One of the most well-studied problems in data mining is computing the collection of frequent itemsets in large transactional databases. Since the introduction of the famous Apriori algorithm [14], many others have been proposed to find the frequent itemsets. Among such algorithms, the approach of mining closed itemsets has raised much interest in data mining community. The algorithms taking this approach include TITANIC [8], CLOSET+ [6], DCI-Closed [4], FCI-Stream [3], GC-Tree [5], TGC-Tree [16] etc. Among these algorithms, FCI-Stream, GC-Tree and TGC-Tree are online algorithms work under sliding window environments. By the performance evaluation in [16], GC-Tree [15] is the fastest one. In this paper, an improved algorithm based on GC-Tree is proposed, the computational complexity of which is proved to be a linear combination of the average transaction size and the average closed itemset size. The algorithm is based on the essential theorem presented in Sect. 4.2. Empirically, the new algorithm is several orders of magnitude faster than the state of art algorithm, GC-Tree.

Frequent Itemsets(FI) mining is a popular and important first step in analyzing datasets across a broad range of applications. There are two main problems with the traditional approach for finding frequent itemsets. Firstly, it may often derive an undesirably huge set of frequent itemsets and association rules. Secondly, it is vulnerable to noise. There are two approaches which have been proposed to address these problems individually. The first problem is addressed by the approach Frequent Closed Itemsets(FCI), FCI removes all the redundant information from the result and makes sure there is no information loss. The second problem is addressed by the approach Approximate Frequent Itemsets(AFI), AFI could identify and fix the noises in the datasets. Each of these two concepts has its own limitations, however, the authors find that if FCI and AFI are put together, they could help each other to overcome the limitations and amplify the advantages. The new integrated approach is termed Noise-tolerant Frequent Closed Itemset(NFCI). The results of the experiments demonstrate the advantages of the new approach: (1) It is noise tolerant. (2) The number of itemsets generated would be dramatically reduced with almost no information loss except for the noise and the infrequent patterns. (3) Hence, it is both time and space efficient. (4) No redundant information is in the result.

In sparsity-based optimization problems for two dimensional (2-D) direction-of-arrival (DOA) estimation using L-shaped nested arrays, one of the major issues is computational complexity. A 2-D DOA estimation algorithm is proposed based on reconsitution sparse Bayesian learning (RSBL) and cross covariance matrix decomposition. A single measurement vector (SMV) model is obtained by the difference coarray corresponding to one-dimensional nested array. Through spatial smoothing, the signal measurement vector is transformed into a multiple measurement vector (MMV) matrix. The signal matrix is separated by singular values decomposition (SVD) of the matrix. Using this method, the dimensionality of the sensing matrix and data size can be reduced. The sparse Bayesian learning algorithm is used to estimate one-dimensional angles. By using the one-dimensional angle estimations, the steering vector matrix is reconstructed. The cross covariance matrix of two dimensions is decomposed and transformed. Then the closed expression of the steering vector matrix of another dimension is derived, and the angles are estimated. Automatic pairing can be achieved in two dimensions. Through the proposed algorithm, the 2-D search problem is transformed into a one-dimensional search problem and a matrix transformation problem. Simulations show that the proposed algorithm has better angle estimation accuracy than the traditional two-dimensional direction finding algorithm at low signal-to-noise ratio and few samples.

In this paper, a deep learning-based secret key generation scheme is proposed for FDD multiple-input and multiple-output (MIMO) systems. We built an encoder-decoder based convolutional neural network to characterize the wireless environment to learn the mapping relationship between the uplink and downlink channel. The designed neural network can accurately predict the downlink channel state information based on the estimated uplink channel state information without any information feedback. Random secret keys can be generated from downlink channel responses predicted by the neural network. Simulation results show that deep learning based SKG scheme can achieve significant performance improvement in terms of the key agreement ratio and achievable secret key rate.

In this paper, the concept of gradient order is introduced and a novel gradient order curve descriptor (GOCD) for curve matching is proposed. The GOCD is constructed in the following main steps: firstly, curve support region independent of the dominant orientation is determined and then divided into several sub-regions based on gradient magnitude order; then gradient order feature (GOF) of each feature point is generated by encoding the local gradient information of the sample points; the descriptor is finally achieved by turning to the description matrix of GOF. Since both the local and the global gradient information are captured by GOCD, it is more distinctive and robust compared with the existing curve matching methods. Experiments under various changes, such as illumination, viewpoint, image rotation, JPEG compression and noise, show the great performance of GOCD. Furthermore, the application of image mosaic proves GOCD can be used successfully in actual field.