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Stock index is an indicator that describes the changes in the total price level of the stock market, and it is susceptible to many dynamic factors, with such characteristics as high dimension, uncertainty, non-linearity, time delay, complexity, etc., resulting in abnormal and missing values in stock index data, which will lead to instability or unreliability of the stock index tracking model. In order to solve these problems, we take the historical stock index as the input, model the internal dynamic changes of features, and learn the change rule. Firstly, we introduce an attention mechanism, that is, to assign different weights to the implicit state of the long short term memory network (LSTM) through mapping weights and learning parameters. We further propose a stock index data preprocessing model of the LSTM based on the attention mechanism. Secondly, the group method of data handling type neural networks (GMDH-NN) is a self-organizing data mining technology, which is especially suitable for modeling complex systems. So we choose a discrete form of Kolmogorov-Gabor ( $K-G$ ) polynomial of the first-order as the reference function of GMDH-NN to establish the general relationship between input and output variables. We further present a deep evolutionary GMDH polynomial neural network (DGMDH) to perform stock index tracking. Moreover, for a high-dimensional stock index dataset, the traditional external criterion can no longer meet the needs of reality, so we propose a tracking error external criterion (TEEC) for stock indices, which is based on the difference between allocation yield and target yield. The TEEC provides better information for selecting the optimal complex DGMDH model. Our experiments clearly show the effectiveness of our methodology.

Urban buildings are essential components of cities and an indispensable source of urban geographic information. While there are many research efforts focused on urban buildings extraction, there are few studies on large-scale urban building mapping based on satellite images. In this research, a large-scale urban building mapping scheme based on Gaofen-2 satellite (GF-2) images is proposed based on a hierarchical approach. In this hierarchical approach, urban buildings are regarded as a mixture of dense low-rise buildings (DLBs) and sparse independent buildings (SIBs) stacked in space, which are extracted by a semantic segmentation model and an instance segmentation model, respectively. In this study, GF-2 images and OpenStreetMap data were used to extract DLB using $U^2$-Net with focal loss. GF-2 images were used to extract SIB using an improved CenterMask model with a deformable convolution network and a spatial coordinate attention module. The main urban area within the 5th ring road of Beijing was selected as the study area. With the trained model, the GF-2 image tiles of Beijing input into the models to first derive coarse maps of DLB and SIB. Postprocessing optimization was performed after combining the maps. The accuracy assessment shows that the overall accuracy of large-scale urban building mapping using the hierarchical approach proposed in this article reaches 91.5%, which is 4.8% higher than that with a traditional method. Overall, the hierarchical approach proposed in this article is effective in large-scale urban building mapping and provides new application opportunities.

Dimensionality reduction is usually involved in the domains of artificial intelligence and machine learning. Linear projection of features is of particular interest for dimensionality reduction since it is simple to calculate and analytically analyze. In this paper, we propose an essentially linear projection technique, called locality-preserved maximum information projection (LPMIP), to identify the underlying manifold structure of a data set. LPMIP considers both the within-locality and the between-locality in the processing of manifold learning. Equivalently, the goal of LPMIP is to preserve the local structure while maximize the out-of locality (global) information of the samples simultaneously. Different from principal component analysis (PCA) that aims to preserve the global information and locality-preserving projections (LPPs) that is in favor of preserving the local structure of the data set, LPMIP seeks a tradeoff between the global and local structures, which is adjusted by a parameter α, so as to find a subspace that detects the intrinsic manifold structure for classification tasks. Computationally, by constructing the adjacency matrix, LPMIP is formulated as an eigenvalue problem. LPMIP yields orthogonal basis functions, and completely avoids the singularity problem as it exists in LPP. Further, we develop an efficient and stable LPMIP/QR algorithm for implementing LPMIP, especially, on high-dimensional data set. Theoretical analysis shows that conventional linear projection methods such as (weighted) PCA, maximum margin criterion (MMC), linear discriminant analysis (LDA), and LPP could be derived from the LPMIP framework by setting different graph models and constraints. Extensive experiments on face, digit, and facial expression recognition show the effectiveness of the proposed LPMIP method. [ABSTRACT FROM AUTHOR]