SCI Writing - Methodology

Tips for warning a strong methodology

 Remeber that your aim is not just to describe your methods, but to show how and why applied them and to demonstrate that your research was rigorously conducted. The methodology section should clearly show why your methods suit your objectives and convince the reader that you chose the best possible approach to answering your problem statement and research questions. Throughout the section, relate your choices back to the central purpose of our dissertation.

Explain your methodological approach overall

 Begin by introduction your overall approach to the research. What research problem or question did you investigate? Depending on your discipline and approach, you might also begin with a discussion of the rationale and assumptions underpinning your methodology.

• Fig. 1 shows an overview of SPADE, our spectral method for black-box adversarial robustness evaluation. There are four key steps in our proposed approach: (a) We first construct graph-based manifolds for both input and output data of a given ML model. (b) We then compute the SPADE score for measuring the robustness of the ML model based on bijective distance mapping under the manifold setting. © We further extend the SPADE score to quantify the robustness of each input data sample. (d) We also develop SPADE-guided methods for adversarial training and robustness evaluation. As discussed in Section 4, the SPADE-guided adversarial training can be done by adaptively setting the size of the norm-bounded perturbation for each data sample according to its SPADE score, such that stronger defenses can be set up for more vulnerable data samples.
  
  Figure 1: Overview of the proposed method. (a) Given bijective input (X) and output (Y ) data samples, SPADE first constructs graph-based manifolds. (b) SPADE exploits distance mapping distortions (DMDs) on manifolds for adversarial robustness evaluation. © Each data sample is given a SPADE score to reflect its level of non-robustness. (d) Applications for SPADE-guided adversarially-robust ML.

Mathmatical symbol

• Given a facial expression dataset D f = { x i , y i } i = 1 n \mathcal{D}_f =\{ {\bf{x}}_i,y_i\}_{i=1}^{n} Df​={ xi​,yi​}i=1n​, a $K$-class facial expression classification network $f_{\theta }$ parametrized with parameter $\theta$ in weight space $\Theta$ is trained to learn in dataset ${\mathcal{D}}_f$, which can be optimized by minimizing a loss function $L_{\theta }$. For FER, assume that we adopt the multi-class cross-entropy, which can be formulated as:$$L_{\theta }=-\sum _{k=1}^K{y}_i^k\log {\widehat{y_i}}^k,$$
  where $y_i^k$ and ${\hat{y}}_i^k$ denote $k$-th entry of the ground truth and predicted vector w.r.t the instance ${\mathbf{x}}_i$, respectively.
  Similarly, assumed an AU dataset D g = { x i , z i } i = 1 n \mathcal{D}_g=\{ {\bf{x}}_i,{\bf{z}}_i\}_{i=1}^{n} Dg​={ xi​,zi​}i=1n​, an $M$-label AU detection network $g_{\phi }$ can be trained in the dataset ${\mathcal{D}}_g$. The network $g_{\phi }$ can be parametrized with parameters $\phi$ in weight space $\Phi$, which can be optimized via a loss function $L_{\phi }$. We can exploit the multi-label sigmoid-entropy loss for AU detection. It can be formulated as$$L_{\phi }=-\sum _{m=1}^M{z}_i^m\log {\hat{z}}_i^m+(1-z_i^m)\log (1-{\hat{z}}_i^m)$$Where $M$ is the number of AUs. z i m ∈ { 0 , 1 } z_i^m \in \{0,1\} zim​∈{ 0,1} denotes the $m$-th ground truth AU label of the input instance ${\mathbf{x}}_i$, and $0\le \sum _{m=1}^M{z}_i^m\le M$. ${\hat{z}}_i^m\in [0,1]$ means the predicted AU score.

Describe your methods fo data collection

 Once you have introduced your overall methodological approach, you should give full details of your data collection mehods. In quantitative research, for vaild generalizable results, you should describe your methods in enough detail for anther researcher to replicate your study. Explain how you operationalized concepts and measured your variables; your sampling method or inclusion/exclusion criteria; and any tools, procedures and materials you used to gather data.

Describe your methods of analysis

 You should indicate how you processed and analyzed the data. Avoid going into too much detail — you should not start presenting or discussing any of your results at this stage. In quantitative research, your analysis will be based on numbers. In the methods section you might include: How you prepared the data before the data before analyzing it (e.g. checking for missing data, removing outliers, transforming variables). Which software you used to analyze the data.

Evaluate and justify your methodogical choices

 Your methodology should make the case for why you chose these particular methods, especially if you did not take the most standard approach to your topic. Discuss why other methods were not suitable for your objectives, and show how this approach contributes new knowledge or understanding. You can acknowledge limitations or weakness in the approach you chose, but justify why these were outweighted by the strengths.