Modeling urban growth in Economic development zones (EDZs) can help planners determine appropriate land policies for these regions. However, sometimes EDZs are established in remote areas outside of central cities that have no historical urban areas. Existing models are unable to simulate the emergence of urban areas without historical urban land in EDZs. In this study, a cellular automaton (CA) model based on fuzzy clustering is developed to address this issue. This model is implemented by coupling an unsupervised classification method and a modified CA model with an urban emergence mechanism based on local maxima. Through an analysis of the planning policies and existing infrastructure, the proposed model can detect the potential start zones and simulate the trajectory of urban growth independent of the historical urban land use. The method is validated in the urban emergence simulation of the Taiping Bay development zone in Dalian, China from 2013 to 2019. The proposed model is applied to future simulation in 2019–2030. The results demonstrate that the proposed model can be used to predict urban emergence and generate the possible future urban form, which will assist planners in determining the urban layout and controlling urban growth in EDZs.

We propose a unified scalable computing framework for three versions of spectral clustering - Normalized Cut (Shi and Malik, 2000), the Ng-Jordan-Weiss (NJW) algorithm (2001), and Diffusion Maps (Coifman and Lafon, 2006), in the setting of cosine similarity. We assume that the input data is either sparse (e.g., as a document-term frequency matrix) or of only a few hundred dimensions (e.g., for small images or data obtained through PCA). We show that in such cases, spectral clustering can be implemented solely based on efficient operations on the data matrix such as elementwise manipulation, matrix-vector multiplication and low-rank SVD, thus entirely avoiding the weight matrix. Our algorithm is simple to implement, fast to run, accurate and robust to outliers. We demonstrate its superior performance through extensive experiments which compare our scalable algorithm with the plain implementation on several benchmark data sets.

We consider the parameter tuning problem for Gaussian-kernel support vector machines, i.e., how to set its two hyperparameters - σ (bandwidth) and C (tradeoff). Among the many methods in the literature, the majority handle this task by maximizing the cross validation accuracy over the first quadrant of the (σ, C) plane. However, they are all computationally expensive because the objective function has no explicit formula so that one has to resort to numerical methods (which require training and testing the classifier many times). Additionally, these methods ignore the intrinsic geometry of training data and always operate in a large set, thus being computationally inefficient. In this paper we propose a two-step procedure for efficient parameter selection: First, we use a nearest neighbor method to directly set the value of σ based on the data geometry; afterwards, for the tradeoff parameter C we employ an elbow method that finds the smallest C leading to “nearly” the highest validation accuracy. By slightly sacrificing the validation accuracy our method gains additional attractive properties such as (1) faster training (i.e., much less candidate points to be examined) and (2) better generalizability (due to larger class margins). We conduct extensive experiments to show that such a combination of simple techniques achieves excellent performance - the classification accuracy of our method is comparable to its competitors in most cases, but it is much faster.

Since the late 1990s, there are growing studies on the development of cellular automata (CA) as a simulation tool for assisting urban and regional planning in China. Rapid urban development is the main reason that this country has become one of the best places to test the methodology of CA and analyze the effectiveness of using these models. This paper attempts to summarize the experiences and issues of using CA to solve various environmental and planning problems in China. The analysis is based on the literature review using the search engines of ISI Web of Science and Google Scholar. These experiences could be important for those who want to apply CA in developing countries. For example, which environmental and ecological problems can be solved by using this bottom-up approach? What are the data inputs to these models and how can they be calibrated? Our analyses indicate that CA have the great potential to support land-use planning and policy analysis for fast-growing regions. Some specific features of using CA in China are also identified in the literature review, including delineation of urban growth boundary, prevention of illegal development and formulating zoning schemes. The CA studies in this fast-growing country provided valuable experiences for other developing countries to solve a series of simulation and planning problems by using this bottom-up approach.

Data sets are often modeled as samples from some probability distribution lying in a very high dimensional space. In practice, they tend to exhibit low intrinsic dimensionality, which enables both fast construction of efficient data representations and solving statistical tasks such as regression of functions on the data, or even estimation of the probability distribution from which the data is generated. In this paper we introduce a novel multiscale density estimator for high dimensional data and apply it to the problem of detecting changes in the distribution of dynamic data, or in a time series of data sets. We also show that our data representations, which are not standard sparse linear expansions, are amenable to compressed measurements. Finally, we test our algorithms on both synthetic data and a real data set consisting of a times series of hyperspectral images, and demonstrate their high accuracy in the detection of anomalies.

Modeling data by multiple low-dimensional planes is an important problem in many applications such as computer vision and pattern recognition. In the most general setting where only coordinates of the data are given, the problem asks to determine the optimal model parameters (i.e., number of planes and their dimensions), estimate the model planes, and cluster the data accordingly. Though many algorithms have been proposed, most of them need to assume prior knowledge of the model parameters and thus address only the last two components of the problem. In this paper we propose an efficient algorithm based on multiscale SVD analysis and spectral methods to tackle the problem in full generality. We also demonstrate its state-of-the-art performance on both synthetic and real data.

This paper presents novel techniques for improving the performance of a multi-way spectral clustering framework (Govindu in Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), vol. 1, pp. 1150–1157, 2005; Chen and Lerman, 2007, preprint in the supplementary webpage) for segmenting affine subspaces. Specifically, it suggests an iterative sampling procedure to improve the uniform sampling strategy, an automatic scheme of inferring the tuning parameter from the data, a precise initialization procedure for K-means, as well as a simple strategy for isolating outliers. The resulting algorithm, Spectral Curvature Clustering (SCC), requires only linear storage and takes linear running time in the size of the data. It is supported by theory which both justifies its successful performance and guides our practical choices. We compare it with other existing methods on a few artificial instances of affine subspaces. Application of the algorithm to several real-world problems is also discussed.

UNLABELLED: We present a fast, versatile and adaptive-multiscale algorithm for analyzing a wide-variety of DNA microarray data. Its primary application is in normalization of array data as well as subsequent identification of 'enriched targets', e.g. differentially expressed genes in expression profiling arrays and enriched sites in ChIP-on-chip experimental data. We show how to accommodate the unique characteristics of ChIP-on-chip data, where the set of 'enriched targets' is large, asymmetric and whose proportion to the whole data varies locally. SUPPLEMENTARY INFORMATION: Supplementary figures, related preprint, free software as well as our raw DNA microarray data with PCR validations are available at http://www.math.umn.edu/~lerman/supp/bioinfo06 as well as Bioinformatics online.