Multi-Modal Feature Selection with Feature Correlation and Feature Structure Fusion for MCI and AD Classification

Feature selection for multiple types of data has been widely applied in mild cognitive impairment (MCI) and Alzheimer’s disease (AD) classification research. Combining multi-modal data for classification can better realize the complementarity of valuable information. In order to improve the classification performance of feature selection on multi-modal data, we propose a multi-modal feature selection algorithm using feature correlation and feature structure fusion (FC2FS). First, we construct feature correlation regularization by fusing a similarity matrix between multi-modal feature nodes. Then, based on manifold learning, we employ feature matrix fusion to construct feature structure regularization, and learn the local geometric structure of the feature nodes. Finally, the two regularizations are embedded in a multi-task learning model that introduces low-rank constraint, the multi-modal features are selected, and the final features are linearly fused and input into a support vector machine (SVM) for classification. Different controlled experiments were set to verify the validity of the proposed method, which was applied to MCI and AD classification. The accuracy of normal controls versus Alzheimer’s disease, normal controls versus late mild cognitive impairment, normal controls versus early mild cognitive impairment, and early mild cognitive impairment versus late mild cognitive impairment achieve 91.85 ± 1.42%, 85.33 ± 2.22%, 78.29 ± 2.20%, and 77.67 ± 1.65%, respectively. This method makes up for the shortcomings of the traditional multi-modal feature selection based on subjects and fully considers the relationship between feature nodes and the local geometric structure of feature space. Our study not only enhances the interpretation of feature selection but also improves the classification performance, which has certain reference values for the identification of MCI and AD.

A minimal-length approach unifies rigidity in underconstrained materials

We present an approach to understand geometric-incompatibility–induced rigidity in underconstrained materials, including subisostatic 2D spring networks and 2D and 3D vertex models for dense biological tissues. We show that in all these models a geometric criterion, represented by a minimal lengthℓ¯min, determines the onset of prestresses and rigidity. This allows us to predict not only the correct scalings for the elastic material properties, but also the precise magnitudes for bulk modulus and shear modulus discontinuities at the rigidity transition as well as the magnitude of the Poynting effect. We also predict from first principles that the ratio of the excess shear modulus to the shear stress should be inversely proportional to the critical strain with a prefactor of 3. We propose that this factor of 3 is a general hallmark of geometrically induced rigidity in underconstrained materials and could be used to distinguish this effect from nonlinear mechanics of single components in experiments. Finally, our results may lay important foundations for ways to estimateℓ¯minfrom measurements of local geometric structure and thus help develop methods to characterize large-scale mechanical properties from imaging data.

Lorentz-Violating Gravity Models and the Linearized Limit

Many models in which Lorentz symmetry is spontaneously broken in a curved spacetime do so via a “Lorentz-violating” (LV) vector or tensor field, which dynamically takes on a vacuum expectation value and provides additional local geometric structure beyond the metric. The kinetic terms of such a field will not necessarily be decoupled from the kinetic terms of the metric, and will generically lead to a set of coupled equations for the perturbations of the metric and the LV field. In some models, however, the imposition of certain additional conditions can decouple these equations, yielding an “effective equation” for the metric perturbations alone. The resulting effective equation may depend on the metric in a gauge-invariant way, or it may be gauge-dependent. The only two known models yielding gauge-invariant effective equations involve differential forms; I show in this work that the obvious generalizations of these models do not yield gauge-invariant effective equations. Meanwhile, I show that a gauge-dependent effective equation may be obtained from any “tensor Klein–Gordon” model under similar assumptions. Finally, I discuss the implications of this work in the search for Lorentz-violating gravitational effects.