Abstract

Abstract
The problem of estimating the motion and orientation parameters of a rigid object from two m - D point set patterns is of significant importance in medical imaging, electrocardiogram (ECG) alignment, and fingerprint matching. The rigid parameters can be defined by an m x m rotation matrix, a diagonal m x m scale matrix, and an m x 1 translation vector. All together, the total number of parameters to be found is m(m + 2). Several least squares based algorithms have recently appeared in the literature. These algorithms are all based on a singular value decomposition (SVD) of the m x m cross-covariance matrix between the two data sets. However, there are cases where the SVD based algorithms return a reflection matrix rather than a rotation matrix. Some authors have introduced a simple correction for guarding against such cases. Other types of algorithm are based on unit quaternions which guarantee obtaining a true rotation matrix. In this paper we introduce a principal component based registration algorithm which is solved in closed-form. By using matrix vectorization properties the problem can be cast as one of finding a rank-1 symmetric projection matrix. This is equivalent to solving a Sylvester equation with equality constraints. Once the solution is obtained, we apply the inverse vectorization operation to estimate the rotation and scale matrices, along with the translation vector. We apply the proposed algorithm to the alignment of ECG signals and compare the results to those obtained by the SVD and quaternion based algorithms.

Abstract
In this paper we analyse the estimates of the matrices produced by the non-biased deterministic-stochastic subspace identification algorithms (NBDSSI) proposed by Van Overschee and De Moor ( 1996). First, an alternate expression is derived for the A and C estimates. It is shown that the Chiuso and Picci result ( Chiuso and Picci 2004) stating that the A and C estimates delivered by this algorithm robust version and by the Verhaegen's MOESP (Verhaegen and Dewilde 1992a, Verhaegen and Dewilde 1992b, Verhaegen 1993, Verhaegen 1994) are equal, can be obtained from this expression. An alternative approach for the estimation of matrices B and D in subspace identification is also described. It is shown that the least squares approach for the estimation of these matrices estimation can be just expressed as an orthogonal projection of the future outputs on a lower dimension subspace in the orthogonal complement of the column space of the extended observability matrix. Since this subspace has a dimension equal to the number of outputs, a simpler and numerically more efficient ( but equally accurate) new subspace algorithm is provided.

Abstract
We tackle the problem of sequence classification using relevant subsequences found in a dataset of protein labelled sequences. A subsequence is relevant if it is frequent and has a minimal length. For each query sequence a vector of features is obtained. The features consist in the number and average length of the relevant subsequences shared with each of the protein families. Classification is performed by combining these features in a Bayes Classifier. The combination of these characteristics results in a multi-class and multi-domain method that is exempt of data transformation and background knowledge. We illustrate the performance of our method using three collections of protein datasets. The performed tests showed that the method has an equivalent performance to state of the art methods in protein classification.

Abstract
Considering the characteristics of biological sequence databases, which typically have a small alphabet, a very long length and a relative small size (several hundreds of sequences), we propose a new sequence mining algorithm (gIL). gIL was developed for linear sequence pattern mining and results from the combination of some of the most efficient techniques used in sequence and itemset mining. The algorithm exhibits a high adaptability, yielding a smooth and direct introduction of various types of features into the mining process, namely the extraction of rigid and arbitrary gap patterns. Both breadth or a depth first traversal are possible. The experimental evaluation, in synthetic and real life protein databases, has shown that our algorithm has superior performance to state-of-the art algorithms. The use of constraints has also proved to be a very useful tool to specify user interesting patterns.

Abstract
In this paper we introduce a new identification algorithm for MIMO bilinear systems driven by white noise inputs. The new algorithm is based on a convergent sequence of linear deterministic-stochastic state space approximations, thus considered a Picard based method. The key to the algorithm is the fact that the bilinear terms behave like white noise processes. Using a linear Kalman filter, the bilinear terms can be estimated and combined with the system inputs at each iteration, leading to a linear system which can be identified with a linear-deterministic subspace algorithm such as MOESP, N4SID, or CVA. Furthermore, the model parameters obtained with the new algorithm converge to those of a bilinear model. Finally, the dimensions of the data matrices are comparable to those of a linear subspace algorithm, thus avoiding the curse of dimensionality.