Feature learning forms the cornerstone for tackling challenging learning problems in domains such as speech, computer vision and natural language processing. In this paper, we consider a novel class of matrix and tensor-valued features, which can be pre-trained using unlabeled samples. We present efficient algorithms for extracting discriminative information, given these pre-trained features an...

Tensor fields are important in digital imaging and computer vision. Hence there is a demand for morphological operations to perform e.g. shape analysis, segmentation or enhancement procedures. Recently, fundamental morphological concepts have been transferred to the setting of fields of symmetric positive definite matrices, which are symmetric rank two tensors. This has been achieved by a matri...

We give a new characterisation of the unparametrised geodesics, or distinguished curves, for affine, pseudo-Riemannian, conformal, and projective geometry. This is type moving incidence relation. The used to provide very general theory construction quantities that are necessarily conserved along curves. formalism immediately yields explicit formulae these curve first integrals. usual role Killi...

Seismic coherence is widely used in seismic interpretation and reservoir characterization to highlight (with low values) faults and stratigraphic features from a seismic image. A coherence image can be computed from the eigenvalues of conventional structure tenors, which are outer products of gradients of a seismic image. I have developed a simple but effective method to improve such a coherenc...

Introduction: Human brain diffusion tensor imaging (DTI) templates developed to date use the mean tensor to summarize the DTI information from a group of subjects. However, spatial normalization of DTI data between subjects contains inaccuracies, and the mean of imperfectly matched tensors may have significantly different characteristics than the individual tensors. It is well known that, in di...

The aim of this paper is to define the productoperation on a family of interval valued events and the notion ofjoint interval valued observable. We show the connection betweenproduct operations for interval valued events and intuitionisticfuzzy events, too. We display the relation between joint intervalvalued observable and joint intuitionistic fuzzy observable. We...

It is argued that the ‘inner’ negation ∼ familiar from 3-valued logic can be interpreted as a form of ‘conditional’ negation: ∼A is read “A is false if it has a truth value”. It is argued that this reading squares well with a particular 3-valued interpretation of a conditional that in the literature has been seen as a serious candidate for capturing the truth conditions of the natural language ...

Even though it is not very often admitted, partial functions do play a significant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using three-valued logic decades ago, but there has not been a satisfactory mechanization. Recent years have seen a thorough investigation of the framework of many-valued truth-functional log...

In this paper, we explain what are tensors and how tensors can help in computing.

While the purpose of conventional proof calculi is to axiomatise the set of valid sentences of a logic, refutation systems axiomatise the invalid sentences. Such systems are relevant not only for proof-theoretic reasons but also for realising deductive systems for nonmonotonic logics. We introduce Gentzen-type refutation systems for two basic three-valued logics and we discuss an application of...