# Errata for First Edition

## 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

\begin{equation*} \sum_{i=1}^n (x_i - \mu)^2 = n(\hat{\mu} - \mu)^2 + \sum_{i=1}^n (x_i - \hat{\mu})^2 \end{equation*}

## 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

• p160, Example 5.15L $$\mathbf{S} = -\mathbf{L} = \mathbf{A}-\mathbf{D}$$ should be $$\mathbf{S} = -\mathbf{L} = \mathbf{A}-\mathbf{\Delta}$$

## 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: $$r c_1 c_2 s_3$$-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 ...

• p387, Alg 15.2, line 20: In the numerator $$K\left(\frac{\mathbf{x}_t - \mathbf{x}_i}{h} \right) \cdot \mathbf{x}_t$$ should be $$K\left(\frac{\mathbf{x}_t - \mathbf{x}_i}{h} \right) \cdot \mathbf{x}_i$$

## 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 be $$\mathbf{K} = \mathbf{M} + \mathbf{I}$$

## 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, Table 18.2: 13/50 should be 11/50

• 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 $$K(\mathbf{x}_i,\mathbf{x}_j) = (1+ \mathbf{x}^T_i \mathbf{x}_j)^2$$