The EM algorithm is short for Expectation-Maximization algorithm. It is based on an iterative optimization of the centers and widths of the kernels. The aim is to optimize the likelihood that the given data points are generated by a mixture of Gaussians. The numbers next to the Gaussians give the relative importance (amplitude) of each component.
This a Bayesian ICA algorithm for the linear instantaneous mixing model with additive Gaussian noise [1]. The inference problem is solved by ML-II, i.e. the sources are found by integration over the source posterior and the noise covariance and mixing matrix are found by maximization of the marginal likelihood [1]. The sufficient statistics are estimated by either variational mean field theory with the linear response correction or by adaptive TAP mean field theory [2,3]. The mean field equations are solved by a belief propagation method [4] or sequential iteration. The computational complexity is N M^3, where N is the number of time samples and M the number of sources.
At the time of writing, and to an extent never seen before, there is an expectation that
almost any information or service that is available through communication systems in
the office or home will be available wherever the user happens to be. This is placing
incredible demands on wireless communications and has been the driver for the gen-
esis and deployment of three generations of cellular systems in the space of 20 years.
Once upon a time, cellular wireless networks provided two basic services: voice
telephony and low-rate text messaging. Users in the network were separated
by orthogonal multiple access schemes, and cells by generous frequency reuse
patterns [1]. Since then, the proliferation of wireless services, fierce competition,
andthe emergenceof new service classes such as wireless data and multimediahave
resulted in an ever increasing pressure on network operators to use resources in a
moreefficient manner.In the contextof wireless networks,two of the most common
resources are power and spectrum—and, due to regulations, these resources are
typically scarce. Hence, in contrast to wired networks, overprovisioning is not
feasible in wireless networks.
Today, electric power transmission systems should face many demanding chal-
lenges, which include balancing between reliability, economics, environmental,
and other social objectives to optimize the grid assets and satisfy the growing
electrical demand.
Moreover, the operational environment of transmission systems is becoming
increasingly rigorous due to continually evolving functions of interconnected
power networks from operation jurisdiction to control responsibly – coupled with
the rising demand and expectation for reliability.
I am presenting this novel book on advances and trends in power electronics and motor
drives to the professional community with the expectation that it will be given the same
wide and enthusiastic acceptance by practicing engineers, R&D professionals, univer-
sity professors, and even graduate students that my other books in this area have. Unlike
the traditional books available in the area of power electronics, this book has a unique
presentation format that makes it convenient for group presentations that use Microsoft’s
PowerPoint software. In fact, a disk is included that has a PowerPoint file on it that is
ready for presentation with the core figures. Presentations can also be organized using
just selected portions of the book
Pattern recognition has its origins in engineering, whereas machine learning grew
out of computer science. However, these activities can be viewed as two facets of
the same field, and together they have undergone substantial development over the
past ten years. In particular, Bayesian methods have grown from a specialist niche to
become mainstream, while graphical models have emerged as a general framework
for describing and applying probabilistic models. Also, the practical applicability of
Bayesian methods has been greatly enhanced through the development of a range of
approximate inference algorithms such as variational Bayes and expectation propa-
gation. Similarly, new models based on kernels have had significant impact on both
algorithms and applications.
