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Deterministic Annealing for Clustering, Compression, Classification, Regression, and Related Optimization Problems
 Proceedings of the IEEE
, 1998
"... this paper. Let us place it within the neural network perspective, and particularly that of learning. The area of neural networks has greatly benefited from its unique position at the crossroads of several diverse scientific and engineering disciplines including statistics and probability theory, ph ..."
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Cited by 248 (11 self)
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this paper. Let us place it within the neural network perspective, and particularly that of learning. The area of neural networks has greatly benefited from its unique position at the crossroads of several diverse scientific and engineering disciplines including statistics and probability theory, physics, biology, control and signal processing, information theory, complexity theory, and psychology (see [45]). Neural networks have provided a fertile soil for the infusion (and occasionally confusion) of ideas, as well as a meeting ground for comparing viewpoints, sharing tools, and renovating approaches. It is within the illdefined boundaries of the field of neural networks that researchers in traditionally distant fields have come to the realization that they have been attacking fundamentally similar optimization problems.
An Automatic Registration Method for Frameless Stereotaxy, Image Guided Surgery, and Enhanced Reality Visualization
, 1996
"... There is a need for frameless guidance systems to help surgeons plan the exact location for incisions, to define the margins of tumors and to precisely identify locations of neighboring critical structures. We have developed an automatic technique for registering clinical data, such as segmented M ..."
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Cited by 106 (12 self)
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There is a need for frameless guidance systems to help surgeons plan the exact location for incisions, to define the margins of tumors and to precisely identify locations of neighboring critical structures. We have developed an automatic technique for registering clinical data, such as segmented MRI or CT reconstructions, with any view of the patient on the operating table, using a series of registration algorithms, which we demonstrate on the specific example of neurosurgery. The method enables a visual mix of live video of the patient with the segmented 3D MRI or CT model, supporting enhanced reality techniques for planning and guiding neurosurgical procedures, and to interactively view extracranial or intracranial structures nonintrusively. Extensions of the method include image guided biopsies, focused therapeutic procedures and clinical studies involving change detection over time sequences of images. 1 Artificial Intelligence Laboratory, Massachusetts Institute of Tech...
A Genetic Local Search Algorithm for Solving Symmetric and Asymmetric Traveling Salesman Problems
 In Proceedings of the 1996 IEEE International Conference on Evolutionary Computation
, 1996
"... The combination of local search heuristics and genetic algorithms is a promising approach for finding nearoptimum solutions to the traveling salesman problem (TSP). In this paper, an approach is presented in which local search techniques are used to find local optima in a given TSP search space, and ..."
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Cited by 77 (12 self)
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The combination of local search heuristics and genetic algorithms is a promising approach for finding nearoptimum solutions to the traveling salesman problem (TSP). In this paper, an approach is presented in which local search techniques are used to find local optima in a given TSP search space, and genetic algorithms are used to search the space of local optima in order to find the global optimum. New genetic operators for realizing the proposed approach are described, and the quality and efficiency of the solutions obtained for a set of symmetric and asymmetric TSP instances are discussed. The results indicate that it is possible to arrive at high quality solutions in reasonable time. I. Introduction In the Traveling Salesman Problem (TSP) [18], [27], a number of cities with distances between them is given and the task is to find the minimumlength closed tour that visits each city once and returns to its starting point. A symmetric TSP (STSP) is one where the distance between any...
Using Generative Models for Handwritten Digit Recognition
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1996
"... We describe a method of recognizing handwritten digits by fitting generative models that are built from deformable Bsplines with Gaussian "ink generators" spaced along the length of the spline. The splines are adjusted using a novel elastic matching procedure based on the Expectation Maximization ( ..."
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Cited by 69 (8 self)
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We describe a method of recognizing handwritten digits by fitting generative models that are built from deformable Bsplines with Gaussian "ink generators" spaced along the length of the spline. The splines are adjusted using a novel elastic matching procedure based on the Expectation Maximization (EM) algorithm that maximizes the likelihood of the model generating the data. This approach has many advantages. (1) After identifying the model most likely to have generated the data, the system not only produces a classification of the digit but also a rich description of the instantiation parameters which can yield information such as the writing style. (2) During the process of explaining the image, generative models can perform recognition driven segmentation. (3) The method involves a relatively small number of parameters and hence training is relatively easy and fast. (4) Unlike many other recognition schemes it does not rely on some form of prenormalization of input images, but can ...
Adaptive elastic models for handprinted character recognition
 ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS
, 1992
"... Handprinted digits can be modeled as splines that are governed by about 8 control points. For each known digit, the control points have preferred "home" locations, and deformations of the digit are generated by moving the control points away from their home locations. Images of digits can be produc ..."
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Cited by 58 (8 self)
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Handprinted digits can be modeled as splines that are governed by about 8 control points. For each known digit, the control points have preferred "home" locations, and deformations of the digit are generated by moving the control points away from their home locations. Images of digits can be produced by placing Gaussian ink generators uniformly along the spline. Real images can be recognized by nding the digit model most likely to have generated the data. For each digit model we use an elastic matching algorithm to minimize an energy function that includes both the deformation energy of the digit model and the log probability that the model would generate the inked pixels in the image. The model with the lowest total energy wins. If a uniform noise process is included in the model of image generation, some of the inked pixels can be rejected as noise as a digit model is tting a poorly segmented image. The digit models learn by modifying the home locations of the control points.
Memetic Algorithms for Combinatorial Optimization Problems: Fitness Landscapes and Effective Search Strategies
, 2001
"... ..."
GTM: A Principled Alternative to the SelfOrganizing Map
 In Advances in Neural Information Processing Systems
, 1997
"... The SelfOrganizing Map (SOM) algorithm has been extensively studied and has been applied with considerable success to a wide variety of problems. However, the algorithm is derived from heuristic ideas and this leads to a number of significant limitations. In this paper, we consider the problem of m ..."
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Cited by 46 (1 self)
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The SelfOrganizing Map (SOM) algorithm has been extensively studied and has been applied with considerable success to a wide variety of problems. However, the algorithm is derived from heuristic ideas and this leads to a number of significant limitations. In this paper, we consider the problem of modelling the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. We introduce a novel form of latent variable model, which we call the GTM algorithm (for Generative Topographic Map), which allows general nonlinear transformations from latent space to data space, and which is trained using the EM (expectationmaximization) algorithm. Our approach overcomes the limitations of the SOM, while introducing no significant disadvantages. We demonstrate the performance of the GTM algorithm on simulated data from flow diagnostics for a multiphase oil pipeline. GTM: A Principled Alternative to the SelfOrganizing Map 2 1 Introduc...
The concaveconvex procedure (CCCP)
, 2003
"... The ConcaveConvex procedure (CCCP) is a way to construct discrete time iterative dynamical systems which are guaranteed to monotonically decrease global optimization/energy functions. This procedure can be applied to almost any optimization problem and many existing algorithms can be interpreted ..."
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Cited by 46 (5 self)
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The ConcaveConvex procedure (CCCP) is a way to construct discrete time iterative dynamical systems which are guaranteed to monotonically decrease global optimization/energy functions. This procedure can be applied to almost any optimization problem and many existing algorithms can be interpreted in terms of it. In particular, we prove that all EM algorithms and classes of Legendre minimization and variational bounding algorithms can be reexpressed in terms of CCCP. We show that many existing neural network and mean field theory algorithms are also examples of CCCP. The Generalized Iterative Scaling (GIS) algorithm and Sinkhorn’s algorithm can also be expressed as CCCP by changing variables. CCCP can be used both as a new way to understand, and prove convergence of, existing optimization algorithms and as a procedure for generating new algorithms.
Latent Variable Models for Neural Data Analysis
, 1999
"... The brain is perhaps the most complex system to have ever been subjected to rigorous scientific investigation. The scale is staggering: over 1011 neurons, each making an average of 10 3 synapses, with computation occurring on scales ranging from a single dendritic spine, to an entire cortical area. ..."
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Cited by 42 (5 self)
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The brain is perhaps the most complex system to have ever been subjected to rigorous scientific investigation. The scale is staggering: over 1011 neurons, each making an average of 10 3 synapses, with computation occurring on scales ranging from a single dendritic spine, to an entire cortical area. Slowly, we are beginning to acquire experimental tools that can gather the massive amounts of data needed to characterize this system. However, to understand and interpret these data will also require substantial strides in inferential and statistical techniques. This dissertation attempts to meet this need, extending and applying the modern tools of latent variable modeling to problems in neural data analysis. It is divided