Cities are spatially evolving complex systems. The order and pattern beneath the apparent chaos and diverse physical forms of cities are still unclear. How the form and structure of a city evolve to improve its functions needs further exploration. To fill thisgap, we examine the geometric fractal (GF), the topological fractal (TF), and the hierarchical fractal (HF) evolution of cities by taking Hong Kong street networks from year 1971 to 2018 as an example. We find that these networks keep to be fractals both in form and structure. The values of GF, TF, and HF dimensions increase with fluctuations, revealing a more mature and complex street network. The radius-length GF dimensions demonstrate the bi-fractal property, with values ranged 1.653–1.832 and 0.677–0.892, respectively, reflecting a core-periphery pattern. The values of TF dimensions increase steadily with a wider gap to GF dimensions, indicating progressively structural optimization of street networks. These street networks keep showing fractal properties in form and structure through spatial extension, local densification, vertical stratification, hierarchies enrichment, and shortcuts construction. Moreover, street networks are GFs and TFs at the city, county, and MSA scales. The discoveries advance our understanding of urban development.

Band selection has been proven to be effective in reducing the dimensionality of the hyperspectral image by finding the most distinctive and informative bands. An essential operation for band selection is to quantify band similarity using metrics, such as entropy and mutual information. For the first time, we proposed that this quantification can also be conducted by borrowing the core ideas from landscape ecology, namely employing landscape metrics. To validate this proposal, we first developed a joint landscape metric and error image approach to quantify the similarity between two bands. Using the quantified similarity and Boltzmann entropy-based information content, we then proposed an efficient priority-based band selection algorithm to search optimal bands. To evaluate the proposed approach, we carried out a comprehensive evaluation involving 80 possible landscape metrics, two methods for quantifying band similarity, four classifiers, and four state-of-the-art, popular approaches as the benchmark. Extensive experimental results demonstrated that the proposed approach exhibited global superiority over these benchmark approaches using all these classifiers. We also found that the best choices of landscape metrics to implement the proposed approach came from the following two categories of metrics: aggregation and diversity. Although this letter presents the first study of its kind in employing landscape metrics for unsupervised band selection, it indicated that landscape metrics might open a door for metric-based approaches for image processing, including band selection.

The label information of training data is crucial for effective machine learning in many domains, while it is expensive to annotate data at a large-scale by domain experts. The problem was intensified by the multiplicity and incompleteness of multiview multi-label (MVML) objects, which is ignored by almost all existing multi-view multi-label active learning approaches. In this paper, we propose an incomplete multi-view multi-label active learning (iMVMAL) approach to reduce the cost of querying MVML data. iMVMAL firstly extends under-complete Autoencoder to learn the shared/individual representations of samples across/within incomplete views by an indicator matrix to indicate the missing samples of respective view. As such, the optimization of the Autoencoder’s parameters will not be impacted by the missing samples. Next, it uses the extracted shared/individual information to train multiple classifiers and to quantify the informativeness of sample-label pairs from these classifiers, from label-wise and sample-wise information also. After that, it selects the sample-label pairs with the highest informativeness for query. Empirical studies on benchmark datasets show that iMVMAL outperforms competitive baselines at the same query cost in the complete multi-view setting, and maintains its effectiveness in the incomplete multi-view setting as well.

Multi-instance learning (MIL) can model complex bags (samples) that are further made of diverse instances (subsamples). In typical MIL, the labels of bags are known while those of individual instances are unknown and to be specified. In this paper we propose an imbalanced deep multi-instance learning approach (IDMIL-III) and apply it to predict genome-wide isoform–isoform interactions (IIIs). This prediction task is crucial for precisely understanding the interactome between proteoforms and to reveal their functional diversity. The current solutions typically formulate the prediction of IIIs as a MIL problem by pairing two genes as a “bag” and any two isoforms spliced from these two genes as “instances.” The key instances (interacting isoform pairs) trigger the label of the positive (interacting) gene bags, which is important for identifying the IIIs. Furthermore, the prediction task was simplified as a balanced classification problem, which in practice is a rather imbalanced one. To address these issues, IDMIL-III fuses RNA-seq, nucleotide sequence, amino acid sequence and exon array data, and further introduces a novel loss function to separately model the loss of positive pairs and of negative pairs, and thus to avoid the expected loss dominated by majority negative pairs. In addition, it includes an attention strategy to identify positive isoform pairs from a positive gene bag. Extensive experimental results prove the effectiveness of IDMIL-III on predicting IIIs. Particularly, IDMIL-III achieves an F1 value as 95.4%, at least 3.8% higher than those of competitive methods at the gene-level; and obtains an F1 as 29.8%, at least 2.4% higher than the state-of-the-art methods at the isoform-level. The code of IDMIL-III is available at http://mlda.swu.edu.cn/codes.php?name=IDMIL-III.

Band selection for hyperspectral images helps improve the efficiency of data processing and even the accuracy of classification. It is to reduce the dimensionality of a hyperspectral image by selecting representative bands. In such a process, the quantification of band similarity is the fundamental issue, and it is usually achieved by using an information-theoretic measure, such as mutual information or relative entropy. However, these measures are incapable of quantifying similarity in terms of both composition and configuration. To solve this problem, the Boltzmann entropy (BE), which captures both configurational and compositional information, is employed in this letter. More precisely, the difference in BE between two bands is used for such quantification. The corresponding search strategy is designed for band selection. Experimental evaluation was carried out using remote sensing images for classification. The results clearly demonstrate the superiority of the proposed band selection method over traditional information-theoretic methods: an increase of up to 27% in classification accuracy was observed when using the difference in relative BE with 20 selected bands. In addition, another comparison with some state-of-the-art methods was conducted. The results show that the proposed method is still very competitive; it outperformed all the others when the number of selected bands ranges from 18 to 23. This letter, the first of its kind, reveals that the BE may form a new base for information-theoretic approaches to image processing and even for spatial information science in a broad sense.

Studies on the structural properties of road network and its close relationship with the traffic flow distribution have received intensive interdisciplinary attention. However, most of these attempts were theoretical. It is also a challenge to understand the relationship between the structure and morphology of a road network and peoples' movement. We developed a new methodology to deal with this challenge in this study. The first attempt was to apply the ego network analysis (which is rooted in social science) to the formation of hierarchical road networks. Then, the ego network was improved to become weighted ego network by assigning a weight to each of the links in a network. A measure called weighted average centrality rank is developed to define the order of links in a complex network. The ego network and the weighted ego network are both evaluated with a notional network and two sets of real-life road networks. Traffic flow data were used as a benchmark for the evaluation of the two approaches. The results show that they both perform well. But the hierarchies formed by weighted ego network analysis are more consistent with the real-life traffic flow, and the improvement is clearly observable.