Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Co-Planar Stereotaxic Atlas of the Human Brain—3-Dimensional Proportional System: An Approach to Cerebral Imaging, J. Talairach, P. Tournoux. Georg Thieme Verlag, New York (1988), 122 pp., 130 figs. DM 268

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

We have witnessed great interest and a wealth of promise in content-based image retrieval as an emerging technology. While the last decade laid foundation to such promise, it also paved the way for a large number of new techniques and systems, got many new people involved, and triggered stronger association of weakly related fields. In this article, we survey almost 300 key theoretical and empirical contributions in the current decade related to image retrieval and automatic image annotation, and in the process discuss the spawning of related subfields. We also discuss significant challenges involved in the adaptation of existing image retrieval techniques to build systems that can be useful in the real world. In retrospect of what has been achieved so far, we also conjecture what the future may hold for image retrieval research.

/pdf/image-retrieval-ideas-influences-and-trends-of-the-new-age-51whw4w7su.pdf

Image retrieval: Ideas, influences, and trends of the new age

The rapid growth of the literature on neuroimaging in humans has led to major advances in our understanding of human brain function but has also made it increasingly difficult to aggregate and synthesize neuroimaging findings. Here we describe and validate an automated brain-mapping framework that uses text-mining, meta-analysis and machine-learning techniques to generate a large database of mappings between neural and cognitive states. We show that our approach can be used to automatically conduct large-scale, high-quality neuroimaging meta-analyses, address long-standing inferential problems in the neuroimaging literature and support accurate 'decoding' of broad cognitive states from brain activity in both entire studies and individual human subjects. Collectively, our results have validated a powerful and generative framework for synthesizing human neuroimaging data on an unprecedented scale.

/pdf/large-scale-automated-synthesis-of-human-functional-2mlxuighir.pdf

Large-scale automated synthesis of human functional neuroimaging data

Earlier work by Driscoll and Healy has produced an efficient algorithm for
computing the Fourier transform of band-limited functions on the 2-sphere. In this article we present
a reformulation and variation of the original algorithm which results in a greatly improved inverse
transform, and consequent improved convolution algorithm for such functions. All require at most
O(N log2
 N) operations where N is the number of sample points. We also address implementation
considerations and give heuristics for allowing reliable and computationally efficient floating point
implementations of slightly modified algorithms. These claims are supported by extensive numerical
experiments from our implementation in C on DEC, HP, SGI and Linux Pentium platforms. These
results indicate that variations of the algorithm are both reliable and efficient for a large range of
useful problem sizes. Performance appears to be architecture-dependent. The article concludes
with a brief discussion of a few potential applications.

/pdf/ffts-for-the-2-sphere-improvements-and-variations-4mm7r7moxd.pdf

FFTs for the 2-Sphere-Improvements and Variations

Many standard computer vision datasets exhibit biases due to a variety of sources including illumination condition, imaging system, and preference of dataset collectors. Biases like these can have downstream effects in the use of vision datasets in the construction of generalizable techniques, especially for the goal of the creation of a classification system capable of generalizing to unseen and novel datasets. In this work we propose Unbiased Metric Learning (UML), a metric learning approach, to achieve this goal. UML operates in the following two steps: (1) By varying hyper parameters, it learns a set of less biased candidate distance metrics on training examples from multiple biased datasets. The key idea is to learn a neighborhood for each example, which consists of not only examples of the same category from the same dataset, but those from other datasets. The learning framework is based on structural SVM. (2) We do model validation on a set of weakly-labeled web images retrieved by issuing class labels as keywords to search engine. The metric with best validation performance is selected. Although the web images sometimes have noisy labels, they often tend to be less biased, which makes them suitable for the validation set in our task. Cross-dataset image classification experiments are carried out. Results show significant performance improvement on four well-known computer vision datasets.

/pdf/unbiased-metric-learning-on-the-utilization-of-multiple-2y2f5nr389.pdf

Unbiased Metric Learning: On the Utilization of Multiple Datasets and Web Images for Softening Bias

We discuss an implementation of an efficient algorithm for the numerical computation of Fourier transforms of bandlimited functions defined on the rotation group SO(3). The implementation is freely available on the web. The algorithm described herein uses O(B
 4) operations to compute the Fourier coefficients of a function whose Fourier expansion uses only (the O(B
 3)) spherical harmonics of degree at most B. This compares very favorably with the direct O(B
 6) algorithm derived from a basic quadrature rule on O(B
 3) sample points. The efficient Fourier transform also makes possible the efficient calculation of convolution over SO(3) which has been used as the analytic engine for some new approaches to searching 3D databases (Funkhouser et al., ACM Trans. Graph. 83–105, [2003]; Kazhdan et al., Eurographics Symposium in Geometry Processing, pp. 167–175, [2003]). Our implementation is based on the “Separation of Variables” technique (see, e.g., Maslen and Rockmore, Proceedings of the DIMACS Workshop on Groups and Computation, pp. 183–237, [1997]). In conjunction with techniques developed for the efficient computation of orthogonal polynomial expansions (Driscoll et al., SIAM J. Comput. 26(4):1066–1099, [1997]), our fast SO(3) algorithm can be improved to give an algorithm of complexity O(B
 3log 2
 B), but at a cost in numerical reliability. Numerical and empirical results are presented establishing the empirical stability of the basic algorithm. Examples of applications are presented as well.

FFTs on the Rotation Group

We describe a computational technique for authenticating works of art, specifically paintings and drawings, from high-resolution digital scans of the original works. This approach builds a statistical model of an artist from the scans of a set of authenticated works against which new works then are compared. The statistical model consists of first- and higher-order wavelet statistics. We show preliminary results from our analysis of 13 drawings that at various times have been attributed to Pieter Bruegel the Elder; these results confirm expert authentications. We also apply these techniques to the problem of determining the number of artists that may have contributed to a painting attributed to Pietro Perugino and again achieve an analysis agreeing with expert opinion.

https://www.pnas.org/content/pnas/101/49/17006.full.pdf

A digital technique for art authentication

We like to think that constitutions are expressions of distinctly national values, speaking for “We the People.” This is especially true of constitutional preambles, which often recount distinct events from national history and speak to national values. This article challenges this popular view by demonstrating the global influences on constitutional preambles. It does so using a new set of tools in linguistic and textual analysis, applied to a database of most constitutional preambles written since 1789. Arguing that legal language can be analogized to memes or genetic material, we analyze “horizontal” transfer of language across countries and “vertical” transfers within a single country over time. We also examine the circumstances in which countries introduce new terms into preambles, showing that countries innovate when neighbors innovate, and that innovations come in global waves. We show that innovation in language is something like punctuated equilibrium within an ecosystem. For long periods of stasis, countries borrow from one another and restrict their language to a set of common terms and phrases. Then, at particular junctures (likely associated with global conflicts), the equilibrium becomes disrupted and a period of innovation ensues. This eventually generates the “new normal” in terms of the set of language that constitutional drafters use. The article provides an example of how text analysis can help us understand the ways in which legal texts are interrelated across space and time.

/pdf/we-the-peoples-the-global-origins-of-constitutional-1htxiyfhf6.pdf

Daniel N. Rockmore

Papers

FFTs for the 2-Sphere-Improvements and Variations

Unbiased Metric Learning: On the Utilization of Multiple Datasets and Web Images for Softening Bias

FFTs on the Rotation Group

A digital technique for art authentication

'We the Peoples': The Global Origins of Constitutional Preambles