Support Vector Machines in One and Two Dimensions
A step-by-step animated walkthrough of two worked SVM examples. The first shows study-hours data on a number line, with fail and pass clusters separated by a decision boundary at 5, support vectors at 3 and 7, and margins of 2 highlighted before classifying new students at 6 and 4 hours. The second extends the idea to two features, study hours and attendance, plotted on a 2D graph to show how SVM separates classes with a boundary and margin. Useful for students learning classification and margin maximization.
16:9 · every frame verified for overlaps, spacing and edges before rendering
The prompt that made it
Create a 2-minute professional animated educational video based on the provided slide: “Support Vector Machine (SVM) – Examples.” The video should teach SVM through the two worked examples shown in the slide, using the same numerical values and concepts. Do not simply display the slide as a static image. Recreate the important tables, data points, graphs, decision boundaries, support vectors, margins, and classification steps as clean animated 2D graphics. PART 1 – SVM WITH ONE FEATURE Begin with the training data: S1: Study Hours = 1 → Fail S2: Study Hours = 2 → Fail S3: Study Hours = 3 → Fail S4: Study Hours = 7 → Pass S5: Study Hours = 8 → Pass S6: Study Hours = 9 → Pass Animate these points appearing on a one-dimensional number line. Clearly show the Fail points at 1, 2, and 3 and the Pass points at 7, 8, and 9. Show the large gap between the two classes. Then animate the SVM decision boundary moving through the gap and settling at 5 study hours. Highlight the closest Fail point at 3 hours and the closest Pass point at 7 hours as the support vectors. Draw the margin from the decision boundary at 5 to each support vector and display: Margin = 2 hours on each side Then introduce two new students: New Student: 6 hours → PASS New Student: 4 hours → FAIL Animate the classification using the decision boundary at 5 hours. PART 2 – SVM WITH TWO FEATURES Transition to a 2D coordinate graph with: X-axis = Study Hours per day Y-axis = Attendance (%) Animate the following training points: S1 = (2, 60) → Fail S2 = (3, 65) → Fail S3 = (4, 70) → Fail S4 = (6, 70) → Pass S5 = (7, 75) → Pass S6 = (8, 80) → Pass Show the two classes appearing on the graph. Then animate the vertical decision boundary at X₁ = 5 separating Fail and Pass. Highlight S3 = (4,70) and S4 = (6,70) as the support vectors, because they are the closest points to the decision boundary. Show the margin on both sides: Boundary = X₁ = 5 Margin = 1 hour on each side Animate the two margin lines at approximately X₁ = 4 and X₁ = 6, and visually show that the support vectors lie on these margin boundaries. Finally, introduce: New Student = (5.5,72) → PASS New Student = (4.2,78) → FAIL Animate each new point appearing on the graph and show which side of the decision boundary it falls on. FINAL SUMMARY End with a clean animated summary showing: SVM finds the best separating boundary by maximizing the margin. Support vectors are the closest training points and determine the position of the boundary. Example 1: Boundary = 5 hours | Margin = 2 hours Example 2: Hyperplane = X₁ = 5 | Margin = 1 hour Use smooth transitions, moving data points, animated arrows, dashed decision-boundary lines, highlighted support vectors, margin measurements, and clear labels. VOICE-OVER: Generate a professional, clear English voice-over automatically during video generation. Synchronize the narration precisely with each animation and calculation. The narration should explain the concepts step-by-step as they appear rather than simply reading the slide text. Use a calm academic female voice, suitable for a university Computer Science lecture. Keep the explanation technically accurate and easy for undergraduate students to understand. CAPTIONS: Add synchronized English subtitles. Highlight important terms such as Decision Boundary, Hyperplane, Margin, Support Vectors, Maximum Margin, Fail, and Pass when they are spoken. STYLE: Clean academic 2D mathematical/ML animation. No human avatar, no presenter, no talking character, no stock footage. Use only graphs, data points, tables, labels, arrows, mathematical diagrams and animated visualizations. FORMAT: 16:9 landscape, approximately 2 minutes, professional university teaching video.
Make the next one in this series
- Show how SVM handles a non-linearly separable dataset using a kernel trick visualization
- Animate the effect of changing the C parameter on margin width and misclassification tolerance
- Compare SVM decision boundaries to logistic regression boundaries on the same dataset
