1
00:00:00,000 --> 00:00:03,540
by the way, just for you, so what we're
doing right now, do you see what

2
00:00:03,540 --> 00:00:07,360
we're doing here? Yeah, so we're taking
the two by two image, we're

3
00:00:07,360 --> 00:00:09,240
unwrapping it, that's called vectorizing.

4
00:00:09,580 --> 00:00:12,840
We're turning it into a row vector and
then we're stacking different images

5
00:00:12,840 --> 00:00:14,380
on top of each other as row vectors.

6
00:00:14,640 --> 00:00:16,680
So that's usually- Oh, you're stacking
that on top of each other.

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00:00:16,740 --> 00:00:20,880
Yeah, yeah. Okay, so- So this row
represents the first

8
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image and this row represents the second
image, right?

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00:00:23,740 --> 00:00:26,860
And we see we have one, zero, zero,

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one,

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zero, one, one, like that.

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But the point is that this

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object is a single point in

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00:00:41,260 --> 00:00:45,500
four dimensions, just like each of these
objects are single

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points in two dimensions.

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I see. So you can take that and roll with
it and you can just

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00:00:51,260 --> 00:00:52,780
make big images, right?

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00:00:52,980 --> 00:00:56,380
250, you know, 64 by 64 images.

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00:00:56,740 --> 00:00:59,400
You can unwrap them into 4,096
coordinates.

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into a single point within space.

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00:01:01,540 --> 00:01:05,440
And you can say that 4096 length vector is
a single point in

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00:01:05,440 --> 00:01:08,920
4096 dimensions. So here's a question for
you.

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00:01:09,060 --> 00:01:13,240
So the current photos that are being sent
back from the James Webb- Yeah.

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Is that- […] huge.

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00:01:15,100 --> 00:01:16,300
So that's a single point.

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Even that alone- Yeah, yeah, yeah, yeah,
anything.

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It's a single point in ridiculously high
dimensional space.

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Yeah, that'd be crazy.

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00:01:23,700 --> 00:01:25,380
Yeah. It's so much data.

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Yeah. Those […] are massive.

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00:01:28,080 --> 00:01:31,980
Yeah, yeah, yeah. So I mean, it would be
an absurdly high space.

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00:01:32,340 --> 00:01:36,260
Right. But the point is, it's still a-
It's still a point- It's still just a

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point within-

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00:01:38,340 --> 00:01:42,080
It's still just a point within- Oh, I see,
I see, I see.

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00:01:42,200 --> 00:01:44,720
Right? So- Because you can always just
unwrap it the same way you did with

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00:01:44,720 --> 00:01:49,180
the small- So is the dimensionality
defined by the amount that you unwrap?

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00:01:49,440 --> 00:01:51,420
Exactly. So it's like 0, 1 to n.

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00:01:51,780 --> 00:01:55,580
Mm-hm. And so like this n being the

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00:01:55,580 --> 00:01:57,660
dimensionality. Exactly, exactly.

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00:01:58,940 --> 00:02:00,320
Oh, that's interesting.

41
00:02:00,600 --> 00:02:03,880
So that's 100 points in however many-
Right.

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00:02:03,880 --> 00:02:08,160
If they're 64 by 64, that's 100 points and
those points live in

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00:02:08,160 --> 00:02:09,420
how many dimensions?

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00:02:10,220 --> 00:02:12,020
If each image is 64 by 64.

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00:02:12,180 --> 00:02:13,000
That's 64 dimensions.

46
00:02:14,000 --> 00:02:17,420
No. Well, wait, did you say- It's a- Each
one is 64 by 64.

47
00:02:18,000 --> 00:02:21,660
Oh, then it's going to be 64 to the 64th
power.

48
00:02:22,040 --> 00:02:23,660
No. No? What would it be?

49
00:02:23,720 --> 00:02:28,120
64 to the 64th power is 64 times 64 times
64 times

50
00:02:28,120 --> 00:02:28,900
64 times 64 times 64 times 64 times 64
times 64 times 64 times 64 times 64

51
00:02:28,900 --> 00:02:29,680
times 64 times 64 times 64 times 64 times
64 times- So it's going to be 64

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00:02:29,680 --> 00:02:32,340
times 64. Exactly. I see.

53
00:02:33,880 --> 00:02:38,260
So let's be really clear about the rows
are observations and the

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00:02:38,260 --> 00:02:42,340
columns are information about those

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00:02:42,340 --> 00:02:46,020
observations. So that's always how data
tables work.

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00:02:47,080 --> 00:02:51,560
So? But at least that's always how we're
going to think about data tables.

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00:02:59,280 --> 00:03:02,480
So observations right here.

58
00:03:02,820 --> 00:03:06,940
Yep. And then this is information.

59
00:03:07,460 --> 00:03:11,200
Yep. Also called the- In machine learning
we would call those the features.

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00:03:17,360 --> 00:03:19,340
Yeah. You could also call it the
dimension.

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00:03:20,520 --> 00:03:24,520
But dimension, I don't really like
dimension because, right, when we talked

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00:03:24,520 --> 00:03:27,680
about that tensor over there, we're saying
that tensor is three-dimensional

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00:03:27,680 --> 00:03:29,500
and that's kind of a different thing.

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00:03:29,500 --> 00:03:30,960
So let's just stick with features.

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00:03:31,260 --> 00:03:34,620
Because there's a few different ways to
interpret dimension and I don't want

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00:03:34,620 --> 00:03:36,800
to get into that. Because that can get a
little confusing.

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00:03:36,940 --> 00:03:40,020
For whoever might be watching this, I
apologize for my handwriting.

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00:03:41,160 --> 00:03:45,600
So okay great so observations are the rows
and the features

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00:03:45,600 --> 00:03:46,580
are the color. This is a good exercise.

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00:03:47,000 --> 00:03:48,360
So now say these are RGB.

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00:03:49,240 --> 00:03:51,280
So now how does that change things?

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00:03:51,420 --> 00:03:52,260
What do we do if they're RGB?

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00:03:52,920 --> 00:03:54,380
Oh interesting, okay.

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00:03:55,100 --> 00:03:57,420
So if they're RGB we then need...

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00:03:57,420 --> 00:04:00,720
Is that... Where's the […]...

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00:04:01,840 --> 00:04:02,940
I'll just grab this one.

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00:04:03,560 --> 00:04:07,900
So if it's RGB then we actually need it to
dictate

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00:04:07,900 --> 00:04:09,740
not to zero to one

79
00:04:11,020 --> 00:04:12,380
it would actually need to...

80
00:04:15,300 --> 00:04:15,820
Okay.

81
00:04:16,620 --> 00:04:19,780
It would be a matrix of

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00:04:19,780 --> 00:04:22,760
the red green blue champ.

83
00:04:22,960 --> 00:04:26,900
I think what it would be is it would be
the first image which would be R.

84
00:04:27,340 --> 00:04:28,820
You'd put all the R information.

85
00:04:29,020 --> 00:04:33,100
So say we'll just put some arbitrary
numbers in here just to

86
00:04:33,100 --> 00:04:36,520
do some […]. Yeah. Um,

87
00:04:37,460 --> 00:04:39,000
one, then zero,

88
00:04:40,080 --> 00:04:44,580
zero, one. Mm-hmm. So the way it would
roll out is it

89
00:04:44,580 --> 00:04:48,380
would still be a single row but then it
would be zero,

90
00:04:49,260 --> 00:04:50,580
one, zero,

91
00:04:51,720 --> 00:04:52,880
one, zero,

92
00:04:53,860 --> 00:04:58,000
one, zero, one. And that would be your
image.

93
00:04:58,260 --> 00:05:01,620
Wait, so where'd you get the zero, one,
zero, one, zero, one, zero, one from?

94
00:05:01,780 --> 00:05:05,720
I'm just dictating an arbitrary value in
there.

95
00:05:05,880 --> 00:05:10,040
Okay. Just so I could explain how it would
be packaged

96
00:05:10,040 --> 00:05:11,460
into a matrix. Got it.

97
00:05:12,020 --> 00:05:12,880
So, um,

98
00:05:13,880 --> 00:05:17,960
yeah. So, I think this brings an important

99
00:05:17,960 --> 00:05:22,240
consideration into account that there's a
lot of different ways to represent

100
00:05:22,240 --> 00:05:26,660
information. Yeah. Um, people actually do
do this in practice a lot

101
00:05:26,660 --> 00:05:27,780
of the time, right? Is this?

102
00:05:27,780 --> 00:05:30,640
So that's, they'll concatenate the red,
green, and blue channels.

103
00:05:30,800 --> 00:05:33,920
Is this, like, it's obviously viable but
is it,

104
00:05:34,240 --> 00:05:38,480
I feel like you, it's not that you're
gonna lose

105
00:05:38,480 --> 00:05:41,360
information. It gets muddy to read at a
point.

106
00:05:41,920 --> 00:05:43,740
Yeah, yeah, but that's fine, right?

107
00:05:43,920 --> 00:05:47,920
I mean, um, how you organize it, it,

108
00:05:48,080 --> 00:05:52,560
if you, if you organize something
differently, then it's just

109
00:05:52,560 --> 00:05:54,900
a different organizational structure a lot
of the time, right?

110
00:05:54,980 --> 00:05:57,400
Like, you can organize it however you want
as long as you don't lose

111
00:05:57,400 --> 00:06:00,080
information and most of the time it'll be
the same result.

112
00:06:00,660 --> 00:06:03,160
So, you'll just, you'll just have three
matrices, right?

113
00:06:03,260 --> 00:06:07,580
Right. You'll have one green matrix, one
red matrix, and one

114
00:06:07,580 --> 00:06:11,800
blue matrix. Um, and then, uh, the nice
thing is that in

115
00:06:11,800 --> 00:06:16,120
practice, you know, with something like,
uh, PyTorch, which, um, or

116
00:06:16,120 --> 00:06:18,080
NumPy, which is what, you know,

117
00:06:18,940 --> 00:06:21,820
ML practitioners would actually use in
practice to store data.

118
00:06:21,820 --> 00:06:25,540
Um, you have this three-dimensional array,
so, right?

119
00:06:25,920 --> 00:06:28,380
Right, so you could store data like, um,

120
00:06:29,900 --> 00:06:33,400
uh, you could store data into one array,
but it would be the first dimension

121
00:06:33,400 --> 00:06:37,600
is the stacks, uh, of, of, of,

122
00:06:38,700 --> 00:06:40,040
think of a cube. Okay.

123
00:06:40,480 --> 00:06:44,360
Right? And stacked on top of each other
are, um,

124
00:06:45,620 --> 00:06:47,360
uh, are images. Okay.

125
00:06:47,360 --> 00:06:49,760
Um, and then, um,

126
00:06:50,560 --> 00:06:52,920
sorry, it's a cube, um.

127
00:06:53,480 --> 00:06:54,480
Do you want to draw it real quick?

128
00:06:54,620 --> 00:06:55,620
Yeah, yeah, yeah, yeah.

129
00:06:55,980 --> 00:07:00,360
It doesn't actually matter how you
organize it, so I would say it

130
00:07:00,360 --> 00:07:03,280
would be like, uh, say you have two, uh,

131
00:07:03,740 --> 00:07:08,240
so this would be your

132
00:07:08,240 --> 00:07:12,240
R layer, this would be your

133
00:07:12,240 --> 00:07:15,100
B layer, and this would be your G layer.

134
00:07:15,100 --> 00:07:17,220
Mm-hmm. Like, like this, right?

135
00:07:17,920 --> 00:07:18,780
Yeah, I see. Like this, right?

136
00:07:19,040 --> 00:07:23,320
And then, in the R layer, you would have,
um, you know, your

137
00:07:23,320 --> 00:07:27,760
first 0, 1, 0. Um, this would be your
first

138
00:07:27,760 --> 00:07:31,080
image, and then you would have a second
image here,

139
00:07:31,480 --> 00:07:35,760
and so on, right? So you would vectorize
it the way that we talked about, but

140
00:07:35,760 --> 00:07:37,960
then you would just stack the red, the
blue, and the green.

141
00:07:37,960 --> 00:07:42,420
So that is the same data structure as that
2D thing, so,

142
00:07:42,420 --> 00:07:44,040
so this is literally,

143
00:07:44,920 --> 00:07:48,400
imagine this, but then there's, like,
layers of that.

144
00:07:48,560 --> 00:07:51,880
Yeah. Right? So, like, you take this
plane, and then you just add two more

145
00:07:51,880 --> 00:07:52,160
planes.