Graph matching with a dual-step EM algorithm

This paper describes a new approach to matching geometric structure in 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying point-correspondence matches. Unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the EM algorithm. According to our EM framework, the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters. These gating probabilities measure the consistency of the matched neighborhoods in the graphs. The recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log-likelihood function. In this way, the two processes bootstrap one another. This provides a means of rejecting structural outliers. We evaluate the technique on two real-world problems. The first involves the matching of different perspective views of 3.5-inch floppy discs. The second example is furnished by the matching of a digital map against aerial images that are subject to severe barrel distortion due to a line-scan sampling process. We complement these experiments with a sensitivity study based on synthetic data

Gaussian processes with linear operator inequality constraints

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence engineering systems, where this kind of information is often made available from phenomenological knowledge. We consider a GP $f$ over functions on $\mathcal{X} \subset \mathbb{R}^{n}$ taking values in $\mathbb{R}$, where the process $\mathcal{L}f$ is still Gaussian when $\mathcal{L}$ is a linear operator. Our goal is to model $f$ under the constraint that realizations of $\mathcal{L}f$ are confined to a convex set of functions. In particular, we require that $a \leq \mathcal{L}f \leq b$, given two functions $a$ and $b$ where $a < b$ pointwise. This formulation provides a consistent way of encoding multiple linear constraints, such as shape-constraints based on e.g. boundedness, monotonicity or convexity. We adopt the approach of using a sufficiently dense set of virtual observation locations where the constraint is required to hold, and derive the exact posterior for a conjugate likelihood. The results needed for stable numerical implementation are derived, together with an efficient sampling scheme for estimating the posterior process.Comment: Published in JMLR: http://jmlr.org/papers/volume20/19-065/19-065.pd

Hybridation of Bayesian networks and evolutionary algorithms for multi-objective optimization in an integrated product design and project management context

A better integration of preliminary product design and project management processes at early steps of system design is nowadays a key industrial issue. Therefore, the aim is to make firms evolve from classical sequential approach (first product design the project design and management) to new integrated approaches. In this paper, a model for integrated product/project optimization is first proposed which allows taking into account simultaneously decisions coming from the product and project managers. However, the resulting model has an important underlying complexity, and a multi-objective optimization technique is required to provide managers with appropriate scenarios in a reasonable amount of time. The proposed approach is based on an original evolutionary algorithm called evolutionary algorithm oriented by knowledge (EAOK). This algorithm is based on the interaction between an adapted evolutionary algorithm and a model of knowledge (MoK) used for giving relevant orientations during the search process. The evolutionary operators of the EA are modified in order to take into account these orientations. The MoK is based on the Bayesian Network formalism and is built both from expert knowledge and from individuals generated by the EA. A learning process permits to update probabilities of the BN from a set of selected individuals. At each cycle of the EA, probabilities contained into the MoK are used to give some bias to the new evolutionary operators. This method ensures both a faster and effective optimization, but it also provides the decision maker with a graphic and interactive model of knowledge linked to the studied project. An experimental platform has been developed to experiment the algorithm and a large campaign of tests permits to compare different strategies as well as the benefits of this novel approach in comparison with a classical EA

Edge Potential Functions (EPF) and Genetic Algorithms (GA) for Edge-Based Matching of Visual Objects

Edges are known to be a semantically rich representation of the contents of a digital image. Nevertheless, their use in practical applications is sometimes limited by computation and complexity constraints. In this paper, a new approach is presented that addresses the problem of matching visual objects in digital images by combining the concept of Edge Potential Functions (EPF) with a powerful matching tool based on Genetic Algorithms (GA). EPFs can be easily calculated starting from an edge map and provide a kind of attractive pattern for a matching contour, which is conveniently exploited by GAs. Several tests were performed in the framework of different image matching applications. The results achieved clearly outline the potential of the proposed method as compared to state of the art methodologies. (c) 2007 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works

Structural graph matching using the EM algorithm and singular value decomposition

This paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions: 1) commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximum-likelihood estimation using the apparatus of the EM algorithm; and 2) we cast the recovery of correspondence matches between the graph nodes in a matrix framework. This allows one to efficiently recover correspondence matches using the singular value decomposition. We experiment with the method on both real-world and synthetic data. Here, we demonstrate that the method offers comparable performance to more computationally demanding method

MODELLING OF STRESS GRADIENT EFFECT ON FATIGUE LIFE USING WEIBULL BASED DISTRIBUTION FUNCTION

In the present paper, a new approach is developed in order to take into account the stress gradient effect on fatigue life of structural components. The proposed approach is based on the weakest link concept in which the shape coefficient of the Weibull distribution becomes a function of a local damage parameter. The function simulates the experimentally observed relationship between the shape of the fatigue life distribution and the stress level. Such an approach allows one to calculate the global probability distribution of the fatigue life for notched structural components in a wide range of fatigue life regime: 104-107 cycles typically. For comparison purposes, the approach is applied to calculate the number of cycles to crack initiation of structural elements under three probability levels: 5%, 63% and 95%. The calculated lifetimes are compared with the lifetimes obtained from experiments performed on notched cruciform specimens and notched round specimens subjected to constant amplitude loading

Bayesian graph edit distance

This paper describes a novel framework for comparing and matching corrupted relational graphs. The paper develops the idea of edit-distance originally introduced for graph-matching by Sanfeliu and Fu [1]. We show how the Levenshtein distance can be used to model the probability distribution for structural errors in the graph-matching problem. This probability distribution is used to locate matches using MAP label updates. We compare the resulting graph-matching algorithm with that recently reported by Wilson and Hancock. The use of edit-distance offers an elegant alternative to the exhaustive compilation of label dictionaries. Moreover, the method is polynomial rather than exponential in its worst-case complexity. We support our approach with an experimental study on synthetic data and illustrate its effectiveness on an uncalibrated stereo correspondence problem. This demonstrates experimentally that the gain in efficiency is not at the expense of quality of match

Modeling of Phenomena and Dynamic Logic of Phenomena

Modeling of complex phenomena such as the mind presents tremendous computational complexity challenges. Modeling field theory (MFT) addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model (also, problem or theory) with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes more certain, then the evaluation criterion is adjusted dynamically to match that change to the model. This process is called the Dynamic Logic of Phenomena (DLP) for model construction and it mimics processes of the mind and natural evolution. This paper provides a formal description of DLP by specifying its syntax, semantics, and reasoning system. We also outline links between DLP and other logical approaches. Computational complexity issues that motivate this work are presented using an example of polynomial models