FAP shows the best performance, while mRMR outperforms Adaboost and SVM. In terms of computational time, LBP and Gabor perform better than SIFT. The optimal combination of SIFT+FAP+mRMR also exhibits a state-of-the-art performance.

Feature-domain super-resolution framework for gabor-based face and iris recognition

The low resolution of images has been one of the major limitations in recognising humans from a distance using their biometric traits, such as face and iris. Superresolution has been employed to improve the resolution and the recognition performance simultaneously, however the majority of techniques employed operate in the pixel domain, such that the biometric feature vectors are extracted from a super-resolved input image. Feature-domain superresolution has been proposed for face and iris, and is shown to further improve recognition performance by capitalising on direct super-resolving the features which are used for recognition. However, current feature-domain superresolution approaches are limited to simple linear features such as Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA), which are not the most discriminant features for biometrics. Gabor-based features have been shown to be one of the most discriminant features for biometrics including face and iris. This paper proposes a framework to conduct super-resolution in the non-linear Gabor feature domain to further improve the recognition performance of biometric systems. Experiments have confirmed the validity of the proposed approach, demonstrating superior performance to existing linear approaches for both face and iris biometrics.

A two week persistent navigation and mapping experiment using RatSLAM : insights and current developments

One of the major challenges in achieving long term robot autonomy is the need for a SLAM algorithm that can perform SLAM over the operational lifetime of the robot, preferably without human intervention or supervision. In this paper we present insights gained from a two week long persistent SLAM experiment, in which a Pioneer robot performed mock deliveries in a busy office environment. We used the biologically inspired visual SLAM system, RatSLAM, combined with a hybrid control architecture that selected between exploring the environment, performing deliveries, and recharging. The robot performed more than a thousand successful deliveries with only one failure (from which it recovered), travelled more than 40 km over 37 hours of active operation, and recharged autonomously 23 times. We discuss several issues arising from the success (and limitations) of this experiment and two subsequent avenues of work.