Started restoring some old images & posts; changed themes to notepadium
3
.gitmodules
vendored
@ -4,3 +4,6 @@
|
|||||||
[submodule "hugo_blag/themes/nofancy"]
|
[submodule "hugo_blag/themes/nofancy"]
|
||||||
path = hugo_blag/themes/nofancy
|
path = hugo_blag/themes/nofancy
|
||||||
url = https://github.com/gizak/nofancy.git
|
url = https://github.com/gizak/nofancy.git
|
||||||
|
[submodule "hugo_blag/themes/hugo-notepadium"]
|
||||||
|
path = hugo_blag/themes/hugo-notepadium
|
||||||
|
url = https://github.com/cntrump/hugo-notepadium.git
|
||||||
|
|||||||
@ -5,11 +5,22 @@ title = "My New Hugo Site"
|
|||||||
#theme = "indigo"
|
#theme = "indigo"
|
||||||
#theme = "zen"
|
#theme = "zen"
|
||||||
# This one *does* use 'highlight' below:
|
# This one *does* use 'highlight' below:
|
||||||
theme = "nofancy"
|
#theme = "nofancy"
|
||||||
|
|
||||||
|
theme = "hugo-notepadium"
|
||||||
|
|
||||||
|
#PygmentsCodeFences = true
|
||||||
|
#PygmentsStyle = "monokai"
|
||||||
|
|
||||||
|
[params.math]
|
||||||
|
enable = true # optional: true, false. Enable globally, default:
|
||||||
|
# false. You can always enable math on per page.
|
||||||
|
# (how?)
|
||||||
|
use = "katex" # option: "katex", "mathjax". default: "katex"
|
||||||
|
|
||||||
[params]
|
[params]
|
||||||
# See themes/nofancy/static/highlight/styles for available options
|
# See themes/nofancy/static/highlight/styles for available options
|
||||||
highlight="tomorrow"
|
#highlight="tomorrow"
|
||||||
# Controls what items are listed in the top nav menu
|
# Controls what items are listed in the top nav menu
|
||||||
# "none", or "categories"
|
# "none", or "categories"
|
||||||
# If you have too many categories to fit in the top nav menu, set this to "none"
|
# If you have too many categories to fit in the top nav menu, set this to "none"
|
||||||
@ -29,3 +40,23 @@ theme = "nofancy"
|
|||||||
# noClasses = true
|
# noClasses = true
|
||||||
# style = "monokai"
|
# style = "monokai"
|
||||||
# tabWidth = 4
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# tabWidth = 4
|
||||||
|
|
||||||
|
[params.nav]
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||||||
|
showCategories = true # /categories/
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||||||
|
showTags = true # /tags/
|
||||||
|
|
||||||
|
[[params.nav.custom]]
|
||||||
|
title = "Posts"
|
||||||
|
url = "/posts"
|
||||||
|
|
||||||
|
[[params.nav.custom]]
|
||||||
|
title = "About"
|
||||||
|
url = "/about"
|
||||||
|
|
||||||
|
[[params.nav.custom]]
|
||||||
|
title = "Old Crap"
|
||||||
|
url = "/old_crap"
|
||||||
|
|
||||||
|
[[params.nav.custom]]
|
||||||
|
title = "Hugo"
|
||||||
|
url = "https://gohugo.io/"
|
||||||
|
|||||||
|
Before Width: | Height: | Size: 409 KiB After Width: | Height: | Size: 409 KiB |
@ -16,7 +16,10 @@ implementation in a slow language for heavy computations
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|||||||
(i.e. Python), but it worked well enough to create some good results
|
(i.e. Python), but it worked well enough to create some good results
|
||||||
like this:
|
like this:
|
||||||
|
|
||||||
|
<!-- TODO: Originally:
|
||||||
[{width=50%}](../images/dla2c.png)\
|
[{width=50%}](../images/dla2c.png)\
|
||||||
|
-->
|
||||||
|

|
||||||
|
|
||||||
After about 3 or 4 failed attempts to optimize this program to not
|
After about 3 or 4 failed attempts to optimize this program to not
|
||||||
take days to generate images, I finally rewrote it reasonably
|
take days to generate images, I finally rewrote it reasonably
|
||||||
|
Before Width: | Height: | Size: 632 KiB After Width: | Height: | Size: 632 KiB |
|
Before Width: | Height: | Size: 751 KiB After Width: | Height: | Size: 751 KiB |
|
Before Width: | Height: | Size: 549 KiB After Width: | Height: | Size: 549 KiB |
|
Before Width: | Height: | Size: 124 KiB After Width: | Height: | Size: 124 KiB |
@ -54,9 +54,15 @@ the 2nd image down below) or
|
|||||||
[OpenFrameworks](http://www.openframeworks.cc/) or one of the
|
[OpenFrameworks](http://www.openframeworks.cc/) or one of the
|
||||||
too-many-completely-different-versions of Acidity I wrote.
|
too-many-completely-different-versions of Acidity I wrote.
|
||||||
|
|
||||||
|
<!-- TODO: Originals (get alt-text in?)
|
||||||
[{width=100%}](../images/hive13-bezier03.png)
|
[{width=100%}](../images/hive13-bezier03.png)
|
||||||
|
|
||||||
[{width=100%}](../images/20110118-sketch_mj2011016e.jpg)
|
[{width=100%}](../images/20110118-sketch_mj2011016e.jpg)
|
||||||
|
-->
|
||||||
|
|
||||||
|

|
||||||
|
|
||||||
|

|
||||||
|
|
||||||
[POV-Ray](http://www.povray.org) was the last program that I
|
[POV-Ray](http://www.povray.org) was the last program that I
|
||||||
3D-rendered extensively in (this was mostly 2004-2005, as my
|
3D-rendered extensively in (this was mostly 2004-2005, as my
|
||||||
@ -92,6 +98,6 @@ all the precision that I would have had in POV-Ray, but I built them
|
|||||||
in probably 1/10 the time. That's the case for the two
|
in probably 1/10 the time. That's the case for the two
|
||||||
work-in-progress Blender images here:
|
work-in-progress Blender images here:
|
||||||
|
|
||||||
[{width=100%}](../images/20110131-mj20110114b.jpg)
|

|
||||||
|
|
||||||
[{width=100%}](../images/20110205-mj20110202-starburst2.jpg)
|

|
||||||
|
Before Width: | Height: | Size: 1.4 MiB After Width: | Height: | Size: 1.4 MiB |
|
Before Width: | Height: | Size: 154 KiB After Width: | Height: | Size: 154 KiB |
|
Before Width: | Height: | Size: 291 KiB After Width: | Height: | Size: 291 KiB |
|
Before Width: | Height: | Size: 188 KiB After Width: | Height: | Size: 188 KiB |
|
Before Width: | Height: | Size: 220 KiB After Width: | Height: | Size: 220 KiB |
|
Before Width: | Height: | Size: 235 KiB After Width: | Height: | Size: 235 KiB |
|
Before Width: | Height: | Size: 274 KiB After Width: | Height: | Size: 274 KiB |
|
Before Width: | Height: | Size: 282 KiB After Width: | Height: | Size: 282 KiB |
|
Before Width: | Height: | Size: 282 KiB After Width: | Height: | Size: 282 KiB |
|
Before Width: | Height: | Size: 284 KiB After Width: | Height: | Size: 284 KiB |
|
Before Width: | Height: | Size: 286 KiB After Width: | Height: | Size: 286 KiB |
@ -48,9 +48,9 @@ expressing an identical image.
|
|||||||
|
|
||||||
One command I've used pretty frequently before posting a large photo online is:
|
One command I've used pretty frequently before posting a large photo online is:
|
||||||
|
|
||||||
```bash
|
{{<highlight bash>}}
|
||||||
jpegtran -optimize -progressive -copy all input.jpg > output.jpg
|
jpegtran -optimize -progressive -copy all input.jpg > output.jpg
|
||||||
```
|
{{< / highlight >}}
|
||||||
|
|
||||||
This losslessly converts *input.jpg* to a progressive version and
|
This losslessly converts *input.jpg* to a progressive version and
|
||||||
optimizes it as well. (*jpegtran* can do some other things losslessly
|
optimizes it as well. (*jpegtran* can do some other things losslessly
|
||||||
@ -108,7 +108,7 @@ Your libjpeg distribution probably contains something called
|
|||||||
**wizard.txt** someplace (say, `/usr/share/docs/libjpeg8a` or
|
**wizard.txt** someplace (say, `/usr/share/docs/libjpeg8a` or
|
||||||
`/usr/share/doc/libjpeg-progs`); I don't know if an online copy is
|
`/usr/share/doc/libjpeg-progs`); I don't know if an online copy is
|
||||||
readily available, but mine is
|
readily available, but mine is
|
||||||
[here](<../images/obscure_jpeg_features/libjpeg-wizard.txt>). I'll
|
[here](<./libjpeg-wizard.txt>). I'll
|
||||||
leave detailed explanation of a scan script to the "Multiple Scan /
|
leave detailed explanation of a scan script to the "Multiple Scan /
|
||||||
Progression Control" section of this document, but note that:
|
Progression Control" section of this document, but note that:
|
||||||
|
|
||||||
@ -124,7 +124,7 @@ Progression Control" section of this document, but note that:
|
|||||||
|
|
||||||
According to that document, the standard script for a progressive JPEG is this:
|
According to that document, the standard script for a progressive JPEG is this:
|
||||||
|
|
||||||
```bash
|
{{<highlight text>}}
|
||||||
# Initial DC scan for Y,Cb,Cr (lowest bit not sent)
|
# Initial DC scan for Y,Cb,Cr (lowest bit not sent)
|
||||||
0,1,2: 0-0, 0, 1 ;
|
0,1,2: 0-0, 0, 1 ;
|
||||||
# First AC scan: send first 5 Y AC coefficients, minus 2 lowest bits:
|
# First AC scan: send first 5 Y AC coefficients, minus 2 lowest bits:
|
||||||
@ -146,31 +146,36 @@ According to that document, the standard script for a progressive JPEG is this:
|
|||||||
1: 1-63, 1, 0 ;
|
1: 1-63, 1, 0 ;
|
||||||
# Y AC lowest bit scan is last; it's usually the largest scan
|
# Y AC lowest bit scan is last; it's usually the largest scan
|
||||||
0: 1-63, 1, 0 ;</pre>
|
0: 1-63, 1, 0 ;</pre>
|
||||||
```
|
{{< / highlight >}}
|
||||||
|
|
||||||
|
|
||||||
And for standard, sequential JPEG it is:
|
And for standard, sequential JPEG it is:
|
||||||
|
|
||||||
```bash
|
{{<highlight text>}}
|
||||||
0 1 2: 0 63 0 0;
|
0 1 2: 0 63 0 0;
|
||||||
```
|
{{< / highlight >}}
|
||||||
|
|
||||||
|
|
||||||
In
|
In
|
||||||
[this image](../images/obscure_jpeg_features/20100713-0107-interleave.jpg)
|
[this image](./20100713-0107-interleave.jpg)
|
||||||
I used a custom scan script that sent all of the Y data, then all Cb,
|
I used a custom scan script that sent all of the Y data, then all Cb,
|
||||||
then all Cr. Its custom scan script was just this:
|
then all Cr. Its custom scan script was just this:
|
||||||
|
|
||||||
```bash
|
{{<highlight text>}}
|
||||||
0;
|
0;
|
||||||
1;
|
1;
|
||||||
2;
|
2;
|
||||||
```
|
{{< / highlight >}}
|
||||||
|
|
||||||
|
|
||||||
While not every browser may do this right, most browsers will render
|
While not every browser may do this right, most browsers will render
|
||||||
the greyscale as its comes in, then add color to it one plane at a
|
the greyscale as its comes in, then add color to it one plane at a
|
||||||
time. It'll be more obvious over a slower connection; I purposely left
|
time. It'll be more obvious over a slower connection; I purposely left
|
||||||
the image fairly large so that the transfer would be slower. You'll
|
the image fairly large so that the transfer would be slower. You'll
|
||||||
note as well that the greyscale arrives much more slowly than the
|
note as well that the greyscale arrives much more slowly than the
|
||||||
color.
|
color. (2020 note: most browsers will now let you use their
|
||||||
|
development tools to simulate a slow connection if you really want to
|
||||||
|
see.)
|
||||||
|
|
||||||
Code & Utilities
|
Code & Utilities
|
||||||
================
|
================
|
||||||
@ -179,16 +184,18 @@ The **cjpeg** tool from libjpeg will (among other things) create a
|
|||||||
JPEG using a custom scan script. Combined with ImageMagick, I used a
|
JPEG using a custom scan script. Combined with ImageMagick, I used a
|
||||||
command like:
|
command like:
|
||||||
|
|
||||||
```bash
|
{{<highlight bash>}}
|
||||||
convert input.png ppm:- | cjpeg -quality 95 -optimize -scans scan_script > output.jpg
|
convert input.png ppm:- | cjpeg -quality 95 -optimize -scans scan_script > output.jpg
|
||||||
```
|
{{< / highlight >}}
|
||||||
|
|
||||||
|
|
||||||
Or if the input is already a JPEG, `jpegtran` will do the same
|
Or if the input is already a JPEG, `jpegtran` will do the same
|
||||||
thing, losslessly (as it's merely reordering coefficients):
|
thing, losslessly (as it's merely reordering coefficients):
|
||||||
|
|
||||||
```bash
|
{{<highlight bash>}}
|
||||||
jpegtran -scans scan_script input.jpg > output.jpg
|
jpegtran -scans scan_script input.jpg > output.jpg
|
||||||
```
|
{{< / highlight >}}
|
||||||
|
|
||||||
|
|
||||||
libjpeg has some interesting features as well. Rather than decoding an
|
libjpeg has some interesting features as well. Rather than decoding an
|
||||||
entire full-resolution JPEG and then scaling it down, for instance (a
|
entire full-resolution JPEG and then scaling it down, for instance (a
|
||||||
@ -197,7 +204,7 @@ decoding so that it will simply do the reduction for you while
|
|||||||
decoding. This takes less time and uses less memory compared with
|
decoding. This takes less time and uses less memory compared with
|
||||||
getting the full decompressed version and resampling afterward.
|
getting the full decompressed version and resampling afterward.
|
||||||
|
|
||||||
The C code below (or [here](../images/obscure_jpeg_features) or this
|
The C code below (or [here](./jpeg_split.c) or this
|
||||||
[gist](https://gist.github.com/9220146)), based loosely on `example.c`
|
[gist](https://gist.github.com/9220146)), based loosely on `example.c`
|
||||||
from libjpeg, will split up a multi-scan JPEG into a series of
|
from libjpeg, will split up a multi-scan JPEG into a series of
|
||||||
numbered PPM files, each one containing a scan. Look for
|
numbered PPM files, each one containing a scan. Look for
|
||||||
@ -207,7 +214,7 @@ processes as much input JPEG as it needs for the next scan. (It needs
|
|||||||
nothing special to build besides a functioning libjpeg. `gcc -ljpeg -o
|
nothing special to build besides a functioning libjpeg. `gcc -ljpeg -o
|
||||||
jpeg_split.o jpeg_split.c` works for me.)
|
jpeg_split.o jpeg_split.c` works for me.)
|
||||||
|
|
||||||
```c
|
{{<highlight c>}}
|
||||||
// jpeg_split.c: Write each scan from a multi-scan/progressive JPEG.
|
// jpeg_split.c: Write each scan from a multi-scan/progressive JPEG.
|
||||||
// This is based loosely on example.c from libjpeg, and should require only
|
// This is based loosely on example.c from libjpeg, and should require only
|
||||||
// libjpeg as a dependency (e.g. gcc -ljpeg -o jpeg_split.o jpeg_split.c).
|
// libjpeg as a dependency (e.g. gcc -ljpeg -o jpeg_split.o jpeg_split.c).
|
||||||
@ -342,20 +349,20 @@ void read_scan(struct jpeg_decompress_struct * cinfo,
|
|||||||
jpeg_finish_output(cinfo);
|
jpeg_finish_output(cinfo);
|
||||||
fclose(outfile);
|
fclose(outfile);
|
||||||
}
|
}
|
||||||
```
|
{{< / highlight >}}
|
||||||
|
|
||||||
Examples
|
Examples
|
||||||
========
|
========
|
||||||
|
|
||||||
Here are all 10 scans from a standard progressive JPEG, separated out with the example code:
|
Here are all 10 scans from a standard progressive JPEG, separated out with the example code:
|
||||||
|
|
||||||

|

|
||||||

|

|
||||||

|

|
||||||

|

|
||||||

|

|
||||||

|

|
||||||

|

|
||||||

|

|
||||||

|

|
||||||

|

|
||||||
@ -852,7 +852,7 @@ C & =M^\top M \\
|
|||||||
D &= \left(M^\top U - (M^\top U)^\top\right) /\ \textrm{max}(1, M^\top M)
|
D &= \left(M^\top U - (M^\top U)^\top\right) /\ \textrm{max}(1, M^\top M)
|
||||||
\end{align}
|
\end{align}
|
||||||
$$
|
$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
where $/$ is Hadamard (i.e. elementwise) division, and $\textrm{max}$ is elementwise maximum with 1. Then, the below gives the prediction for how user $u$ will rate movie $j$:
|
where $/$ is Hadamard (i.e. elementwise) division, and $\textrm{max}$ is elementwise maximum with 1. Then, the below gives the prediction for how user $u$ will rate movie $j$:
|
||||||
|
|
||||||
@ -860,7 +860,7 @@ where $/$ is Hadamard (i.e. elementwise) division, and $\textrm{max}$ is element
|
|||||||
$$
|
$$
|
||||||
P(u)_j = \frac{[M_u \odot (C_j > 0)] \cdot (D_j + U_u) - U_{u,j}}{M_u \cdot (C_j > 0)}
|
P(u)_j = \frac{[M_u \odot (C_j > 0)] \cdot (D_j + U_u) - U_{u,j}}{M_u \cdot (C_j > 0)}
|
||||||
$$
|
$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
$D_j$ and $C_j$ are row $j$ of $D$ and $C$, respectively. $M_u$ and $U_u$ are column $u$ of $M$ and $U$, respectively. $\odot$ is elementwise multiplication.
|
$D_j$ and $C_j$ are row $j$ of $D$ and $C$, respectively. $M_u$ and $U_u$ are column $u$ of $M$ and $U$, respectively. $\odot$ is elementwise multiplication.
|
||||||
|
|
||||||
@ -891,7 +891,7 @@ S_{j,i}(\chi)} u_j - u_i = \frac{1}{card(S_{j,i}(\chi))}\left(\sum_{u
|
|||||||
\in S_{j,i}(\chi)} u_j - \sum_{u \in S_{j,i}(\chi)} u_i\right)
|
\in S_{j,i}(\chi)} u_j - \sum_{u \in S_{j,i}(\chi)} u_i\right)
|
||||||
\end{split}
|
\end{split}
|
||||||
$$
|
$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
where:
|
where:
|
||||||
|
|
||||||
@ -930,7 +930,7 @@ matrix multiplication:
|
|||||||
|
|
||||||
<div>
|
<div>
|
||||||
$$C=M^\top M$$
|
$$C=M^\top M$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
since $C\_{i,j}=card(S\_{j,i}(\chi))$ is the dot product of row $i$ of $M^T$ - which is column
|
since $C\_{i,j}=card(S\_{j,i}(\chi))$ is the dot product of row $i$ of $M^T$ - which is column
|
||||||
$i$ of $M$ - and column $j$ of $M$.
|
$i$ of $M$ - and column $j$ of $M$.
|
||||||
@ -940,7 +940,7 @@ We still need the other half:
|
|||||||
|
|
||||||
<div>
|
<div>
|
||||||
$$\sum_{u \in S_{j,i}(\chi)} u_j - \sum_{u \in S_{j,i}(\chi)} u_i$$
|
$$\sum_{u \in S_{j,i}(\chi)} u_j - \sum_{u \in S_{j,i}(\chi)} u_i$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
We can apply a similar trick here. Consider first what $\sum\_{u \in
|
We can apply a similar trick here. Consider first what $\sum\_{u \in
|
||||||
S\_{j,i}(\chi)} u\_j$ means: It is the sum of only those ratings of
|
S\_{j,i}(\chi)} u\_j$ means: It is the sum of only those ratings of
|
||||||
@ -958,7 +958,7 @@ $M\_j$ (consider the definition of $M\_j$) computes this, and so:
|
|||||||
|
|
||||||
<div>
|
<div>
|
||||||
$$\sum_{u \in S_{j,i}(\chi)} u_j = M_i \cdot U_j$$
|
$$\sum_{u \in S_{j,i}(\chi)} u_j = M_i \cdot U_j$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
and as with $C$, since we want every pairwise dot product, this summation just
|
and as with $C$, since we want every pairwise dot product, this summation just
|
||||||
equals element $(i,j)$ of $M^\top U$. The other half of the summation,
|
equals element $(i,j)$ of $M^\top U$. The other half of the summation,
|
||||||
@ -967,13 +967,13 @@ the transpose of this matrix:
|
|||||||
|
|
||||||
<div>
|
<div>
|
||||||
$$\sum_{u \in S_{j,i}(\chi)} u_j - \sum_{u \in S_{j,i}(\chi)} u_i = M^\top U - (M^\top U)^\top = M^\top U - U^\top M$$
|
$$\sum_{u \in S_{j,i}(\chi)} u_j - \sum_{u \in S_{j,i}(\chi)} u_i = M^\top U - (M^\top U)^\top = M^\top U - U^\top M$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
So, finally, we can compute an entire deviation matrix at once like:
|
So, finally, we can compute an entire deviation matrix at once like:
|
||||||
|
|
||||||
<div>
|
<div>
|
||||||
$$D = \left(M^\top U - (M^\top U)^\top\right) /\ M^\top M$$
|
$$D = \left(M^\top U - (M^\top U)^\top\right) /\ M^\top M$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
where $/$ is Hadamard (i.e. elementwise) division, and $D\_{j,i} = \textrm{dev}\_{j,i}$.
|
where $/$ is Hadamard (i.e. elementwise) division, and $D\_{j,i} = \textrm{dev}\_{j,i}$.
|
||||||
|
|
||||||
@ -987,7 +987,7 @@ Finally, the paper gives the formula to predict how user $u$ will rate movie $j$
|
|||||||
$$
|
$$
|
||||||
P(u)_j = \frac{1}{card(R_j)}\sum_{i\in R_j} \left(\textrm{dev}_{j,i}+u_i\right) = \frac{1}{card(R_j)}\sum_{i\in R_j} \left(D_{j,i} + U_{u,j} \right)
|
P(u)_j = \frac{1}{card(R_j)}\sum_{i\in R_j} \left(\textrm{dev}_{j,i}+u_i\right) = \frac{1}{card(R_j)}\sum_{i\in R_j} \left(D_{j,i} + U_{u,j} \right)
|
||||||
$$
|
$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
where $R\_j = \{i | i \in S(u), i \ne j, card(S\_{j,i}(\chi)) > 0\}$, and $S(u)$ is the set of movies that user $u$ has rated. To unpack the paper's somewhat dense notation, the summation is over every movie $i$ that user $u$ rated and that at least one other user rated, except movie $j$.
|
where $R\_j = \{i | i \in S(u), i \ne j, card(S\_{j,i}(\chi)) > 0\}$, and $S(u)$ is the set of movies that user $u$ has rated. To unpack the paper's somewhat dense notation, the summation is over every movie $i$ that user $u$ rated and that at least one other user rated, except movie $j$.
|
||||||
|
|
||||||
@ -995,7 +995,7 @@ We can apply the usual trick yet one more time with a little effort. The summati
|
|||||||
|
|
||||||
<div>
|
<div>
|
||||||
$$P(u)_j = \frac{[M_u \odot (C_j > 0)] \cdot (D_j + U_u) - U_{u,j}}{M_u \cdot (C_j > 0)}$$
|
$$P(u)_j = \frac{[M_u \odot (C_j > 0)] \cdot (D_j + U_u) - U_{u,j}}{M_u \cdot (C_j > 0)}$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
#### 5.2.2.4. Approximation
|
#### 5.2.2.4. Approximation
|
||||||
|
|
||||||
@ -1003,7 +1003,7 @@ The paper also gives a formula that is a suitable approximation for larger data
|
|||||||
|
|
||||||
<div>
|
<div>
|
||||||
$$p^{S1}(u)_j = \bar{u} + \frac{1}{card(R_j)}\sum_{i\in R_j} \textrm{dev}_{j,i}$$
|
$$p^{S1}(u)_j = \bar{u} + \frac{1}{card(R_j)}\sum_{i\in R_j} \textrm{dev}_{j,i}$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
where $\bar{u}$ is user $u$'s average rating. This doesn't change the formula much; we can compute $\bar{u}$ simply as column means of $U$.
|
where $\bar{u}$ is user $u$'s average rating. This doesn't change the formula much; we can compute $\bar{u}$ simply as column means of $U$.
|
||||||
|
|
||||||
@ -1169,7 +1169,7 @@ In that sense, $P$ and $Q$ give us a model in which ratings are an interaction b
|
|||||||
|
|
||||||
<div>
|
<div>
|
||||||
$$\hat{r}_{ui}=q_i^\top p_u$$
|
$$\hat{r}_{ui}=q_i^\top p_u$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
However, some things aren't really interactions. Some movies are just (per the ratings) overall better or worse. Some users just tend to rate everything higher or lower. We need some sort of bias built into the model to comprehend this.
|
However, some things aren't really interactions. Some movies are just (per the ratings) overall better or worse. Some users just tend to rate everything higher or lower. We need some sort of bias built into the model to comprehend this.
|
||||||
|
|
||||||
@ -1177,7 +1177,7 @@ Let's call $b_i$ the bias for movie $i$, $b_u$ the bias for user $u$, and $\mu$
|
|||||||
|
|
||||||
<div>
|
<div>
|
||||||
$$\hat{r}_{ui}=\mu + b_i + b_u + q_i^\top p_u$$
|
$$\hat{r}_{ui}=\mu + b_i + b_u + q_i^\top p_u$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
This is the basic model we'll implement, and the same one described in the references at the top.
|
This is the basic model we'll implement, and the same one described in the references at the top.
|
||||||
|
|
||||||
@ -1187,7 +1187,7 @@ More formally, the prediction model is:
|
|||||||
|
|
||||||
<div>
|
<div>
|
||||||
$$\hat{r}_{ui}=\mu + b_i + b_u + q_i^\top p_u$$
|
$$\hat{r}_{ui}=\mu + b_i + b_u + q_i^\top p_u$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
where:
|
where:
|
||||||
|
|
||||||
@ -1215,7 +1215,7 @@ $$
|
|||||||
\frac{\partial E}{\partial b_i} &= 2 \sum_{r_{ui}} \left(\lambda b_i + r_{ui} - \hat{r}_{ui}\right)
|
\frac{\partial E}{\partial b_i} &= 2 \sum_{r_{ui}} \left(\lambda b_i + r_{ui} - \hat{r}_{ui}\right)
|
||||||
\end{split}
|
\end{split}
|
||||||
$$
|
$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
Gradient with respect to $p_u$ proceeds similarly:
|
Gradient with respect to $p_u$ proceeds similarly:
|
||||||
|
|
||||||
@ -1229,7 +1229,7 @@ p_u}q_i^\top p_u \right) + 2 \lambda p_u \\
|
|||||||
\frac{\partial E}{\partial p_u} &= 2 \sum_{r_{ui}} \lambda p_u - \left(r_{ui} - \hat{r}_{ui}\right)q_i^\top
|
\frac{\partial E}{\partial p_u} &= 2 \sum_{r_{ui}} \lambda p_u - \left(r_{ui} - \hat{r}_{ui}\right)q_i^\top
|
||||||
\end{split}
|
\end{split}
|
||||||
$$
|
$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
Gradient with respect to $b\_u$ is identical form to $b\_i$, and gradient with respect to $q\_i$ is identical form to $p\_u$, except that the variables switch places. The full gradients then have the standard form for gradient descent, i.e. a summation of a gradient term for each individual data point, so they turn easily into update rules for each parameter (which match the ones in the Surprise link) after absorbing the leading 2 into learning rate $\gamma$ and separating out the summation over each data point. That's given below, with $e\_{ui}=r\_{ui} - \hat{r}\_{ui}$:
|
Gradient with respect to $b\_u$ is identical form to $b\_i$, and gradient with respect to $q\_i$ is identical form to $p\_u$, except that the variables switch places. The full gradients then have the standard form for gradient descent, i.e. a summation of a gradient term for each individual data point, so they turn easily into update rules for each parameter (which match the ones in the Surprise link) after absorbing the leading 2 into learning rate $\gamma$ and separating out the summation over each data point. That's given below, with $e\_{ui}=r\_{ui} - \hat{r}\_{ui}$:
|
||||||
|
|
||||||
@ -1242,7 +1242,7 @@ $$
|
|||||||
\frac{\partial E}{\partial q_i} &= 2 \sum_{r_{ui}} \lambda q_i - e_{ui}p_u^\top\ \ \ &\longrightarrow q_i' &= q_i - \gamma\frac{\partial E}{\partial q_i} &= q_i + \gamma\left(e_{ui}p_u - \lambda q_i \right) \\
|
\frac{\partial E}{\partial q_i} &= 2 \sum_{r_{ui}} \lambda q_i - e_{ui}p_u^\top\ \ \ &\longrightarrow q_i' &= q_i - \gamma\frac{\partial E}{\partial q_i} &= q_i + \gamma\left(e_{ui}p_u - \lambda q_i \right) \\
|
||||||
\end{split}
|
\end{split}
|
||||||
$$
|
$$
|
||||||
</pre>
|
</div>
|
||||||
|
|
||||||
The code below is a direct implementation of this by simply iteratively applying the above equations for each data point - in other words, stochastic gradient descent.
|
The code below is a direct implementation of this by simply iteratively applying the above equations for each data point - in other words, stochastic gradient descent.
|
||||||
|
|
||||||
|
|||||||
@ -20,20 +20,21 @@ compilation, namespaces, multiple return values, packages, a mostly
|
|||||||
sane build system, no C preprocessor, *minimal* object-oriented
|
sane build system, no C preprocessor, *minimal* object-oriented
|
||||||
support, interfaces, anonymous functions, and closures. Those aren't
|
support, interfaces, anonymous functions, and closures. Those aren't
|
||||||
trivialities; they're all rather great things. They're all missing in
|
trivialities; they're all rather great things. They're all missing in
|
||||||
C and C++ (for the most part). They're all such common problems that
|
C and C++ (for the most part - excluding that C++11 has started
|
||||||
nearly every "practical" C/C++ project uses a lot of ad-hoc solutions
|
incorporating some). They're all such common problems that nearly
|
||||||
sitting both inside and outside the language - libraries, abuse of
|
every "practical" C/C++ project uses a lot of ad-hoc solutions sitting
|
||||||
macros, more extensive code generation, lots of tooling, and a whole
|
both inside and outside the language - libraries, abuse of macros,
|
||||||
lot of "best practices" slavishly followed - to try to solve them.
|
more extensive code generation, lots of tooling, and a whole lot of
|
||||||
(No, I don't want to hear about how this lack of very basic features
|
"best practices" slavishly followed - to try to solve them. (No, I
|
||||||
is actually a feature. No, I don't want to hear about how
|
don't want to hear about how this lack of very basic features is
|
||||||
painstakingly fucking around with pointers is the hairshirt that we
|
actually a feature. No, I don't want to hear about how painstakingly
|
||||||
all must wear if we wish for our software to achieve a greater state
|
fucking around with pointers is the hairshirt that we all must wear if
|
||||||
of piety than is accessible to high-level languages. No, I don't want
|
we wish for our software to achieve a greater state of piety than is
|
||||||
to hear about how ~$arbitrary_abstraction_level~ is the level that
|
accessible to high-level languages. No, I don't want to hear about
|
||||||
*real* programmers work at, any programmer who works above that level
|
how ~$arbitrary_abstraction_level~ is the level that *real*
|
||||||
is a loser, and any programmer who works below that level might as
|
programmers work at, any programmer who works above that level is a
|
||||||
well be building toasters. Shut up.)
|
loser, and any programmer who works below that level might as well be
|
||||||
|
building toasters. Shut up.)
|
||||||
|
|
||||||
I'm a functional programming nerd. I just happen to also have a lot of
|
I'm a functional programming nerd. I just happen to also have a lot of
|
||||||
experience being knee-deep in C and C++ code. I'm looking at Go from
|
experience being knee-deep in C and C++ code. I'm looking at Go from
|
||||||
@ -53,13 +54,12 @@ less transparently.
|
|||||||
|
|
||||||
Concurrency was made a central aim in this language. If you've not
|
Concurrency was made a central aim in this language. If you've not
|
||||||
watched Rob Pike's [[https://blog.golang.org/concurrency-is-not-parallelism][Concurrency is not parallelism]] talk, go do it now.
|
watched Rob Pike's [[https://blog.golang.org/concurrency-is-not-parallelism][Concurrency is not parallelism]] talk, go do it now.
|
||||||
While it's perhaps not my favorite approach to concurrency. While I
|
While I may not be a fan of the style of concurrency that it uses
|
||||||
may not be a fan of the style of concurrency that it uses (based on
|
(based on [[https://en.wikipedia.org/wiki/Communicating_sequential_processes][CSP]] rather than the more Erlang-ian message passing), this
|
||||||
[[https://en.wikipedia.org/wiki/Communicating_sequential_processes][CSP]] rather than the more Erlang-ian message passing), this is still a
|
is still a far superior style to the very popular concurrency paradigm
|
||||||
far superior style to the very popular concurrency paradigm of
|
of Concurrency Is Easy, We'll Just Ignore It Now and Duct-Tape the
|
||||||
Concurrency Is Easy, We'll Just Ignore It Now and Duct-Tape the
|
Support On Later, How Hard Could It Possibly Be. [[http://jordanorelli.com/post/31533769172/why-i-went-from-python-to-go-and-not-nodejs][Why I went from
|
||||||
Support On Later. [[http://jordanorelli.com/post/31533769172/why-i-went-from-python-to-go-and-not-nodejs][Why I went from Python to Go (and not node.js)]], in
|
Python to Go (and not node.js)]], in my opinion, is spot-on.
|
||||||
my opinion, is spot-on.
|
|
||||||
|
|
||||||
Many packages are available for it, and from all I've seen, they are
|
Many packages are available for it, and from all I've seen, they are
|
||||||
sensible packages - not [[https://www.reddit.com/r/programming/comments/4bjss2/an_11_line_npm_package_called_leftpad_with_only/][leftpad]]-style idiocy. I'm sure that if I look
|
sensible packages - not [[https://www.reddit.com/r/programming/comments/4bjss2/an_11_line_npm_package_called_leftpad_with_only/][leftpad]]-style idiocy. I'm sure that if I look
|
||||||
@ -92,7 +92,11 @@ system is also still very limited - particularly, things like the lack
|
|||||||
of any parametric polymorphism. I'd probably prefer something more
|
of any parametric polymorphism. I'd probably prefer something more
|
||||||
like in [[https://www.rust-lang.org][Rust]]. I know this was largely intentional as well: Go was
|
like in [[https://www.rust-lang.org][Rust]]. I know this was largely intentional as well: Go was
|
||||||
designed for people who don't want a more powerful type system, but do
|
designed for people who don't want a more powerful type system, but do
|
||||||
want types.
|
want types, and further, to support this kind of polymorphism involves
|
||||||
|
tradeoffs it looks like they were avoiding, like those Russ Cox gives
|
||||||
|
in [[https://research.swtch.com/generic][The Generic Dilemma]]. (Later note: the [[https://github.com/golang/proposal/blob/master/design/go2draft-contracts.md][Contracts - Draft Design]]
|
||||||
|
proposal for Go 2 offers a possible approach for parametric
|
||||||
|
polymorphism.)
|
||||||
|
|
||||||
My objections aren't unique. [[https://www.teamten.com/lawrence/writings/why-i-dont-like-go.html][Ten Reasons Why I Don't Like Golang]] and
|
My objections aren't unique. [[https://www.teamten.com/lawrence/writings/why-i-dont-like-go.html][Ten Reasons Why I Don't Like Golang]] and
|
||||||
[[http://yager.io/programming/go.html][Why Go Is Not Good]] have criticisms I can't really disagree with.
|
[[http://yager.io/programming/go.html][Why Go Is Not Good]] have criticisms I can't really disagree with.
|
||||||
|
|||||||
1
hugo_blag/themes/hugo-notepadium
Submodule
@ -0,0 +1 @@
|
|||||||
|
Subproject commit e479cd6fc378e0c236dac90e0a10360c232927a5
|
||||||