Week 4
$$\gdef \sam #1 {\mathrm{softargmax}(#1)}$$
$$\gdef \vect #1 {\boldsymbol{#1}} $$
$$\gdef \matr #1 {\boldsymbol{#1}} $$
$$\gdef \E {\mathbb{E}} $$
$$\gdef \V {\mathbb{V}} $$
$$\gdef \R {\mathbb{R}} $$
$$\gdef \N {\mathbb{N}} $$
$$\gdef \relu #1 {\texttt{ReLU}(#1)} $$
$$\gdef \D {\,\mathrm{d}} $$
$$\gdef \deriv #1 #2 {\frac{\D #1}{\D #2}}$$
$$\gdef \pd #1 #2 {\frac{\partial #1}{\partial #2}}$$
$$\gdef \set #1 {\left\lbrace #1 \right\rbrace} $$
% My colours
$$\gdef \aqua #1 {\textcolor{8dd3c7}{#1}} $$
$$\gdef \yellow #1 {\textcolor{ffffb3}{#1}} $$
$$\gdef \lavender #1 {\textcolor{bebada}{#1}} $$
$$\gdef \red #1 {\textcolor{fb8072}{#1}} $$
$$\gdef \blue #1 {\textcolor{80b1d3}{#1}} $$
$$\gdef \orange #1 {\textcolor{fdb462}{#1}} $$
$$\gdef \green #1 {\textcolor{b3de69}{#1}} $$
$$\gdef \pink #1 {\textcolor{fccde5}{#1}} $$
$$\gdef \vgrey #1 {\textcolor{d9d9d9}{#1}} $$
$$\gdef \violet #1 {\textcolor{bc80bd}{#1}} $$
$$\gdef \unka #1 {\textcolor{ccebc5}{#1}} $$
$$\gdef \unkb #1 {\textcolor{ffed6f}{#1}} $$
% Vectors
$$\gdef \vx {\pink{\vect{x }}} $$
$$\gdef \vy {\blue{\vect{y }}} $$
$$\gdef \vb {\vect{b}} $$
$$\gdef \vz {\orange{\vect{z }}} $$
$$\gdef \vtheta {\vect{\theta }} $$
$$\gdef \vh {\green{\vect{h }}} $$
$$\gdef \vq {\aqua{\vect{q }}} $$
$$\gdef \vk {\yellow{\vect{k }}} $$
$$\gdef \vv {\green{\vect{v }}} $$
$$\gdef \vytilde {\violet{\tilde{\vect{y}}}} $$
$$\gdef \vyhat {\red{\hat{\vect{y}}}} $$
$$\gdef \vycheck {\blue{\check{\vect{y}}}} $$
$$\gdef \vzcheck {\blue{\check{\vect{z}}}} $$
$$\gdef \vztilde {\green{\tilde{\vect{z}}}} $$
$$\gdef \vmu {\green{\vect{\mu}}} $$
$$\gdef \vu {\orange{\vect{u}}} $$
% Matrices
$$\gdef \mW {\matr{W}} $$
$$\gdef \mA {\matr{A}} $$
$$\gdef \mX {\pink{\matr{X}}} $$
$$\gdef \mY {\blue{\matr{Y}}} $$
$$\gdef \mQ {\aqua{\matr{Q }}} $$
$$\gdef \mK {\yellow{\matr{K }}} $$
$$\gdef \mV {\lavender{\matr{V }}} $$
$$\gdef \mH {\green{\matr{H }}} $$
% Coloured math
$$\gdef \cx {\pink{x}} $$
$$\gdef \ctheta {\orange{\theta}} $$
$$\gdef \cz {\orange{z}} $$
$$\gdef \Enc {\lavender{\text{Enc}}} $$
$$\gdef \Dec {\aqua{\text{Dec}}}$$
Practicum
We start with a brief review of linear algebra and then extend the topic to convolutions using audio data as an example. Key concepts like locality, stationarity and Toeplitz matrix are reiterated. Then we give a live demo of convolution performance in pitch analysis. Finally, there is a short digression about the dimensionality of different data.