Let \( C_1 \) and \( C_2 \) be two sets of objects. Let \( D(x, y) \) be a measure of dissimilarity between two objects \( x \) and \( y \). Consider the following definitions of dissimilarity between \( C_1 \) and \( C_2 \):
\[
\text{DIS-1}(C_1, C_2) = \max_{x \in C_1, y \in C_2} D(x, y)
\]
\[
\text{DIS-2}(C_1, C_2) = \min_{x \in C_1, y \in C_2} D(x, y)
\]
Which of the following statements is/are correct?
Show Hint
- Single Linkage Clustering uses DIS-1
- Single Linkage Clustering uses DIS-2
- Complete Linkage Clustering uses DIS-2
- Complete Linkage Clustering uses DIS-1
The Correct Option is B, D
Solution and Explanation
Option (A): "Single Linkage Clustering uses DIS-1" is incorrect. Single Linkage uses DIS-2, not DIS-1.
Option (B): "Single Linkage Clustering uses DIS-2" is correct. Single Linkage uses the minimum dissimilarity between clusters, which is DIS-2.
Option (C): "Complete Linkage Clustering uses DIS-2" is incorrect. Complete Linkage uses DIS-1, not DIS-2.
Option (D): "Complete Linkage Clustering uses DIS-1" is correct. Complete Linkage uses the maximum dissimilarity between clusters, which is DIS-1.
Thus, the correct answers are Option (B) and Option (D).
Top Questions on Machine Learning
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Consider the neural network shown in the figure with \[ \text{inputs: } u = 2, \, v = 3 \] \[ \text{weights: } a = 1, b = 1, c = 1, d = -1, e = 4, f = -1 \] \[ \text{output: } y \] R denotes the ReLU function, \( R(x) = \max(0, x) \).
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Consider designing a linear classifier
\[ y = \text{sign}(f(x; w, b)), \quad f(x; w, b) = w^T x + b \]on a dataset \( D = \{(x_1, y_1), (x_2, y_2), \dots, (x_N, y_N)\} \), where \( x_i \in \mathbb{R}^d \), \( y_i \in \{+1, -1\} \), for \( i = 1, 2, \dots, N \).
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\[ w_{\text{new}} = w_{\text{old}} + y_n x_n, \quad b_{\text{new}} = b_{\text{old}} + y_n \]whenever \( \text{sign}(f(x_n; w_{\text{old}}, b_{\text{old}})) \neq y_n \).
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