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The recognition rate of some face recognition methods that require a certain number of samples will be significantly reduced in case only one sample is available for training. Aim at this situation, a new feature extraction method, HOG–LDB (histogram of oriented gradients–local difference binary), is proposed. Then, we combined this method with SVDL (sparse variation dictionary learning) to recognize the probe images with different facial variations (e.g., illuminations, poses, expressions and disguises). The descriptor of HOG–LDB can extract the edge features and local pattern features of the image. After the feature extraction, SVDL is employed in the generic training set and the generic variation dictionary is obtained. Then, the dictionary is used for predicting the subjects of the probe images with different facial variations. Finally, experimental results on the AR dataset, the Yale dataset, the Extended Yale B dataset and the CMU-PIE dataset proved the validity of the proposed method.

A model with both market production and home production is used to show that, ignoring administrative costs and indirect effects (such as rent-seeking), even if both the home and the market sectors have the condition of increasing returns and there are no pre-existing taxes, it is still efficient to tax the home sector to finance a subsidy on the market sector to offset the under-production of the latter. This under-production is due to the failure of price-taking consumers to take account of the effects of higher consumption in reducing the average costs and hence prices, through increasing returns or the publicness nature of fixed costs. Within market production, it is efficient to subsidize more the sector with a higher fixed cost, a lower elasticity of substitution between goods (higher value of diversity), and a lower degree of importance in preference which all increases the degree of increasing returns.

This paper applies the inframarginal analysis, which is a combination of marginal and total cost-benefit analysis, to investigate the relationship between division of labor, the extent of the market, productivity and inequality of income distribution. The model with transaction costs and exogenous and endogenous comparative advantages shows that as trading efficiency is improved the general equilibrium discontinuously jumps from autarky to partial division of labor with a dual structure, then to the complete division of labor where dual structure disappears. In this process different groups of individuals with different trading efficiency become involved in a certain level of division of labor at different stages of development. As the leading group becomes involved in a higher level of division of labor leaving others behind, a dual structure emerges and inequality increases. As latecomers catch up dual structure disappears and inequality declines. When the leader goes to an even higher level of specialization, dual structure occurs and inequality increases again. Inequality decreases again as the latecomers catch up. Hence, the equilibrium degree of inequality fluctuates in this development process. The relationship between inequality and productivity is neither monotonically positive nor monotonically negative. It might not be an inverted U-curve. The key driving force of economic development and trade is improvement in trading efficiency.