Recommender Systems have become a very useful tool for a large variety of domains. Researchers have been attempting to improve their algorithms in order to issue better predictions to the users. However, one of the current challenges in the area refers to how to properly evaluate the predictions generated by a recommender system. In the extent of offline evaluations, some traditional concepts of evaluation have been explored, such as accuracy, Root Mean Square Error and P@N for top-k recommendations. In recent years, more research have proposed some new concepts such as novelty, diversity and serendipity. These concepts have been addressed with the goal to satisfy the users' requirements. Numerous definitions and metrics have been proposed in previous work. On the absence of a specific summarization on evaluations of recommendation combining traditional metrics and recent progresses, this paper surveys and organizes the main research that present definitions about concepts and propose metrics or strategies to evaluate recommendations. In addition, this survey also settles the relationship between the concepts, categorizes them according to their objectives and suggests potential future topics on user satisfaction.

The main objective of this study was to enhance the performance of sleep stage classification using single-channel electroencephalograms (EEGs), which are highly desirable for many emerging technologies, such as telemedicine and home care. The proposed method consists of decomposing EEGs by a discrete wavelet transform and computing the kurtosis, skewness and variance of its coefficients at selected levels. A random forest predictor is trained to classify each epoch into one of the Rechtschaffen and Kales' stages. By performing a comprehensive set of tests on 106,376 epochs available from the Physionet public database, it is demonstrated that the use of these three statistical moments has enhanced performance when compared to their application in the time domain. Furthermore, the chosen set of features has the advantage of exhibiting a stable classification performance for all scoring systems, i.e., from 2- to 6-state sleep stages. The stability of the feature set is confirmed with ReliefF tests which show a performance reduction when any individual feature is removed, suggesting that this group of feature cannot be further reduced. The accuracies and kappa coefficients yield higher than 90 % and 0.8, respectively, for all of the 2- to 6-state sleep stage classification cases.

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The principal component analysis (PCA) is widely used for data decorrelation and dimensionality reduction. However, the use of PCA may be impractical in real-time applications, or in situations were energy and computing constraints are severe. In this context, the discrete cosine transform (DCT) becomes a low-cost alternative to data decorrelation. This paper presents a method to derive computationally efficient approximations to the DCT. The proposed method aims at the minimization of the angle between the rows of the exact DCT matrix and the rows of the approximated transformation matrix. The resulting transformations matrices are orthogonal and have extremely low arithmetic complexity. Considering popular performance measures, one of the proposed transformation matrices outperforms the best competitors in both matrix error and coding capabilities. Practical applications in image and video coding demonstrate the relevance of the proposed transformation. In fact, we show that the proposed approximate DCT can outperform the exact DCT for image encoding under certain compression ratios. The proposed transform and its direct competitors are also physically realized as digital prototype circuits using FPGA technology.

A low-complexity orthogonal multiplierless approximation for the 16-point discrete cosine transform (DCT) was introduced. The proposed method was designed to possess a very low computational cost. A fast algorithm based on matrix factorization was proposed requiring only 60 additions. The proposed architecture outperforms classical and state-of-the-art algorithms when assessed as a tool for image and video compression. Digital VLSI hardware implementations were also proposed being physically realized in FPGA technology and implemented in 45 nm up to synthesis and place-route levels. Additionally, the proposed method was embedded into a high efficiency video coding (HEVC) reference software for actual proof-of-concept. Obtained results show negligible video degradation when compared to Chen DCT algorithm in HEVC. standards, such as JPEG [10], MPEG-1 [11], MPEG-2 [12], H.261 [13], H.263 [14], and H.264 [15].Moreover, numerous fast algorithms were proposed for its computation [16][17][18][19][20][21][22].Designing fast algorithms for the DCT is a mature area of research [17,[23][24][25]; thus it is not realistic to expect major advances by means of standards techniques. On the other hand, the development of low-complexity approximations for DCT is an open field of research. In particular, the 8-point DCT was given several approximations, such as the signed DCT [26], the level 1 DCT approximation [27], the Bouguezel-Ahmad-Swamy (BAS) series of transforms [4,5,7,28,29], the rounded DCT (RDCT) [8], the modified RDCT [30], the multiplier-free DCT approximation for RF imaging [31], and the improved approximate DCT proposed in [9]. Such approximations reduce the computational demands of the DCT evaluation, leading to low-power consumption and highspeed hardware realizations [9]. At the same time, approximate transforms can provide adequate numerical accuracy for image and video processing.

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An orthogonal 16-point approximate discrete cosine transform (DCT) is introduced. The proposed transform requires neither multiplications nor bit-shifting operations. A fast algorithm based on matrix factorization is introduced, requiring only 44 additions-the lowest arithmetic cost in literature. To assess the introduced transform, computational complexity, similarity with the exact DCT, and coding performance measures are computed. Classical and state-of-the-art 16-point low-complexity transforms were used in a comparative analysis. In the context of image compression, the proposed approximation was evaluated via PSNR and SSIM measurements, attaining the best cost-benefit ratio among the competitors. For video encoding, the proposed approximation was embedded into a HEVC reference software for direct comparison with the original HEVC standard. Physically realized and tested using FPGA hardware, the proposed transform showed 35% and 37% improvements of area-time and area-time-squared VLSI metrics when compared to the best competing transform in the literature. IntroductionThe discrete cosine transform (DCT) [1, 2] is a fundamental building-block for several image and video processing applications. In fact, the DCT closely approximates the Karhunen-Loève transform (KLT) [1], which is capable of optimal data decorrelation and energy compaction of first-order stationary Markov signals [1].This class of signals is particularly appropriate for the modeling of natural images [1,3]. Thus, the DCT finds applications in several contemporary image and video compression standards, such as the JPEG [4] and the H.26x family of codecs [5][6][7]. Indeed, several fast algorithms for computing the exact DCT were proposed [8][9][10][11][12][13][14][15]. However, these methods require the use of arithmetic multipliers [16,17], which are time, power, and hardware demanding arithmetic operations, when compared to additions or bit-shifting operations [18].

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