High-dimensional and incomplete (HDI) data are omnipresent in a variety of Big Data-related applications. Latent feature analysis (LFA) is a typical representation learning method that can extract useful yet latent knowledge from HDI data via low-rank embedding. Existing LFA-based models mostly adopt a single-metric-based modeling strategy, where the representation designed for the embeddingLossfunction is fixed and exclusive. However, real-world HDI data are commonly heterogeneous and have large diverse underlying patterns, making a single-metric-based model cannot represent such HDI data in a comprehensive and unbiased fashion. Motivated by this discovery, this article proposes a multi-metric latent feature (MMLF) model whose ideas are two-fold: 1) two vector spaces and threeLp-norms are simultaneously adopted to develop six LFA variants, each of which possesses a unique merit, and 2) all the variants are aggregated with a tailored, self-adaptive weighting strategy. As such, the proposed MMLF enjoys the merits originated from a set of disparate metric spaces all at once, achieving the comprehensive and unbiased representation of HDI data. Theoretical study guarantees that MMLF attains evident performance gain. Extensive experiments on ten real-world HDI matrices, spanning a wide range of industrial and scientific areas, verify that the proposed MMLF significantly outperforms nine state-of-the-art, shallow and deep counterparts.

Quality-of-Service (QoS), which describes the non-functional characteristics of Web service, is of great significance in service selection. Since users cannot invoke all services to obtain the corresponding QoS data, QoS prediction becomes a hot yet thorny issue. To date, a latent factor analysis (LFA)-based QoS predictor is one of the most successful and popular approaches to address this issue. However, current LFA-based QoS predictors are mostly modeled on inner product space with anL2-norm-orientedLossfunction only. They cannot comprehensively represent the characteristics of target QoS data to make accurate predictions because inner product space andL2-norm have their respective limitations. To address this issue, this study proposes a Double-space and Double-norm Ensembled Latent Factor (D2E-LF) model. Its main idea is three-fold: 1) Double-space—inner product space and distance space are employed to model two kinds of LFA-based QoS predictors, respectively, 2) Double-norm—both of these two predictors adopt anL1-and-L2-norm-orientedLossfunction, and 3) Ensembled—building an ensemble of these two predictors by a weighting strategy. By doing so, D2E-LF integrates multi-merits originating from inner product space, distance space,L1-norm, andL2-norm, making it achieve highly accurate QoS prediction. Experiments on two real-world QoS datasets demonstrate that D2E-LF has significantly higher prediction accuracy than state-of-the-art models.