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Linear discriminant analysis (LDA) is widely used for dimensionality reduction under supervised learning settings. Traditional LDA objective aims to minimize the ratio of squared Euclidean distances that may not perform optimally on noisy data sets. Multiple robust LDA objectives have been proposed to address this problem, but their implementations have two major limitations. One is that their mean calculations use the squared l2-norm distance to center the data, which is not valid when the objective does not use the Euclidean distance. The second problem is that there is no generalized optimization algorithm to solve different robust LDA objectives. In addition, most existing algorithms can only guarantee the solution to be locally optimal, rather than globally optimal. In this paper, we review multiple robust loss functions and propose a new and generalized robust objective for LDA. Besides, to better remove the mean value within data, our objective uses an optimal way to center the data through learning. As one important algorithmic contribution, we derive an efficient iterative algorithm to optimize the resulting non-smooth and non-convex objective function. We theoretically prove that our solution algorithm guarantees that both the objective and the solution sequences converge to globally optimal solutions at a sub-linear convergence rate. The experimental results demonstrate the effectiveness of our new method, achieving significant improvements compared to the other competing methods. 

Abstract. Understanding the dominant climate forcings in the Pliocene is crucial to assessing the usefulness of the Pliocene as an analogue for our warmer future. Here, we implement a novel yet simple linear factorisation method to assess the relative influence of CO2 forcing in seven models of the Pliocene Model Intercomparison Project Phase 2 (PlioMIP2) ensemble. Outputs are termed “FCO2” and show the fraction of Pliocene climate change driven by CO2. The accuracy of the FCO2 method is first assessed through comparison to an energy balance analysis previously used to assess drivers of surface air temperature in the PlioMIP1 ensemble. After this assessment, the FCO2 method is applied to achieve an understanding of the drivers of Pliocene sea surface temperature and precipitation for the first time. CO2 is found to be the most important forcing in the ensemble forPliocene surface air temperature (global mean FCO2=0.56), sea surface temperature (global mean FCO2=0.56), and precipitation (global mean FCO2=0.51). The range between individual models is found to be consistent between these three climate variables, and the models generally show good agreement on the sign of the most important forcing. Our results provide the most spatially complete view of the drivers ofPliocene climate to date and have implications for both data–modelcomparison and the use of the Pliocene as an analogue for the future. ThatCO2 is found to be the most important forcing reinforces thePliocene as a good palaeoclimate analogue, but the significant effect ofnon-CO2 forcing at a regional scale (e.g. orography and ice sheet forcing at high latitudes) reminds us that it is not perfect, and these additional influencing factors must not be overlooked. This comparison is further complicated when considering the Pliocene as a state in quasi-equilibrium with CO2 forcing compared to the transient warming being experienced at present. 

Recent advances in thermally localized solar evaporation hold significant promise for vapor generation, seawater desalination, wastewater treatment, and medical sterilization. However, salt accumulation is one of the key bottlenecks for reliable adoption. Here, we demonstrate highly efficient (>80% solar-to-vapor conversion efficiency) and salt rejecting (20 weight % salinity) solar evaporation by engineering the fluidic flow in a wick-free confined water layer. With mechanistic modeling and experimental characterization of salt transport, we show that natural convection can be triggered in the confined water. More notably, there exists a regime enabling simultaneous thermal localization and salt rejection, i.e., natural convection significantly accelerates salt rejection while inducing negligible additional heat loss. Furthermore, we show the broad applicability by integrating this confined water layer with a recently developed contactless solar evaporator and report an improved efficiency. This work elucidates the fundamentals of salt transport and offers a low-cost strategy for high-performance solar evaporation.

 

Abstract Despite tectonic conditions and atmospheric CO 2 levels ( pCO 2 ) similar to those of present-day, geological reconstructions from the mid-Pliocene (3.3-3.0 Ma) document high lake levels in the Sahel and mesic conditions in subtropical Eurasia, suggesting drastic reorganizations of subtropical terrestrial hydroclimate during this interval. Here, using a compilation of proxy data and multi-model paleoclimate simulations, we show that the mid-Pliocene hydroclimate state is not driven by direct CO 2 radiative forcing but by a loss of northern high-latitude ice sheets and continental greening. These ice sheet and vegetation changes are long-term Earth system feedbacks to elevated pCO 2 . Further, the moist conditions in the Sahel and subtropical Eurasia during the mid-Pliocene are a product of enhanced tropospheric humidity and a stationary wave response to the surface warming pattern, which varies strongly with land cover changes. These findings highlight the potential for amplified terrestrial hydroclimate responses over long timescales to a sustained CO 2 forcing. 

Nonnegative Matrix Factorization (NMF) is broadly used to determine class membership in a variety of clustering applications. From movie recommendations and image clustering to visual feature extractions, NMF has applications to solve a large number of knowledge discovery and data mining problems. Traditional optimization methods, such as the Multiplicative Updating Algorithm (MUA), solves the NMF problem by utilizing an auxiliary function to ensure that the objective monotonically decreases. Although the objective in MUA converges, there exists no proof to show that the learned matrix factors converge as well. Without this rigorous analysis, the clustering performance and stability of the NMF algorithms cannot be guaranteed. To address this knowledge gap, in this article, we study the factor-bounded NMF problem and provide a solution algorithm with proven convergence by rigorous mathematical analysis, which ensures that both the objective and matrix factors converge. In addition, we show the relationship between MUA and our solution followed by an analysis of the convergence of MUA. Experiments on both toy data and real-world datasets validate the correctness of our proposed method and its utility as an effective clustering algorithm. 

Abstract. Palaeoclimate simulations improve our understanding ofthe climate, inform us about the performance of climate models in adifferent climate scenario, and help to identify robust features of theclimate system. Here, we analyse Arctic warming in an ensemble of 16simulations of the mid-Pliocene Warm Period (mPWP), derived from thePliocene Model Intercomparison Project Phase 2 (PlioMIP2). The PlioMIP2 ensemble simulates Arctic (60–90∘ N) annual meansurface air temperature (SAT) increases of 3.7 to 11.6 ∘Ccompared to the pre-industrial period, with a multi-model mean (MMM) increase of7.2 ∘C. The Arctic warming amplification ratio relative to globalSAT anomalies in the ensemble ranges from 1.8 to 3.1 (MMM is 2.3). Sea iceextent anomalies range from −3.0 to -10.4×106 km2, with a MMManomaly of -5.6×106 km2, which constitutes a decrease of 53 %compared to the pre-industrial period. The majority (11 out of 16) of models simulatesummer sea-ice-free conditions (≤1×106 km2) in their mPWPsimulation. The ensemble tends to underestimate SAT in the Arctic whencompared to available reconstructions, although the degree of underestimationvaries strongly between the simulations. The simulations with the highestArctic SAT anomalies tend to match the proxy dataset in its current formbetter. The ensemble shows some agreement with reconstructions of sea ice,particularly with regard to seasonal sea ice. Large uncertainties limit theconfidence that can be placed in the findings and the compatibility of thedifferent proxy datasets. We show that while reducing uncertainties in thereconstructions could decrease the SAT data–model discord substantially,further improvements are likely to be found in enhanced boundary conditionsor model physics. Lastly, we compare the Arctic warming in the mPWP toprojections of future Arctic warming and find that the PlioMIP2 ensemblesimulates greater Arctic amplification than CMIP5 future climate simulationsand an increase instead of a decrease in Atlantic Meridional OverturningCirculation (AMOC) strength compared topre-industrial period. The results highlight the importance of slow feedbacks inequilibrium climate simulations, and that caution must be taken when usingsimulations of the mPWP as an analogue for future climate change. 

Abstract. The Pliocene epoch has great potential to improve ourunderstanding of the long-term climatic and environmental consequences of an atmospheric CO2 concentration near ∼400 parts permillion by volume. Here we present the large-scale features of Plioceneclimate as simulated by a new ensemble of climate models of varyingcomplexity and spatial resolution based on new reconstructions ofboundary conditions (the Pliocene Model Intercomparison Project Phase 2;PlioMIP2). As a global annual average, modelled surface air temperaturesincrease by between 1.7 and 5.2 ∘C relative to the pre-industrial erawith a multi-model mean value of 3.2 ∘C. Annual mean totalprecipitation rates increase by 7 % (range: 2 %–13 %). On average, surface air temperature (SAT) increases by 4.3 ∘C over land and 2.8 ∘C over the oceans. There is a clear pattern of polar amplification with warming polewards of 60∘ N and 60∘ S exceeding the global mean warming by a factor of 2.3. In the Atlantic and Pacific oceans, meridional temperature gradients are reduced, while tropical zonal gradients remain largely unchanged. There is a statistically significant relationship between a model's climate response associated with a doubling in CO2 (equilibrium climate sensitivity; ECS) and its simulated Pliocene surface temperature response. The mean ensemble Earth system response to a doubling of CO2 (including ice sheet feedbacks) is 67 % greater than ECS; this is larger than the increase of 47 % obtained from the PlioMIP1 ensemble. Proxy-derived estimates of Pliocene sea surface temperatures are used to assess model estimates of ECS and give an ECS range of 2.6–4.8 ∘C. This result is in general accord with the ECS range presented by previous Intergovernmental Panel on Climate Change (IPCC) Assessment Reports.