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Fixed typo
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seanlaw committed Jan 9, 2022
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Expand Up @@ -72,7 +72,7 @@
"\n",
"Note that while $2 * \\sqrt {m}$ (i.e., anti-correlated) is obviously larger than $\\sqrt {2m}$ (i.e., uncorrelated), it is basically impossible for a matrix profile distance to be \"worse\" than uncorrelated (i.e., larger than $\\sqrt {2m}$) due to the fact that it is defined as the distance to its one-nearest-neighbor. For example, given a subsequence `T[i : i + m]`, the matrix profile is supposed to return the z-norm distance to its one-nearest-neighbor. So, even if there existed another z-norm subsequence, `T[j : j + m]`, along the time series that was perfectly anti-correlated with `T[i : i + m]`, then any subsequence that is even slightly shifted away from location `j` must have a smaller distance than $2 * \\sqrt {m}$. Therefore, a perfectly anti-correlated subsequence would/could (almost?) never be a one-nearest-neighbor to `T[i : i + m]` especially if `T` is long.\n",
"\n",
"However, for normalizing pan matrix profiles, $2 * \\sqrt {m}$ (anti-correlated) produces nearly identical visual results as $\\sqrt {2m}$) (correlated). Thus, we chose to normalize with $2 * \\sqrt {m}$ (anti-correlated) as it is the most obvious and intuitive choice."
"However, for normalizing pan matrix profiles, $2 * \\sqrt {m}$ (anti-correlated) produces nearly identical visual results as $\\sqrt {2m}$ (uncorrelated). Thus, we chose to normalize with $2 * \\sqrt {m}$ (anti-correlated) as it is the most obvious and intuitive choice."
]
}
],
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