1
00:00:00,000 --> 00:00:04,658
[MUSIC]

2
00:00:04,658 --> 00:00:08,449
But before we get to our mixture model, I
want to provide some background on one of

3
00:00:08,449 --> 00:00:11,959
the components that's going to be a really
really key component to the model

4
00:00:11,959 --> 00:00:16,050
that we're going to describe, and this is
something called a Gaussian distribution.

5
00:00:17,440 --> 00:00:21,230
So, let's go back to this histogram
over blue intensities just for

6
00:00:21,230 --> 00:00:22,930
the cloud images, and

7
00:00:22,930 --> 00:00:27,300
we said this histogram might look
something like this bell-shaped curve.

8
00:00:27,300 --> 00:00:31,350
Well, when we're taking our probabilistic
model-based approach, we're going to treat

9
00:00:31,350 --> 00:00:34,958
the blue intensity in every image
as an observed random quantity.

10
00:00:34,958 --> 00:00:39,430
And we're going to place a distribution
over that random quantity, and

11
00:00:39,430 --> 00:00:41,910
that distribution is going to
have a set of perimeters, and

12
00:00:41,910 --> 00:00:45,120
we are going to aim to learn
those perimeters from the data.

13
00:00:45,120 --> 00:00:48,010
And so the distribution that
we are going to use here,

14
00:00:48,010 --> 00:00:53,300
to model this type of shape,
this type of spread of data points,

15
00:00:53,300 --> 00:00:56,470
is something called
a Gaussian distribution.

16
00:00:56,470 --> 00:00:59,340
And in this application,
we're going to assume that a Gaussian

17
00:00:59,340 --> 00:01:04,890
distribution provides
a pretty good fit for every

18
00:01:04,890 --> 00:01:10,650
different image category,
like clouds, sunsets, and forests.

19
00:01:10,650 --> 00:01:14,620
And every dimension of the observed
vector, whether we're looking at the red,

20
00:01:14,620 --> 00:01:16,110
green, or blue dimension.

21
00:01:18,740 --> 00:01:24,330
So for example, when we're just looking
at our blue intensity dimension,

22
00:01:24,330 --> 00:01:30,540
then this Gaussian is fully specified by
two parameters, a mean and a variance.

23
00:01:30,540 --> 00:01:33,660
Or sometimes people refer instead
to the square root of the variance,

24
00:01:33,660 --> 00:01:36,100
which is called the standard deviation.

25
00:01:36,100 --> 00:01:42,290
So the mean specifies where this Gaussian
lives, so it centers the distribution,

26
00:01:42,290 --> 00:01:44,900
and the variance determines
the spread of the distribution.

27
00:01:45,960 --> 00:01:50,300
So for example, here's a Gaussian
with the same variance, but

28
00:01:50,300 --> 00:01:56,390
a different mean, so a smaller mean
than the example we showed before.

29
00:01:56,390 --> 00:02:01,290
And now here's a Gaussian
with the same mean, but

30
00:02:01,290 --> 00:02:06,900
smaller variance, and here examples
with larger and larger variances.

31
00:02:06,900 --> 00:02:10,030
So we can see how tuning these
two different parameters

32
00:02:10,030 --> 00:02:15,710
changes what this distribution looks like,
in terms of its location and its spread.

33
00:02:15,710 --> 00:02:20,840
And we're going to notate this Gaussian
distribution as follows with this N,

34
00:02:20,840 --> 00:02:24,220
sometimes the Gaussian distribution is
referred to as the normal distribution,

35
00:02:24,220 --> 00:02:26,090
that's where the N comes in.

36
00:02:26,090 --> 00:02:28,620
And this X is going to refer to

37
00:02:28,620 --> 00:02:32,430
the random variable over which
this distribution is placed.

38
00:02:32,430 --> 00:02:36,367
So, in the example we're looking at,
that's the blue intensity in the image.

39
00:02:36,367 --> 00:02:40,802
And then, everything to the right
of the bar represents the fixed

40
00:02:40,802 --> 00:02:44,684
parameters of the Gaussian,
the mean and the variance.

41
00:02:44,684 --> 00:02:48,949
[MUSIC]