Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Machine Learning : A Probabilistic Perspective

On robust estimation of the location parameter

There is a special reason for reviewing this book at this time: it is the 50th edition of a compendium that is known and used frequently in most chemical and physical laboratories in many parts of the world. Surely, a publication that has been published for 56 years, withstanding the vagaries of science in this century, must have had something to offer. There is another reason: while the book is a standard fixture in most chemical and physical laboratories, including those in medical centers, it is not as frequently seen in the laboratories of physician's offices (those either in solo or group practice). I believe that the Handbook can be useful in those laboratories. One of the reasons, among others, is that the various basic items of information it offers may be helpful in new tests, either physical or chemical, which are continuously being published. The basic information may relate

Handbook of Chemistry and Physics

Information Theory and Reliable Communication

Real and Complex Analysis

We consider the problem of rotation averaging under the L 1 norm. This problem is related to the classic Fermat-Weber problem for finding the geometric median of a set of points in IRn. We apply the classical Weiszfeld algorithm to this problem, adapting it iteratively in tangent spaces of SO(3) to obtain a provably convergent algorithm for finding the L 1 mean. This results in an extremely simple and rapid averaging algorithm, without the need for line search. The choice of L 1 mean (also called geometric median) is motivated by its greater robustness compared with rotation averaging under the L 2 norm (the usual averaging process). We apply this problem to both single-rotation averaging (under which the algorithm provably finds the global L 1 optimum) and multiple rotation averaging (for which no such proof exists). The algorithm is demonstrated to give markedly improved results, compared with L 2 averaging. We achieve a median rotation error of 0.82 degrees on the 595 images of the Notre Dame image set.

http://users.cecs.anu.edu.au/~trumpf/pubs/Hartley_Aftab_Trumpf_CVPR2011.pdf

L1 rotation averaging using the Weiszfeld algorithm

This paper proposes a design methodology for non-linear state observers for invariant kinematic systems posed on finite dimensional connected Lie groups, and studies the associated fundamental system structure. The concept of synchrony of two dynamical systems is specialized to systems on Lie groups. For invariant systems this leads to a general factorization theorem of a nonlinear observer into a synchronous (internal model) term and an innovation term. The synchronous term is fully specified by the system model. We propose a design methodology for the innovation term based on gradient-like terms derived from invariant or non-invariant cost functions. The resulting nonlinear observers have strong (almost) global convergence properties and examples are used to demonstrate the relevance of the proposed approach.

http://users.cecs.anu.edu.au/~trumpf/pubs/LagTruMah_TAC2009.pdf

Gradient-Like Observers for Invariant Dynamics on a Lie Group

To establish an underwater communication system for a swarm of submersibles, we developed an optical communication transceiver, small in size, combining the IrDA physical layer with 3 Watt high power light emitting diodes, emitting light in the green and blue part of the visible spectrum. This paper presents experimental results in air and under water. Furthermore, we show how this digital communication link can be used for accurate distance measurements without any modications.

/pdf/visible-spectrum-optical-communication-and-distance-sensing-242pubkidb.pdf

Visible Spectrum Optical Communication and Distance Sensing for Underwater Applications

With the emergence of unmanned marine robots, underwater communication systems have received much attention in recent years. To successfully develop radio wave based communication solutions, it is essential to understand properties of electromagnetic wave transmission in seawater. These properties are determined by the frequency variation of the permittivity of seawater. Existing models for the permittivity of saline water are empirical ones that best fit experimental data. We propose a physically realistic model, similar to the one used in plasma physics, for the variation of the dielectric constant of water with varying frequencies and salinities. Our model is in excellent agreement with existing empirical fits for frequencies between 1 and 256 GHz. We use this model to study the propagation of electromagnetic waves in seawater. We explain that large propagation distances would be possible at MHz frequencies if the conductivity of seawater decreases at small field strengths due to the hydrogen bonding of water molecules. However, we were unable to experimentally verify any reduction in the conductivity of seawater

Frequency, Temperature and Salinity Variation of the Permittivity of Seawater

This paper proposes a design methodology for non-linear state observers for invariant kinematic systems posed on finite dimensional connected Lie groups, and studies the associated fundamental system structure. The concept of synchrony of two dynamical systems is specialised to systems on Lie groups. For invariant systems this leads to a general factorisation theorem of a nonlinear observer into a synchronous (internal model) term and an innovation term. The synchronous term is fully specified by the system model. We propose a design methodology for the innovation term based on gradient-like terms derived from invariant or non-invariant cost functions. The resulting nonlinear observers have strong (almost) global convergence properties and examples are used to demonstrate the relevance of the proposed approach.

Jochen Trumpf

Papers

L1 rotation averaging using the Weiszfeld algorithm

Gradient-Like Observers for Invariant Dynamics on a Lie Group

Visible Spectrum Optical Communication and Distance Sensing for Underwater Applications

Frequency, Temperature and Salinity Variation of the Permittivity of Seawater

Gradient-like observers for invariant dynamics on a Lie group