# Errata

Please email us if you find any errors in the book. We will list known errata on this page.

### Chapter 1: Data Mining and Analysis

- p4, Section 1.3, line 13: "as
*linear combination*"should be "as a*linear combination*" - p9, Example 1.3, 3rd line from end: "\((153)^{1/3}\)" should be "\((152)^{1/3}\)"
- p9, Example 1.3, last line: "\( (4^3 + (-1)^3)^{1/3} = (63)^{1/3} = 3.98\)" should be "\( (4^3 + |-1|^3)^{1/3} = (65)^{1/3} = 4.02\)"
- p24, Section 1.4.3, last line of subsection
**Univariate Sample**: "where \(f_\mathbf{X}\) is the probability mass or density function for \(\mathbf{X}\)" should be "where \(f_X\) is the probability mass or density function for \(X\)" - p30, Section 1.7, Q1: "in (1.5)" should be "in Eq. (1.5)"

### Chapter 2: Numeric Attributes

- p34, Equation (2.2): "\( \hat{F}(x) \ge q \)" should be "\( F(x) \ge q \)"
- p34, Line after Equation (2.2):
"That is, the inverse CDF gives the least value of \( X\), for which \(q\) fraction of the values are higher, and \(1 − q\) fraction of the values are lower."should be"That is, the inverse CDF gives the least value of \( X\), for which \(q\) fraction of the values are
**lower**, and \(1 − q\) fraction of the values are**higher**." - p53, Example 2.6, line 1: "... range for \({\tt Income}\) is \(2700-300=2400\)" should be "... range for \({\tt Income}\) is \(6000-300=5700\)"
- p55, In Eq (2.32): "\(P(-k \le z \le k) = P\bigl(0 \le t \le k/\sqrt{2}\bigr) \)" should be "\(P(-k \le z \le k) = 2 \cdot P\bigl(0 \le t \le k/\sqrt{2}\bigr) \)"
- p58, Total and Generalized Variance, Line 2: "...product of its eigenvectors" should be "...product of its eigenvalues"
- p58, two lines above Example 2.8: "\(tr(\Lambda)\)" should be "\( tr(\mathbf{\Lambda}) \)"
- p61, Q3: "\(mu\)" should be "\(\mu\)" so that it reads

$$\sum_{i=1}^n (x_i - \mu)^2 = n(\hat{\mu} - \mu)^2 + \sum_{i=1}^n (x_i - \hat{\mu})^2$$

### Chapter 3: Categorical Attributes

- p81, Table 3.6, Attribute value for \(X_2\): "\( {\tt Short} ( a_{23}) \)" should be "\( {\tt Long} ( a_{23}) \)"

### Chapter 4: Graph Data

- p103, 2 lines above Eq (4.3): "\(\gamma_{jk} = 0 \)" should be "\(\gamma_{jk}(v_i) = 0 \)"
- p103, Eq (4.3): "\(\gamma_{jk} \)" should be "\(\gamma_{jk}(v_i) \)"
- p103, Example 4.5, last line: "\(\gamma_{jk} > 0 \)" should be "\(\gamma_{jk}(v_5) > 0 \)"
- p104, Example 4.5:
\(c(v_5) = \gamma_{18} + \gamma_{24} + \gamma_{27} + \gamma_{28} + \gamma_{38} + \gamma_{46} + \gamma_{48} + \gamma_{67} + \gamma_{68}\)should be\(c(v_5) = \gamma_{18}(v_5) + \gamma_{24}(v_5) + \gamma_{27}(v_5) + \gamma_{28}(v_5) + \gamma_{38}(v_5) + \gamma_{46}(v_5) + \gamma_{48}(v_5) + \gamma_{67}(v_5) + \gamma_{68}(v_5)\)
- p107: \(\mathbf{p}_1 = \frac{1}{2} \pmatrix{1\\ 1\\ 2\\ 1\\ 2}\) should be \(\mathbf{p}_1 = \frac{1}{2} \pmatrix{1\\ 2\\ 2\\ 1\\ 2}\)
- p127, 4th Line after Eq (4.22): "initial \(n_0\) edges" should be "initial \(n_0\) nodes"

### Chapter 5: Kernel Methods

- p138, Example 5.4:

$$\mathbf{\mu}_\phi = \sum_{i=1}^5 \phi(\mathbf{x}_i) = \sum_{i=1}^5 \mathbf{x}_i$$

- should be

$$\mathbf{\mu}_\phi = \frac{1}{5}\sum_{i=1}^5 \phi(\mathbf{x}_i) = \frac{1}{5} \sum_{i=1}^5 \mathbf{x}_i$$

- p140, 7th Line after Eq (5.3): "\(\sum_{i=1}^{m_a} \sum_{j=1}^{m_a} \alpha_i \alpha_{\!j} K(\mathbf{x}_i, \mathbf{x})\)" should be "\(\sum_{i=1}^{m_a} \sum_{j=1}^{m_a} \alpha_i \alpha_{\!j} K(\mathbf{x}_i, \mathbf{x}_j)\)"
- p141, 3rd line and 10th Line before Sec 5.1.2: There is an extra left bracket in definition of \(\phi(\mathbf{x})\), that is,
"\(\big( ( K(\mathbf{x}_1, \mathbf{x}), ... \)" should be "\( \big( K(\mathbf{x}_1, \mathbf{x}), ... \)"
- p144, 2nd line: "\(\int a(\mathbf{x})^2\; d\mathbf{x} < 0\)" should be "\(\int a(\mathbf{x})^2\; d\mathbf{x} < \infty\)"
- p144, last line: "\(\sum_{k=1}^q\)" should be "\(\sum_{k=0}^q\)"
- p156, Section 5.4.2: all occurrences of "path/paths" should be "walk/walks"

### Chapter 6: High-dimensional Data

- p164: In the definitions of the hyperball and and hypersphere
"\(\mathbf{x} = (x_1, x_2, \ldots, x_d)\)" should be "\(\mathbf{x} = (x_1, x_2, \ldots, x_d)^T\)"
- p171: "\( \mathbf{0}_d = (0_1,0_2,\ldots,0_d) \)" should be "\(\mathbf{0}_d = (0_1,0_2,\ldots,0_d)^T\)"
- p172, Section 6.6, 1st Line after Eq. (6.11):
\(\mu\) in equation "\(\mu=\mathbf{0}_d\)" should be in bold.
- p178, section "Volume in d dimensions":
"\(x_1 = r \cos\theta_1\cos\theta_2 \cos\theta_3 = r c_2 c_2 c_3\)" should be "\(x_1 = r \cos\theta_1\cos\theta_2 \cos\theta_3 = r c_1 c_2 c_3\)""\(x_3 = r \cos\theta_1\sin\theta_2 = r c_1 s_1\)" should be "\(x_3 = r \cos\theta_1\sin\theta_2 = r c_1 s_2\)"
- p178, Equation for \(J(\theta_1, \theta_2, \theta_3) \), Entry in first row, fourth column: "\( r c_1 c_2 s_3 \)"should be "\(-r c_1 c_2 s_3 \)"
- p207, line 3, Alg 7.2: "\(\eta_1, \eta_2, ..., \eta_d\)" should be "\(\eta_1, \eta_2, ..., \eta_n\)"

### Chapter 7: Dimensionality Reduction

- p186, line 1: "\( \mathbf{a}_r \) is vector" should be "\( \mathbf{a}_r \) is a vector"
- p207, line 3, Alg 7.2: "\(\eta_1, \eta_2, ..., \eta_d \)" should be "\(\eta_1, \eta_2, ..., \eta_n \)"

### Chapter 8: Itemset Mining

- p235, Example 8.13, 2nd last line: "\(...,AB(3), AD(4),...\)" should be "\(..., AB(4), AD(3), ...\)"
- p236, 5th line: "\(...,AD(4),...\)" should be "\(..., AD(3),...\)"

### Chapter 9: Summarizing Itemsets

- p250, 2nd line under
**Generalized Itemsets**: "\(k\)-tidsets" should be "\(k\) tidsets" - p250, 4th line from bottom: "\(Z = Y \setminus X\)" should be "\(Z = X \setminus Y\)"
- p252, Eq. (9.3) and Eq. (9.4): "\( \bigl|X\setminus Y\bigr| \)" should be "\( \bigl|X\setminus W\bigr| \)" on the right hand side in both equations, so that they read

$$ \textbf{Upper Bounds} \bigl(\bigl|X\setminus Y\bigr| \text{is odd} \bigr): sup(X) \leq\sum_{Y \subseteq W \subset X} -1^{\bigl(\bigl|X\setminus W\bigr|+1\bigr)} sup(W) $$ $$ \textbf{Lower Bounds} \bigl(\bigl|X\setminus Y\bigr| \text{is even}\bigr): sup(X) \geq\sum_{Y \subseteq W \subset X} -1^{\bigl(\bigl|X\setminus W\bigr|+1\bigr)} sup(W) $$

- p254, Section
**Nonderivable Itemsets**, 1st Equation after line 1: "\( \bigl|X\setminus Y\bigr| \)" should be "\( \bigl|X\setminus W\bigr| \)" , so that it reads

$$\mathit{IE}(Y) = \sum_{Y \subseteq W \subset X}\, -1^{\bigl(\bigl|X\setminus W\bigr|+1\bigr)} \cdot sup(W)$$

### Chapter 10: Sequence Mining

- p264, alg 10.2, line 9: "\(\mathbf{P}\)" should be "\( P_a \)"

### Chapter 11: Graph Pattern Mining

- p288, sec 11.3, 2nd paragraph, line 6: "\( sup(C) = sup(t) \)" should be "\( sup(C') = sup(t) \)"
- p290, Figure 11.8: The last tuple in the DFS-code for graph \(C_{19}\) should be "\( \langle 2, 0, a, a \rangle\)" and not "\( \langle 2, 0, a, b\rangle \)"
- p292, Algorithm 11.2, Line 14: "\( b=\langle u_r, v, L(u_r), L(v), L(u_r, v)\rangle \)" should be "\( b=\langle u_r, v, L(\phi(u_r)), L(\phi(v)), L(\phi(u_r),\phi(v))\rangle \)"
- p293, Figure 11.9 (c): There there should be one more extension for \(\phi_5\), namely \( \langle 0, 3, a, b\rangle \)
- p294, Algorithm 11.3, Line 12: "\( N_{G_j} \)" should be "\( N_{G} \)"
- p295, Algorithm 11.4, Line 0: "\(C\)" should be "\(C = \{t_1, t_2, ..., t_k\}\)"

### Chapter 12: Pattern and Rule Assessment

- p322 (Alg 12.1) and p326 (Alg 12.2): replace "=" with "\(\gets\)"

### Chapter 13: Representative-based Clustering

- p343, in 3rd equation: "\(P(C_i)\)" should be "\(P(C_1)\)"
- p335, Algorithm 13.1, line 7: "\(\mathbf{\mu}^t_i\)" should be "\(\mathbf{\mu}^{t-1}_i\)"

### Chapter 14: Hierarchical Clustering

- p366, Fig 14.2: "(a) \(m=1\)", "(b) \(m=2\)", and "(c) \(m=3\)" should be "(a) \(n=1\)", "(b) \(n=2\)", and "(c) \(n=3\)", respectively.
- p373, sec 14.4: "EXERCISES AND PROJECTS" should be "EXERCISES"
- p373, Q1, "\(SMC(X_i, X_j)\), \(JC(X_i, X_j)\), \(RC(X_i, X_j)\)" should be "\(SMC(\mathbf{x}_i, \mathbf{x}_j)\), \(JC(\mathbf{x}_i, \mathbf{x}_j)\), \(RC(\mathbf{x}_i, \mathbf{x}_j)\)", respectively.

### Chapter 15: Density-based Clustering

- p385, line after Eq. (15.6): "... having two parts. A vector ... " should be "... having two parts: a vector ..."

### Chapter 16: Spectral and Graph Clustering

- p411, 2nd last equation: "\( \frac{1}{2}p_{rs} \)" should be "\( p_{rs} \)" so that it reads

$$ p_{rs} = \frac{d_r}{2m}\frac{d_s}{2m} = \frac{d_r d_s}{4m^2} $$

- p413, Line 5: "\(\sum_{j=1}^n \mathbf{d}^T \mathbf{c}_i\)" should be "\(\mathbf{d}^T \mathbf{c}_i\)"
- p413, Line 10: "\((\mathbf{d}_i^T\mathbf{c}_i)^2\)" should be "\((\mathbf{d}^T\mathbf{c}_i)^2\)"
- p424, Q5: "\( \mathbf{c}_n = \frac{1}{\sqrt{n}} \mathbf{1}\)" should be "\( \mathbf{c}_n = \frac{1}{\sqrt{\sum_{i=1}^n d_i}} \mathbf{\Delta}^{1/2}\mathbf{1}\)"
- p424, Q6 (b): "\( \mathbf{K} = \mathbf{M} \)" should "\( \mathbf{K} = \mathbf{M} + \mathbf{I}\)"

### Chaper 17: Clustering Validation

- p428, Example 17.1, Table below 2nd para: "\(n=100\)" should be "\(n=150\)" for the total count
- p463, Q10: Add the sentence "Assume that the clusters are: \(C_1 = \{a,b, c,d, e\}, C_2 = \{g, i\}, C_3 = \{f,h, j \}, C_4 = \{k\}\)."

### Chapter 18: Probabilistic Classification

- p472, Example 18.2, 2nd Para, lines 6 and 7: "\(P(c_1|\mathbf{x})\)" and "\(P(c_2|\mathbf{x})\)" should be "\(\hat{P}(c_1|\mathbf{x})\)" and "\(\hat{P}(c_2|\mathbf{x})\)", respectively.

### Chapter 20: Linear Discriminant Analysis

- p503: Example 20.2: There should be no transpose operator "\(T\)" on the mean vectors, i.e.,

$$\mathbf{\mu}_1 = \pmatrix{5.01\\3.42}^T \qquad \mathbf{\mu}_2 = \pmatrix{6.26\\2.87}^T \qquad \mathbf{\mu}_1 - \mathbf{\mu}_2= \pmatrix{-1.256\\0.546}^T$$

- should be

$$\mathbf{\mu}_1 = \pmatrix{5.01\\3.42} \qquad \mathbf{\mu}_2 = \pmatrix{6.26\\2.87} \qquad \mathbf{\mu}_1 - \mathbf{\mu}_2 = \pmatrix{-1.256\\0.546}$$

- p509, Example 20.4, line 4: "
*iris-virginica*" should be "\({\tt Iris\text{-}versicolor}\)" - p512, Q1: In part (a) "\(\mathbf{S}_B\)" should be "\(\mathbf{B}\)", and in (b) "\(\mathbf{S}_W\)" should be "\(\mathbf{S}\)"

### Chapter 21: Support Vector Machines

- p526, 7th line, in \(L_{dual}\): "\((C - \alpha_i + \beta_i)\)" should be "\((C - \alpha_i - \beta_i)\)"
- p536, Algorithm 21.1, line 15: "\( \mathbf{\alpha}_{t+1} = \alpha \)" should be "\( \alpha_{t+1} \gets \alpha \)"
- p538, Example 21.8, line 5: "homogeneous quadratic kernel \(K(\mathbf{x}_i,\mathbf{x}_j) = ( \mathbf{x}^T_i \mathbf{x}_j)^2\)" should be "inhomogeneous quadratic kernel \(K(\mathbf{x}_i,\mathbf{x}_j) = (1+ \mathbf{x}^T_i \mathbf{x}_j)^2\)"