There are several problems in the recommendation method based on k nearest neighbors, such as high dimensionality of rating features, slow speed of searching nearest neighbors and cold start problem of ratings. To solve these problems, a recommendation method based on k nearest neighbors using data dimensionality reduction and Exact Euclidean Locality-Sensitive Hashing (E ²LSH) was proposed. Firstly, the rating data, the user attribute data and the item category data were integrated as the input data to train the Stack Denoising Auto-encoder (SDA) neutral network, of which the last hidden layer values were used as the feature coding of the input data to complete data dimensionality reduction. Then, the index of the reduced dimension data was built by the Exact Euclidean Local-Sensitive Hash algorithm, and the target users or the target items were retrieved to get their similar nearest neighbors. Finally, the similarities between the target and the neighbors were calculated, and the target user's similarity-weighted prediction rating for the target item was obtained. The experimental results on standard data sets show that the mean square error of the proposed method is reduced by an average of about 7.2% compared with the recommendation method based on Locality-Sensitive Hashing (LSH-ICF), and the average run time of the proposed method is the same as LSH-ICF. It shows that the proposed method alleviates the rating cold start problem on the premiss of keeping the efficiency of LSH-ICF.

Concerning the power complementary limitation due to the time-reversed assumption of prototype filter in the design of traditional DFT (Discrete Fourier Transform) modulated filter banks, a time domain modified method was introduced to design the DFT filter banks from the time domain perfect reconstruction perspectives in this paper. Moreover, the designed filter banks were applied to the filter banks based multi-carrier transceivers. The time domain modified method relaxed the time-reversed assumption of prototype filter, that is, the filter banks at the receiver were conjugate transpose form of the filter banks at the transmitter. Moreover, it adopted the time domain formula of the perfect reconstruction property as the solution to design the filter banks at the receiver, which would ensure the perfect reconstruction of filter banks and avoid the power complementary limitation in the design of prototype filter at the same time. Compared to the traditional design method, the time domain modified method improves the design freedom of prototype in the filter banks, so suitable prototype filters could be obtained according to the various application environments without considering power complementary restrictions. Moreover, the time domain modified DFT filter banks based multi-carrier transceivers has a better SER (Symbol Error Ratio) performance in QPSK (Quadrature Reference Phase Shift Keying) modulation, ideal and the 3GPP TS 25.104 pedestrian multipath channel and one-tap frequency-domain equalization.