13,499 research outputs found
Spectral reordering of a range-dependent weighted random graph
Reordering under a random graph hypothesis can be regarded as an extension of clustering and fits into the general area of data mining. Here, we consider a generalization of Grindrod's model and show how an existing spectral reordering algorithm that has arisen in a number of areas may be interpreted from a maximum likelihood range-dependent random graph viewpoint. Looked at this way, the spectral algorithm, which uses eigenvector information from the graph Laplacian, is found to be automatically tuned to an exponential edge density. The connection is precise for optimal reorderings, but is weaker when approximate reorderings are computed via relaxation. We illustrate the performance of the spectral algorithm in the weighted random graph context and give experimental evidence that it can be successful for other edge densities. We conclude by applying the algorithm to a data set from the biological literature that describes cortical connectivity in the cat brain
On Spectral Graph Embedding: A Non-Backtracking Perspective and Graph Approximation
Graph embedding has been proven to be efficient and effective in facilitating
graph analysis. In this paper, we present a novel spectral framework called
NOn-Backtracking Embedding (NOBE), which offers a new perspective that
organizes graph data at a deep level by tracking the flow traversing on the
edges with backtracking prohibited. Further, by analyzing the non-backtracking
process, a technique called graph approximation is devised, which provides a
channel to transform the spectral decomposition on an edge-to-edge matrix to
that on a node-to-node matrix. Theoretical guarantees are provided by bounding
the difference between the corresponding eigenvalues of the original graph and
its graph approximation. Extensive experiments conducted on various real-world
networks demonstrate the efficacy of our methods on both macroscopic and
microscopic levels, including clustering and structural hole spanner detection.Comment: SDM 2018 (Full version including all proofs
Skill set profile clustering based on student capability vectors computed from online tutoring data
In educational research, a fundamental goal is identifying which skills students have mastered, which skills they have not, and which skills they are in the process of mastering. As the number of examinees, items, and skills increases, the estimation of even simple cognitive diagnosis models becomes difficult. To address this, we introduce a capability matrix showing for each skill the proportion correct on all items tried by each student involving that skill. We apply variations of common clustering methods to this matrix and discuss conditioning on sparse subspaces. We demonstrate the feasibility and scalability of our method on several simulated datasets and illustrate the difficulties inherent in real data using a subset of online mathematics tutor data. We also comment on the interpretability and application of the results for teachers
Unsupervised spectral sub-feature learning for hyperspectral image classification
Spectral pixel classification is one of the principal techniques used in hyperspectral image (HSI) analysis. In this article, we propose an unsupervised feature learning method for classification of hyperspectral images. The proposed method learns a dictionary of sub-feature basis representations from the spectral domain, which allows effective use of the correlated spectral data. The learned dictionary is then used in encoding convolutional samples from the hyperspectral input pixels to an expanded but sparse feature space. Expanded hyperspectral feature representations enable linear separation between object classes present in an image. To evaluate the proposed method, we performed experiments on several commonly used HSI data sets acquired at different locations and by different sensors. Our experimental results show that the proposed method outperforms other pixel-wise classification methods that make use of unsupervised feature extraction approaches. Additionally, even though our approach does not use any prior knowledge, or labelled training data to learn features, it yields either advantageous, or comparable, results in terms of classification accuracy with respect to recent semi-supervised methods
Collaboration in sensor network research: an in-depth longitudinal analysis of assortative mixing patterns
Many investigations of scientific collaboration are based on statistical
analyses of large networks constructed from bibliographic repositories. These
investigations often rely on a wealth of bibliographic data, but very little or
no other information about the individuals in the network, and thus, fail to
illustrate the broader social and academic landscape in which collaboration
takes place. In this article, we perform an in-depth longitudinal analysis of a
relatively small network of scientific collaboration (N = 291) constructed from
the bibliographic record of a research center involved in the development and
application of sensor network and wireless technologies. We perform a
preliminary analysis of selected structural properties of the network,
computing its range, configuration and topology. We then support our
preliminary statistical analysis with an in-depth temporal investigation of the
assortative mixing of selected node characteristics, unveiling the researchers'
propensity to collaborate preferentially with others with a similar academic
profile. Our qualitative analysis of mixing patterns offers clues as to the
nature of the scientific community being modeled in relation to its
organizational, disciplinary, institutional, and international arrangements of
collaboration.Comment: Scientometrics (In press
A Holistic Approach to Forecasting Wholesale Energy Market Prices
Electricity market price predictions enable energy market participants to
shape their consumption or supply while meeting their economic and
environmental objectives. By utilizing the basic properties of the
supply-demand matching process performed by grid operators, known as Optimal
Power Flow (OPF), we develop a methodology to recover energy market's structure
and predict the resulting nodal prices by using only publicly available data,
specifically grid-wide generation type mix, system load, and historical prices.
Our methodology uses the latest advancements in statistical learning to cope
with high dimensional and sparse real power grid topologies, as well as scarce,
public market data, while exploiting structural characteristics of the
underlying OPF mechanism. Rigorous validations using the Southwest Power Pool
(SPP) market data reveal a strong correlation between the grid level mix and
corresponding market prices, resulting in accurate day-ahead predictions of
real time prices. The proposed approach demonstrates remarkable proximity to
the state-of-the-art industry benchmark while assuming a fully decentralized,
market-participant perspective. Finally, we recognize the limitations of the
proposed and other evaluated methodologies in predicting large price spike
values.Comment: 14 pages, 14 figures. Accepted for publication in IEEE Transactions
on Power System
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