Dimensionality reduction of image features using the canonical contextual correlation projection

A linear, discriminative, supervised technique for reducing feature vectors extracted from image data to a lower-dimensional representation is proposed. It is derived from classical linear discriminant analysis (LDA), extending this technique to cases where there is dependency between the output variables, i.e., the class labels, and not only between the input variables. (The latter can readily be dealt with in standard LDA.) The novel method is useful, for example, in supervised segmentation tasks in which high-dimensional feature vectors describe the local structure of the image.

The principal idea is that where standard LDA merely takes into account a single class label for every feature vector, the new technique incorporates class labels of its neighborhood in the analysis as well. In this way, the spatial class label configuration in the vicinity of every feature vector is accounted for, resulting in a technique suitable for, e.g. image data.

This extended LDA, that takes spatial label context into account, is derived from a formulation of standard LDA in terms of canonical correlation analysis. The novel technique is called the canonical contextual correlation projection (CCCP).

An additional drawback of LDA is that it cannot extract more features than the number of classes minus one. In the two-class case this means that only a reduction to one dimension is possible. Our contextual LDA approach can avoid such extreme deterioration of the classification space and retain more than one dimension.

The technique is exemplified on a pixel-based medical image segmentation problem in which it is shown that it may give significant improvement in segmentation accuracy.     

基于半监督典型相关分析的多视图维数约简

为了有效地在半监督多视图情景下进行维数约简,提出了使用非负低秩图进行标签传播的半监督典型相关分析方法。非负低秩图捕获的全局线性近邻可以利用直接邻居和间接可达邻居的信息维持全局簇结构,同时,低秩的性质可以保持图的压缩表示。当无标签样本通过标签传播算法获得估计的标签信息后,在每个视图上构建软标签矩阵和概率类内散度矩阵。然后,通过最大化不同视图同类样本间相关性的同时最小化每个视图低维特征空间类内变化来提升特征鉴别能力。实验表明所提方法比已有相关方法能够取得更好的识别性能且更鲁棒。     

Multi-view dimensionality reduction via canonical random correlation analysis

Canonical correlation analysis (CCA) is one of the most well-known methods to extract features from multi-view data and has attracted much attention in recent years. However, classical CCA is unsupervised and does not take discriminant information into account. In this paper, we add discriminant information into CCA by using random cross-view correlations between within-class samples and propose a new method for multi-view dimensionality reduction called canonical random correlation analysis (RCA). In RCA, two approaches for randomly generating cross-view correlation samples are developed on the basis of bootstrap technique. Furthermore, kernel RCA (KRCA) is proposed to extract nonlinear correlations between different views. Experiments on several multi-view data sets show the effectiveness of the proposed methods.     

Controller reduction by component cost analysis

Component cost analysis [1] is used to develop a method for controller reduction. The reduction of the controller is based upon the participation of the controller states in the value of a quadratic performance metric. The controller states which have the smallest contribution to the performance metric are truncated to produce the reduced controllers. An error index is defined to evaluate the reduced controller compared to the optimal LQG controller, and bounds on this index are derived. A numerical example is included to illustrate the procedure.     

Controller reduction: concepts and approaches

The problem of passing from a linear time-invariant high-order controller designed for a linear time-invariant plant (of presumably high order) to a low-order approximation of the controller is discussed. The approximation problem is often best posed as a frequency-weighted L_∞ approximation problem. Many different controller representations are possible, giving different performances of the various reduction algorithms     

A geometric approach to stochastic model reduction by canonical variables

The reduced-order representation of possibly nonstationary observations of Markovian processes with additive measurement noise is considered. A canonical variable model reduction scheme is derived in a geometric setting.     

Computing unique canonical covers for simple FDs via transitive reduction

Although there is a rich body of research on dependency theory, only few results concerning simple functional dependencies (FDs) have been published. In this paper, the following key results regarding simple FDs are shown. First, given an acyclic set F of simple FDs there exists exactly one canonical cover for F. Second, this uniquely determined canonical cover can be computed via transitive reduction. Third, it is shown how a uniquely determined canonical cover can be fixed in case of arbitrary simple FDs via transitive reduction.     

Controller reduction via stable factorization and balancing

A controller reduction procedure based on a representation of a controller as a matrix function defined using stable proper transfer functions and employing a balancing technique is studied in this paper. For a certain right coprime factorization of an LQG designed controller K(s) = N(s)D^-1(s), we approximate using a balancing technique the pair [D(s), N(s)]^T by a low-order pair [D₁(s), N₁(s)]^T defining a factorization of the reduced-order controller K ₁(s) = N₁(s)D₁ ^-1(s). We show that reducing the controller order in this way is motivated in a natural way, which leads to the expectation of both good stability properties and good accuracy of approximation of closed-loop behaviour. This is also demonstrated in some examples.     

Drawing planar graphs using the canonical ordering

We introduce a new method to optimize the required area, minimum angle, and number of bends of planar graph drawings on a grid. The main tool is a new type of ordering on the vertices and faces of triconnected planar graphs. Using this method linear-time-and-space algorithms can be designed for many graph-drawing problems. Our main results are as follows:

Every triconnected planar graphG admits a planar convex grid drawing with straight lines on a (2n?4)×(n?2) grid, wheren is the number of vertices.

Every triconnected planar graph with maximum degree 4 admits a planar orthogonal grid drawing on ann×n grid with at most [3n/2]+4 bends, and ifn>6, then every edge has at most two bends.

Every planar graph with maximum degree 3 admits a planar orthogonal grid drawing with at most [n/2]+1 bends on an [n/2]×[n/2] grid.

Every triconnected planar graphG admits a planar polyline grid drawing on a (2n?6)×(3n?9) grid with minimum angle larger than 2/d radians and at most 5n?15 bends, withd the maximum degree.

These results give in some cases considerable improvements over previous results, and give new bounds in other cases. Several other results, e.g., concerning visibility representations, are included.     

Reduced-complexity LQR design using canonical correlation analysis

Canonical correlation analysis is developed for the discrete infinite time LQR problem having an asymptotically stable plant. It is shown that the optimal control sequence belongs to the range space of the canonical vectors weighted by the canonical correlation coefficients. Using this analysis a reduced-complexity controller for the LQR problem is obtained. Furthermore, it is established that when this reduced-complexity controller is applied to the original plant, the corresponding closed loop system is asymptotically stable.     

Sliding mode control design using canonical homogeneous norm

The problem of sliding mode control design for a nonlinear plant is studied. The necessary and sufficient conditions of quadratic‐like stability (stabilizability) for a nonlinear homogeneous (control) system are obtained. Sufficient conditions of robust stability/stabilizability are deduced. The results are supported with academic examples of sliding mode control design.     

A note on characterizing canonical cuts using geometry

In this technical note we introduce a set of cuts for 0–1 integer programming with a strong geometrical flavor. These are the spherical and cylindrical inequalities. We show that the geometrical cuts are in one‐to‐one correspondence with the canonical cuts introduced by Balas and Jeroslow. Moreover, we show how the well‐known subtour elimination constraints for the Traveling Salesman Problem can be obtained via geometrical cuts. By presenting the subtour elimination constraints in this way, we give another easy and intuitive way to explain the validity of such inequalities. We show that the arguments used to derive the subtour elimination constraint as geometrical cut can be repeated to derive strong valid inequalities that are known for other combinatorial optimization problems.     

Numerical analysis of the reduction of linear systems into orthogonal canonical form

An efficient numerically stable computational algorithm for reduction of linear systems into orthogonal canonical form is described. The algorithm is based on QR decomposition with column pivoting. Exact error bounds and operation count for the algorithm are derived.     

Controller design and reduction of bullwhip for a model supply chain system using z-transform analysis

In this work, a discrete time series model of a supply chain system is derived using material balances and information flow. Transfer functions for each unit in the supply chain are obtained by z-transform. The entire chain can be modeled by combining these transfer functions into a close loop transfer function for the network. The model proves to be very useful in revealing the dynamics characteristic of the system. The system can be viewed as a linear discrete system with lead time and operating constraints. The stability of the system can be analyzed using the characteristic equation. Controllers are designed using frequency analysis. The bullwhip effect, i.e. magnification of amplitudes of demand perturbations from the tail to upstream levels of the supply chain, is a very important phenomenon for supply chain systems. We proved that intuitive operation of a supply chain system with demand forecasting will cause bullwhip. Moreover, lead time alone would not cause bullwhip. It does so only when accompanied by demand forecasting. Furthermore, we show that by implementing a proportional intergral or a cascade inventory position control and properly synthesizing the controller parameters, we can effectively suppress the bullwhip effect. Moreover, the cascade control structure is superior in meeting customer demand due to its better tracking of long term trends of customer demand.     

Controller order reduction with guaranteed performance via coprime factorization

In this paper the problems of the suboptimal H_∞ controller order reduction and strictly positive real (SPR) controller order reduction via coprime factorization are studied. The sufficient conditions to ensure the reduced order controllers also being suboptimal H_∞ controllers and SPR are given, respectively. The conditions presented may be considered as frequency weighted model reduction problems. We generalize the result of C?(θ) approach in Goddard (Ph.D. Thesis, Trinity College, Cambridge, 1995) for controller order reduction with an H_∞ framework and the relationship between our results and some other existing results is established. Copyright © 2003 John Wiley & Sons, Ltd.     

Buckling load of symmetric plane frames using canonical forms

The main objective of this paper is to develop a methodology for an efficient calculation of buckling loads for symmetric frame structures in order to reduce the size of the eigensolution problems involved. This is achieved by decomposing a symmetric model into two submodels followed by their healing to obtain the factors of the model. The buckling load of the entire structure is then obtained by calculating the buckling loads of its factors. The methods of this paper, provide a mathematical foundation and a logical means for dealing with symmetry, in place of looking for various boundary conditions to be imposed for symmetric structures, as in the traditional methods. Examples are provided to illustrate the simplicity and efficiency of the present method.     

Super-resolution of human face image using canonical correlation analysis

Super-resolution reconstruction of face image is the problem of reconstructing a high resolution face image from one or more low resolution face images. Assuming that high and low resolution images share similar intrinsic geometries, various recent super-resolution methods reconstruct high resolution images based on a weights determined from nearest neighbors in the local embedding of low resolution images. These methods suffer disadvantages from the finite number of samples and the nature of manifold learning techniques, and hence yield unrealistic reconstructed images.To address the problem, we apply canonical correlation analysis (CCA), which maximizes the correlation between the local neighbor relationships of high and low resolution images. We use it separately for reconstruction of global face appearance, and facial details. Experiments using a collection of frontal human faces show that the proposed algorithm improves reconstruction quality over existing state-of-the-art super-resolution algorithms, both visually, and using a quantitative peak signal-to-noise ratio assessment.     

Fast active appearance model search using canonical correlation analysis

A fast AAM search algorithm based on canonical correlation analysis (CCA-AAM) is introduced. It efficiently models the dependency between texture residuals and model parameters during search. Experiments show that CCA-AAMs, while requiring similar implementation effort, consistently outperform standard search with regard to convergence speed by a factor of four.