Bruno Bellomo,1 Gian Luca Giorgi,2 Fernando Galve,2 Rosario Lo Franco,1,3 Giuseppe Compagno,1 and Roberta Zambrini2 1Dipartimento di Fisica, Università di Palermo, via Archirafi 36, I-90123 Palermo, Italy 2IFISC (UIB-CSIC), Instituto de Fı́sica Interdisciplinar y Sistemas Complejos, UIB Campus, E-07122 Palma de Mallorca, Spain 3CSFNSM and Dipartimento di Fisica e Astronomia, Università di Catani...

In this note we give lower and upper bounds for the optimal p-norm condition number achievable by two-sided diagonal scalings. There are no assumptions on the irreducibility of certain matrices. The bounds are shown to be optimal for the 2-norm. For the 1-norm and inf-norm the (known) exact value of the optimal condition number is confirmed. We give means how to calculate the minimizing diagona...

Traditional bidirectional two-dimension (2D) principal component analysis ((2D)PCA-L2) is sensitive to outliers because its objective function is the least squares criterion based on L2-norm. This paper proposes a simple but effective L1-norm-based bidirectional 2D principal component analysis ((2D)PCA-L1), which jointly takes advantage of the merits of bidirectional 2D subspace learning and L1...

This paper describes a fuzzy union based approach for automatically evaluating machine generated extract summaries. The proposed method represents every sentence within a machine generated summary as a fuzzy set. Sentences in the reference summary are assigned membership grades in each of these fuzzy sets using cosine distance measure. Finally Fuzzy union (s-norm operation) is used to compute a...

Abstract. In this paper we analyze iterative regularization with the Bregman distance of the total variation semi norm. Moreover, we prove existence of a solution of the corresponding flow equation as introduced in [8] in a functional analytical setting using methods from convex analysis. The results are generalized to variational denoising methods with L-norm fit-to-data terms and Bregman dist...

Dimensionality reduction plays an important role in many machine learning and pattern recognition tasks. In this paper, we present a novel dimensionality reduction algorithm called multilinear maximum distance embedding (MDE), which includes three key components. To preserve the local geometry and discriminant information in the embedded space, MDE utilizes a new objective function, which aims ...

We give a survey of basic results on the cut norm and cut metric for graphons (and sometimes more general kernels), with emphasis on the equivalence problem. The main results are not new, but we add various technical complements. We allow graphons on general probability spaces whenever possible. We also give some new results for {0,1}-valued graphons.

We use mixed norm estimates for the spherical averaging operator to obtain some results concerning pinned distance sets.