Errata for First Edition

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)

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

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

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 $\mathbf{S} = -\mathbf{L} = \mathbf{A}-\mathbf{\Delta}$

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: $r c_1 c_2 s_3`**should be** :math:$-r c_1 c_2 s_3`

p207, line 3, Alg 7.2: $\eta_1, \eta_2, ..., \eta_d$ should be $\eta_1, \eta_2, ..., \eta_n$

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

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

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

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 $\mathbf{S}$