Product quantization (PQ) seems to have become the most efficient framework of performing approximate nearest neighbor (ANN) search for high-dimensional data. However, almost all existing PQ-based ANN techniques uniformly allocate precious bit budget to each subspace. This is not optimal, because data are often not evenly distributed among different subspaces. A better strategy is to achieve an improved balance between data distribution and bit budget within each subspace. Motivated by this observation, we propose to develop an optimized PQ (OPQ) technique, named distribution sensitive PQ (DSPQ) in this paper. The DSPQ dynamically analyzes and compares the data distribution based on a newly defined aggregate degree for high-dimensional data; whenever further optimization is feasible, resources such as memory and bits can be dynamically rearranged from one subspace to another. Our experimental results have shown that the strategy of bit rearrangement based on aggregate degree achieves modest improvements on most datasets. Moreover, our approach is orthogonal to the existing optimization strategy for PQ; therefore, it has been found that distribution sensitive OPQ can even outperform previous OPQ in the literature.

Rough set theory, as one of the most useful soft computing methods dealing with vague and uncertain information, has been successfully applied to many fields, and one of its main applications is to perform attribute reduction. Although many heuristic attribute reduction algorithms have been proposed within the framework of the rough set theory, these methods are still computationally time consuming. In order to overcome this deficit, we propose, in this paper, two quick feature selection algorithms based on the neighbor inconsistent pair, which can reduce the time consumed in finding a reduct. At first, we propose several concepts regarding simplified decision table(U') and neighbor inconsistent pairs. Based on neighbor inconsistent pairs, we constructed two new attribute significance measures. Furthermore, we put forward two new attribute reduction algorithms based on quick neighbor inconsistent pairs. The key characteristic of the presented algorithms is that they only need to calculate U'/R once under the process of selecting the best attribute from attribute sets: C - R, while most existing algorithms need to calculate partition of U' for |C - R| times. In addition, the proposed algorithms need only to deal with the equivalent classes in U'/R that contain at least one neighbor inconsistent pair, while most existing algorithms need to consider all objects in U'. The experimental results show that the proposed algorithms are feasible and efficient.

In complex pattern recognition tasks, objects are typically characterized by means of multimodality attributes, including categorical, numerical, text, image, audio, and even videos. In these cases, data are usually high dimensional, structurally complex, and granular. Those attributes exhibit some redundancy and irrelevant information. The evaluation, selection, and combination of multimodality attributes pose great challenges to traditional classification algorithms. Multikernel learning handles multimodality attributes by using different kernels to extract information coming from different attributes. However, it cannot consider the aspects fuzziness in fuzzy classification. Fuzzy rough sets emerge as a powerful vehicle to handle fuzzy and uncertain attribute reduction. In this paper, we design a framework of multimodality attribute reduction based on multikernel fuzzy rough sets. First, a combination of kernels based on set theory is defined to extract fuzzy similarity for fuzzy classification with multimodality attributes. Then, a model of multikernel fuzzy rough sets is constructed. Finally, we design an efficient attribute reduction algorithm for large scale multimodality fuzzy classification based on the proposed model. Experimental results demonstrate the effectiveness of the proposed model and the corresponding algorithm.