# Information Fusion for Multi-Source Material Data: Progress and Challenges
## 3 Progress of Information Fusion for Multi-Source Material Data
### Algorithms for Material Data Fusion
#### 3.4.1 Data-Level Fusion  
Data-level fusion is the lowest level of data fusion, which aims to directly process the acquired raw data and resolve possible conflicts. For resolving data conflicts in data fusion, there are many conflict resolution and data merging methods based on different ideas, which can be classified as follows:  
1. Manual methods, e.g., using crowdsourcing to solve conflicts that are easy to be judged by humans [38]. The basic goal of crowdsourcing algorithms is to select a set of tasks to ask crowds, in order to improve the confidence of data under limited budgets, which is an optimization problem. The crowdsourcing fusion system architecture is shown in Figure 4.  
Figure 4: The working process of a crowdsourcing fusion system.  
Figure 3: The fusion process, including three levels.  
2. Truth finding methods. In the literature [39], the authors ranked multiple material data sources by considering the relationships between them to discover truth in material science databases. CRH [23] is an amenable framework for material data fusion, which resolves conflicts from different sources for each entry. It provides more accurate results compared with the voting-based approach. The proposed objective function in the CRH framework characterizes the overall difference between unknown truths and input data, while modeling source reliability as unknown source weights. The CRH framework can improve the performance of existing approaches due to its ability of tightly coupling various data types in the conflict resolution and source reliability estimation process. Running time on both single and Hadoop cluster machines demonstrates its efficiency, which has great potential for material data fusion due to the large amount of material data.  
3. Mathematic statistic-based methods, e.g., MRF (Markov Random Field). In the literature [40], measurements from one or multiple sensors need to be combined in a consistent manner in order to build a grid map, which is a grid-mapping problem. GMRFs (Gaussian Markov Random Fields) can be used to learn a prior map by using the conditional independence property between spatial locations to obtain a representation of the state with a sparse information matrix. GMRFs are MRFs where all variables \(\xi_{1}\),..., \(\xi_{n}\) are jointly Gaussians. The Markov property is depicted as: For \(i\
eq j\), \(\xi_{i}\) and \(\xi_{j}\) are independent, conditional on the other variables. The continuously indexed GMRF is used to build the prior map \(p(\xi|X)\sim N(\eta,Q^{-1})\). Considering \(n\) observations \(y_{i}\) at locations \(x_{i}\), \(i=1\),..., \(n\), the model is shown in Equation (1).  
\[y_{i}=\xi_{i}+\varepsilon_{i}=f(x_{i})+\varepsilon_{i}\,\ \xi\sim N\Big{(}m(X),\ Q^{-1}(X,X)\Big{)} \tag{1}\]  
where \(m\) is the mean function, the function \(f\) models the underlying process and \(\varepsilon_{i}\) is the \(i^{\text{th}}\) noise term. The noise is considered independent, distributed as \(N(0,\ \sigma_{\varepsilon,i}^{2})\). Having obtained the spatially correlated prior map \(p(\xi|X)\sim N\left(\eta,Q^{-1}\right)\), we model the new independent measurements \(z\) as Gaussian distributed, which is shown in Equation (2).  
\[p(z|\xi,x)=N\Big{(}\mu_{z},Q_{z}^{-1}\Big{)} \tag{2}\]