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Expand Up @@ -17,7 +17,7 @@
"\n",
"### Notation\n",
"\n",
"A dataset is a set of $M$ data vectors: $\\text{X} = \\{\\vec{x}^{(j)}\\,|\\,j\\in [M]\\}$, where each vector is $N$ dimensional, that is, $\\vec{x}^{(j)}=(\\vec{x}^{(j)}_1,\\ldots,\\vec{x}^{(j)}_N)\\in\\mathbb{R}^N$. This could be extended to complex data features. In his lesson, we may occasionally use these notations for the full set $(\\text{X}),$ and its specific elements like $\\vec{x}^{(j)}$. But we will mostly refer to the loading of a single vector from our dataset at a time, and will often simply refer to a single vector of $N$ features as $\\vec{x}$.\n",
"A dataset is a set of $M$ data vectors: $\\text{X} = \\{\\vec{x}^{(j)}\\,|\\,j\\in [M]\\}$, where each vector is $N$ dimensional, that is, $\\vec{x}^{(j)}=(\\vec{x}^{(j)}_1,\\ldots,\\vec{x}^{(j)}_N)\\in\\mathbb{R}^N$. This could be extended to complex data features. In this lesson, we may occasionally use these notations for the full set $(\\text{X}),$ and its specific elements like $\\vec{x}^{(j)}$. But we will mostly refer to the loading of a single vector from our dataset at a time, and will often simply refer to a single vector of $N$ features as $\\vec{x}$.\n",
"\n",
"Additionally, it is common to use the symbol $\\Phi(\\vec{x})$ to refer to the feature mapping $\\Phi$ of data vector $\\vec{x}$. In quantum computing specifically, it is common to refer to mappings in quantum computing using $U(\\vec{x}),$ a notation that reinforces the unitary nature of these operations. One could correctly use the same symbol for both; both are feature mappings. Throughout this course, we tend to use:\n",
"* $\\Phi(\\vec{x})$ when discussing feature mappings in machine learning, generally, and\n",
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