Biomedical subjects

Alessandro Verri

Publications and source records attributed to Alessandro Verri.

3 recordsLinked to original sources

PubMed2005

Building kernels from binary strings for image matching.

In the statistical learning framework, the use of appropriate kernels may be the key for substantial improvement in solving a given problem. In essence, a kernel is a similarity measure between input points satisfying some mathematical requirements and possibly capturing the domain knowledge. In this paper, we focus on kernels for images: we represent the image information content with binary strings and discuss various bitwise manipulations obtained using logical operators and convolution with nonbinary stencils. In the theoretical contribution of our work, we show that histogram intersection is a Mercer's kernel and we determine the modifications under which a similarity measure based on the notion of Hausdorff distance is also a Mercer's kernel. In both cases, we determine explicitly the mapping from input to feature space. The presented experimental results support the relevance of our analysis for developing effective trainable systems.

Algorithms↗

PubMed2005

A novel kernel method for clustering.

Kernel Methods are algorithms that, by replacing the inner product with an appropriate positive definite function, implicitly perform a nonlinear mapping of the input data into a high-dimensional feature space. In this paper, we present a kernel method for clustering inspired by the classical K-Means algorithm in which each cluster is iteratively refined using a one-class Support Vector Machine. Our method, which can be easily implemented, compares favorably with respect to popular clustering algorithms, like K-Means, Neural Gas, and Self-Organizing Maps, on a synthetic data set and three UCI real data benchmarks (IRIS data, Wisconsin breast cancer database, Spam database).

Algorithms↗

PubMed2004

Are loss functions all the same?

In this letter, we investigate the impact of choosing different loss functions from the viewpoint of statistical learning theory. We introduce a convexity assumption, which is met by all loss functions commonly used in the literature, and study how the bound on the estimation error changes with the loss. We also derive a general result on the minimizer of the expected risk for a convex loss function in the case of classification. The main outcome of our analysis is that for classification, the hinge loss appears to be the loss of choice. Other things being equal, the hinge loss leads to a convergence rate practically indistinguishable from the logistic loss rate and much better than the square loss rate. Furthermore, if the hypothesis space is sufficiently rich, the bounds obtained for the hinge loss are not loosened by the thresholding stage.

Learning↗