We present a novel architecture for an AI system that allows a priori knowledge to combine with deep learning. In traditional neural networks, all available data is pooled at the input layer. Our alternative neural network is constructed so that partial representations (invariants) are learned in the intermediate layers, which can then be combined with a priori knowledge or with other predictive analyses of the same data. This leads to smaller training datasets due to more efficient learning. In addition, because this architecture allows inclusion of a priori knowledge and interpretable predictive models, the interpretability of the entire system increases while the data can still be used in a black box neural network. Our system makes use of networks of neurons rather than single neurons to enable the representation of approximations (invariants) of the output.
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Author supplied: "This paper gives a linearised adjustment model for the affine, similarity and congruence transformations in 3D that is easily extendable with other parameters to describe deformations. The model considers all coordinates stochastic. Full positive semi-definite covariance matrices and correlation between epochs can be handled. The determination of transformation parameters between two or more coordinate sets, determined by geodetic monitoring measurements, can be handled as a least squares adjustment problem. It can be solved without linearisation of the functional model, if it concerns an affine, similarity or congruence transformation in one-, two- or three-dimensional space. If the functional model describes more than such a transformation, it is hardly ever possible to find a direct solution for the transformation parameters. Linearisation of the functional model and applying least squares formulas is then an appropriate mode of working. The adjustment model is given as a model of observation equations with constraints on the parameters. The starting point is the affine transformation, whose parameters are constrained to get the parameters of the similarity or congruence transformation. In this way the use of Euler angles is avoided. Because the model is linearised, iteration is necessary to get the final solution. In each iteration step approximate coordinates are necessary that fulfil the constraints. For the affine transformation it is easy to get approximate coordinates. For the similarity and congruence transformation the approximate coordinates have to comply to constraints. To achieve this, use is made of the singular value decomposition of the rotation matrix. To show the effectiveness of the proposed adjustment model total station measurements in two epochs of monitored buildings are analysed. Coordinate sets with full, rank deficient covariance matrices are determined from the measurements and adjusted with the proposed model. Testing the adjustment for deformations results in detection of the simulated deformations."
MULTIFILE
This study explored the dimensionality and measurement invariance of a multidimensional measure for evaluating teachers’ perceptions of the quality of their relationships with principals at the dyadic level. Participants were 630 teachers (85.9% female) from 220 primary and 204 secondary schools across the Netherlands. Teachers completed the 10-item Principal–Teacher Relationship Scale (PTRS) for their principals. Confirmatory factor analyses (CFA) provided evidence for a two-factor model, including a relational Closeness and Conflict dimension. Additionally, multigroup CFA results indicated strong invariance of the PTRS across school type, teacher gender, and teaching experience. Last, secondary school teachers and highly experienced teachers reported lower levels of Closeness and higher levels of Conflict in the relationship with their principal compared to primary school teachers and colleagues with less experience. Accordingly, the PTRS can be considered a valid and reliable measure that adds to the methodological repertoire of educational leadership research by focusing on both positive and negative aspects of dyadic principal–teacher relationships.
