Personalizing Computer Science Education by Leveraging Multimodal Learning Analytics
Summary (2 min read)
Introduction
- In the last two decades, Synthetic Aperture Radar (SAR) polarimetry has shown promise through airborne research campaigns, which lead to the planning of space-borne missions that offer fully polarimetric modes (i.e., ALOS-PALSAR, TerraSAR-X and RADARSAT-2).
- SAR data classification is known to be challenging due to speckle, that results in large variation of the backscatter across neighboring pixels within the same distributed target (e.g., a field of wheat).
- Over the last two decades, research in computer vision has sought methodologies that can utilize these ideas and in the last few years a promising technique for grouping applications, spectral graph partitioning, has emerged [3], [4].
- Utilizing multiple cues that contribute to perceptual grouping process (i.e., similarity in brightness, color or texture, proximity, and contour continuity) results in segmentations that are perceptually plausible (i.e., consistent with what humans perceive).
- Detailed analysis of different aspects of the proposed scheme and validation for multiple data sets is underway.
II. SPECTRAL GRAPH PARTITIONING
- Both clustering and image segmentation can be formulated as a graph partitioning problem, by representing a set of points in an arbitrary feature space using an undirected graph G = {V,E}, where V and E represent the nodes and the edges (i.e., connections) respectively.
- Each node on the graph corresponds to a data point in feature space and the edge between two nodes, u and υ, is associated with a weight, ω(u, υ), that indicates the similarity of that pair.
- Note that the expression in (3) is the Rayleigh quotient, and if the condition on y is relaxed so that it can take on real values, the solution can be obtained by solving the generalized eigenvalue system, (D − W )y = λD y (4) where D −W is known as the graph Laplacian.
- The eigenvector that corresponds to the second smallest eigenvalue is the real valued solution for (3).
A. An algorithm for k-way partitioning: Spectral Clustering
- Based on the approach described in the previous section, the spectral clustering algorithm given by Ng et al. [4] provides k-way partitioning.
- A slightly different notation is used, where the matrix W is now called the affinity matrix, A, and I −L is replaced with L, the normalized affinity matrix.
- Therefore the eigenvectors that correspond to the largest eigenvalues are used instead of the smallest ones.
- 12 ) 5) Cluster rows of Y using the K-means algorithm Since pairwise similarities are used to determine the groups, it becomes possible to recover complicated manifold structures in the feature space, which can not be achieved by central grouping techniques (e.g., k-means or EM) that require each group member to be close to a prototype (i.e., the cluster center).
- This procedure automates the parameter selection and provides good results by adaptively choosing a scaling parameter σi for each point si.
B. Computational Complexity and Fast Approximate Solutions
- The spectral graph partitioning framework involves solving the eigenvalue problem for the normalized affinity matrix, of size N ×N , where N is the number of points (or pixels for image segmentation problems).
- The computational cost of this dense solution quickly becomes prohibitive for images of useful size.
- Therefore, an iterative method (e.g., Lanczos) can be used to obtain the solution with the time complexity of O(N2); 2) Sparse representation:.
- In the context of solving the eigenvalue problem for the normalized affinity matrix, this turns out to be very useful.
- The details of this method with application to spectral clustering can be found in [6].
III. PROPOSED SCHEME FOR CLASSIFICATION OF POLARIMETRIC SAR DATA
- The proposed scheme for classification of POLSAR data is based on the spectral clustering algorithm: Perform multi-looking on single look complex (SLC) data (i.e., for Convair-580 data set, use 10 azimuth looks).
- Apply a polarimetric SAR speckle filter, as suggested in Lee et al. [7] (i.e., use window size of 7 × 7) Apply the spectral clustering algorithm with the following modifications:.
- 4) Perform Steps 2 to 5 in the spectral clustering algorithm as in Section II-A (i.e., form matrix D and L, calculate the first k eigenvectors of L, form matrix X , normalize its rows and cluster using the K-means algorithm).
IV. RESULTS AND DISCUSSION
- The results presented in this section are obtained using a subset of the Westham Island scene shown in Figure 1.
- Therefore the authors have chosen the region of interest (ROI) shown in Figure 1(b), where most of the fields have ground truth information given in Figure 1(d).
- Figure 2 shows a set of results obtained using the proposed scheme and the Wishart classifier.
- This figure demonstrates how these normalized eigenvectors can be used to obtain “SC Result” in Figure 3.
V. CONCLUSION
- A new technique based on spectral graph partitioning is proposed for polarimetric SAR data classification and the spectral clustering algorithm is modified to account for the properties of such data.
- Edge-aligned patch-based similarity measured by the χ2 distance between histograms and spatial proximity of pixels are used to form the affinity matrix.
- It is shown that this approach not only outperforms the Wishart classifier, but also allows further improvement by offering flexibility in using additional cues (e.g., continuity, texture, optical data) and different affinity functions.
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Frequently Asked Questions (9)
Q2. How do the authors build a digital footprint for students?
For each student, the authors build a digital footprint by leveraging the data modalities available and modelling student interaction, engagement and effort in programming courses.
Q3. What is the purpose of the course?
This course introduces first-year students to more advanced programming concepts, particularly object-oriented programming, programming libraries, data structures and file handling.
Q4. How did the authors measure the predictive power of their features?
The authors measured the predictive power of their features by calculating the correlation between the students’ grades and their target, the next laboratory exam results, using the linear (Pearson) and non-linear (Spearman) correlation coefficients.
Q5. What is the main purpose of PF3?
In PF2, students learn to design simple algorithms using structured data types like lists and dictionaries, and write and debug computer programs requiring these data structures in Python.
Q6. What is the way to grade programming submissions?
Their programming grading system also provides real-time feedback on each submission by running a suite of test cases but provides no code suggestions or personalised help for errors.
Q7. What was the approach used for the programming recommendations?
The approach the authors chose for the programming recommendations was to pick the closest text program from top-ranked students in the class that year.
Q8. What was the classifier for the fail class?
In SH1, Random Forest looked like the most promising classifier with the highest fail class F1score, 74.26% but a very low value for the pass class: 32.20%.
Q9. What are the advantages of using automatic interventions for programming classes?
Automatic interventions for programming classes are having great success in other institutions and environments and the authors are eager to develop their own strategies using their platforms and resources.