206,540 research outputs found
Image patch analysis of sunspots and active regions. I. Intrinsic dimension and correlation analysis
The flare-productivity of an active region is observed to be related to its
spatial complexity. Mount Wilson or McIntosh sunspot classifications measure
such complexity but in a categorical way, and may therefore not use all the
information present in the observations. Moreover, such categorical schemes
hinder a systematic study of an active region's evolution for example. We
propose fine-scale quantitative descriptors for an active region's complexity
and relate them to the Mount Wilson classification. We analyze the local
correlation structure within continuum and magnetogram data, as well as the
cross-correlation between continuum and magnetogram data. We compute the
intrinsic dimension, partial correlation, and canonical correlation analysis
(CCA) of image patches of continuum and magnetogram active region images taken
from the SOHO-MDI instrument. We use masks of sunspots derived from continuum
as well as larger masks of magnetic active regions derived from the magnetogram
to analyze separately the core part of an active region from its surrounding
part. We find the relationship between complexity of an active region as
measured by Mount Wilson and the intrinsic dimension of its image patches.
Partial correlation patterns exhibit approximately a third-order Markov
structure. CCA reveals different patterns of correlation between continuum and
magnetogram within the sunspots and in the region surrounding the sunspots.
These results also pave the way for patch-based dictionary learning with a view
towards automatic clustering of active regions.Comment: Accepted for publication in the Journal of Space Weather and Space
Climate (SWSC). 23 pages, 11 figure
Categorical invariance and structural complexity in human concept learning
An alternative account of human concept learning based on an invariance measure of the categorical\ud
stimulus is proposed. The categorical invariance model (CIM) characterizes the degree of structural\ud
complexity of a Boolean category as a function of its inherent degree of invariance and its cardinality or\ud
size. To do this we introduce a mathematical framework based on the notion of a Boolean differential\ud
operator on Boolean categories that generates the degrees of invariance (i.e., logical manifold) of the\ud
category in respect to its dimensions. Using this framework, we propose that the structural complexity\ud
of a Boolean category is indirectly proportional to its degree of categorical invariance and directly\ud
proportional to its cardinality or size. Consequently, complexity and invariance notions are formally\ud
unified to account for concept learning difficulty. Beyond developing the above unifying mathematical\ud
framework, the CIM is significant in that: (1) it precisely predicts the key learning difficulty ordering of\ud
the SHJ [Shepard, R. N., Hovland, C. L.,&Jenkins, H. M. (1961). Learning and memorization of classifications.\ud
Psychological Monographs: General and Applied, 75(13), 1-42] Boolean category types consisting of three\ud
binary dimensions and four positive examples; (2) it is, in general, a good quantitative predictor of the\ud
degree of learning difficulty of a large class of categories (in particular, the 41 category types studied\ud
by Feldman [Feldman, J. (2000). Minimization of Boolean complexity in human concept learning. Nature,\ud
407, 630-633]); (3) it is, in general, a good quantitative predictor of parity effects for this large class of\ud
categories; (4) it does all of the above without free parameters; and (5) it is cognitively plausible (e.g.,\ud
cognitively tractable)
The Structured Process Modeling Theory (SPMT): a cognitive view on why and how modelers benefit from structuring the process of process modeling
After observing various inexperienced modelers constructing a business process model based on the same textual case description, it was noted that great differences existed in the quality of the produced models. The impression arose that certain quality issues originated from cognitive failures during the modeling process. Therefore, we developed an explanatory theory that describes the cognitive mechanisms that affect effectiveness and efficiency of process model construction: the Structured Process Modeling Theory (SPMT). This theory states that modeling accuracy and speed are higher when the modeler adopts an (i) individually fitting (ii) structured (iii) serialized process modeling approach. The SPMT is evaluated against six theory quality criteria
Learning shape correspondence with anisotropic convolutional neural networks
Establishing correspondence between shapes is a fundamental problem in
geometry processing, arising in a wide variety of applications. The problem is
especially difficult in the setting of non-isometric deformations, as well as
in the presence of topological noise and missing parts, mainly due to the
limited capability to model such deformations axiomatically. Several recent
works showed that invariance to complex shape transformations can be learned
from examples. In this paper, we introduce an intrinsic convolutional neural
network architecture based on anisotropic diffusion kernels, which we term
Anisotropic Convolutional Neural Network (ACNN). In our construction, we
generalize convolutions to non-Euclidean domains by constructing a set of
oriented anisotropic diffusion kernels, creating in this way a local intrinsic
polar representation of the data (`patch'), which is then correlated with a
filter. Several cascades of such filters, linear, and non-linear operators are
stacked to form a deep neural network whose parameters are learned by
minimizing a task-specific cost. We use ACNNs to effectively learn intrinsic
dense correspondences between deformable shapes in very challenging settings,
achieving state-of-the-art results on some of the most difficult recent
correspondence benchmarks
On the Design and Analysis of Multiple View Descriptors
We propose an extension of popular descriptors based on gradient orientation
histograms (HOG, computed in a single image) to multiple views. It hinges on
interpreting HOG as a conditional density in the space of sampled images, where
the effects of nuisance factors such as viewpoint and illumination are
marginalized. However, such marginalization is performed with respect to a very
coarse approximation of the underlying distribution. Our extension leverages on
the fact that multiple views of the same scene allow separating intrinsic from
nuisance variability, and thus afford better marginalization of the latter. The
result is a descriptor that has the same complexity of single-view HOG, and can
be compared in the same manner, but exploits multiple views to better trade off
insensitivity to nuisance variability with specificity to intrinsic
variability. We also introduce a novel multi-view wide-baseline matching
dataset, consisting of a mixture of real and synthetic objects with ground
truthed camera motion and dense three-dimensional geometry
Angle Tree: Nearest Neighbor Search in High Dimensions with Low Intrinsic Dimensionality
We propose an extension of tree-based space-partitioning indexing structures
for data with low intrinsic dimensionality embedded in a high dimensional
space. We call this extension an Angle Tree. Our extension can be applied to
both classical kd-trees as well as the more recent rp-trees. The key idea of
our approach is to store the angle (the "dihedral angle") between the data
region (which is a low dimensional manifold) and the random hyperplane that
splits the region (the "splitter"). We show that the dihedral angle can be used
to obtain a tight lower bound on the distance between the query point and any
point on the opposite side of the splitter. This in turn can be used to
efficiently prune the search space. We introduce a novel randomized strategy to
efficiently calculate the dihedral angle with a high degree of accuracy.
Experiments and analysis on real and synthetic data sets shows that the Angle
Tree is the most efficient known indexing structure for nearest neighbor
queries in terms of preprocessing and space usage while achieving high accuracy
and fast search time.Comment: To be submitted to IEEE Transactions on Pattern Analysis and Machine
Intelligenc
Creativity as Cognitive design \ud The case of mesoscopic variables in Meta-Structures\ud
Creativity is an open problem which has been differently approached by several disciplines since a long time. In this contribution we consider as creative the constructivist design an observer does on the description levels of complex phenomena, such as the self-organized and emergent ones ( e.g., Bènard rollers, Belousov-Zhabotinsky reactions, flocks, swarms, and more radical cognitive and social emergences). We consider this design as related to the Gestaltian creation of a language fit for representing natural processes and the observer in an integrated way. Organised systems, both artificial and most of the natural ones are designed/ modelled according to a logical closed model which masters all the inter-relation between their constitutive elements, and which can be described by an algorithm or a single formal model. We will show there that logical openness and DYSAM (Dynamical Usage of Models) are the proper tools for those phenomena which cannot be described by algorithms or by a single formal model. The strong correlation between emergence and creativity suggests that an open model is the best way to provide a formal definition of creativity. A specific application relates to the possibility to shape the emergence of Collective Behaviours. Different modelling approaches have been introduced, based on symbolic as well as sub-symbolic rules of interaction to simulate collective phenomena by means of computational emergence. Another approach is based on modelling collective phenomena as sequences of Multiple Systems established by percentages of conceptually interchangeable agents taking on the same roles at different times and different roles at the same time. In the Meta-Structures project we propose to use mesoscopic variables as creative design, invention, good continuity and imitation of the description level. In the project we propose to define the coherence of sequences of Multiple Systems by using the values taken on by the dynamic mesoscopic clusters of its constitutive elements, such as the instantaneous number of elements having, in a flock, the same speed, distance from their nearest neighbours, direction and altitude. In Meta-Structures the collective behaviour’s coherence corresponds, for instance, to the scalar values taken by speed, distance, direction and altitude along time, through statistical strategies of interpolation, quasi-periodicity, levels of ergodicity and their reciprocal relationship. In this case the constructivist role of the observer is considered creative as it relates to neither non-linear replication nor transposition of levels of description and models used for artificial systems, like reductionism. Creativity rather lies in inventing new mesoscopic variables able to identify coherent patterns in complex systems. As it is known, mesoscopic variables represent partial macroscopic properties of a system by using some of the microscopic degrees of freedom possessed by composing elements. Such partial usage of microscopic as well as macroscopic properties allows a kind of Gestaltian continuity and imitation between levels of descriptions for mesoscopic modelling. \ud
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