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Natalka [10]
3 years ago
9

In this problem set, you will implement multidimensional scaling (MDS) from scratch. You may use standard matrix/vector librarie

s (e.g. numpy) but you must implement two dimensional MDS itself on your own and not use an existing software package. MDS attempts to find an arrangement of points such that the distances between points match human-judged similarities. To do this, we will minimize the stress, which is the squared difference between psychological and MDS distances:
Engineering
1 answer:
EleoNora [17]3 years ago
8 0

Features of Multidimensional scaling(MDS) from scratch is described below.

Explanation:

Multidimensional scaling (MDS) is a way to reduce the dimensionality of data to visualize it.  We basically want to project our (likely highly dimensional) data into a lower dimensional space and preserve the distances between points.  

If we have some highly complex data that we project into some lower N dimensions, we will assign each point from our data a coordinate in this lower dimensional space, and the idea is that these N dimensional coordinates are ordered based on their ability to capture variance in the data.  Since we can only visualize things in 2D, this is why it is common to assess your MDS based on plotting the first and second dimension of the output.  

If you look at the output of an MDS algorithm, which will be points in 2D or 3D space, the distances represent similarity. So very close points = very similar, and points farther away from one another = less similar.

Working of MDS

The input to the MDS algorithm is our proximity matrix.  There are  two kinds of classical MDS that we could use:  Classical (metric) MDS is for data that has metric properties, like actual distances from a map or calculated from a vector .Nonmetric MDS is for more ordinal data (such as human-provided similarity ratings) for which we can say a 1 is more similar than a 2, but there is no defined (metric) distance between the values of 1 and 2.

Uses

Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a dataset. MDS is used to translate "information about the pairwise 'distances' among a set of n objects or individuals" into a configuration of n points mapped into an abstract Cartesian space.

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Chemical milling is used in an aircraft plant to create pockets in wing sections made of an aluminum alloy. The starting thickne
Lelu [443]

Answer:

a) metal removal rate is 1915.37 mm³/min

b) the time required to etch to the specified depth is 500 min or 8.333 hrs

Explanation:

Given the data in the question;

starting thickness of one work part of interest = 20 mm

depth of series of rectangular-shaped pockets = 12 mm

dimension of pocket = 200 mm by 400 mm

radius of corners of each rectangle = 15 mm

penetration rate = 0.024 mm/minute

etch factor = 1.75

a)

To get the metal removal rate MRR;

The initial area will be smaller compare to the given dimensions of 200mm by 400mm and the metal removal rate would increase during the cut as area is increased. so'

A = 200 × 400 - ( 30 × 30 - ( π × 15² ) )

= 80000 - ( 900 - 707 )      

= 80000 - 193

A = 79807 mm²

Hence, metal removal rate MRR = penetration rate × A

MRR = 0.024 mm/minute × 79807 mm²

MRR = 1915.37 mm³/min

Therefore, metal removal rate is 1915.37 mm³/min

b) To get the time required to etch to the specified depth;

Time to machine ( etch ) =  depth of series of rectangular-shaped pockets / penetration rate

we substitute

Time to machine ( etch ) = 12 mm / 0.024 mm/minute

Time to machine ( etch ) = 500 min or 8.333 hrs

Therefore, the time required to etch to the specified depth is 500 min or 8.333 hrs

3 0
3 years ago
Is there a way to get the answers to a NCCER book test?
sergeinik [125]

Answer:

go on google and type NCEER book answers

3 0
3 years ago
Pipe (2) is supported by a pin at bracket C and by tie rod (1). The structure supports a load P at pin B. Tie rod (1) has a diam
Galina-37 [17]

Answer:

P_max = 25204 N

Explanation:

Given:

- Rod 1 : Diameter D = 12 mm , stress_1 = 110 MPa

- Rod 2: OD = 48 mm , thickness t = 5 mm , stress_2 = 65 MPa

- x_1 = 3.5 mm ; x_2 = 2.1 m ; y_1 = 3.7 m

Find:

- Maximum Force P_max that this structure can support.

Solution:

- We will investigate the maximum load that each Rod can bear by computing the normal stress due to applied force and the geometry of the structure.

- The two components of force P normal to rods are:

               Rod 1 : P*cos(Q)  

               Rod 2: - P*sin(Q)

where Q: angle subtended between x_1 and Rod 1 @ A. Hence,

               Q = arctan ( y_1 / x_1)

               Q = arctan (3.7 / 2.1 ) = 60.422 degrees.

- The normal stress in each Rod due to normal force P are:

               Rod 1 : stress_1 = P*cos(Q)  / A_1

               Rod 2: stress_2 = - P*sin(Q)  / A_2

- The cross sectional Area of both rods are A_1 and A_2:

               A_1 = pi*D^2 / 4

               A_2 = pi*(OD^2 - ID^2) / 4

- The maximum force for the given allowable stresses are:

               Rod 1: P_max =  stress_1 * A_1 / cos(Q)

                          P_max = (110*10^6)*pi*0.012^2 / 4*cos(60.422)

                          P_max = 25203.61848 N

               Rod 2: P_max =  stress_2 * A_2 / sin(Q)

                          P_max = (65*10^6)*pi*(0.048^2 - 0.038^2) / 4*sin(60.422)

                          P_max = 50483.4 N

- The maximum force that the structure can with-stand is governed by the member of the structure that fails first. In our case Rod 1 with P_max = 25204 N.

             

8 0
3 years ago
0 - 1"<br> -20<br> -15<br> -10<br> 5<br> 0 1 2 3<br> 0
faust18 [17]

Answer:

#WeirdestQuestionOfAllTime

Explanation:

8 0
3 years ago
It is said that Archimedes discovered his principle during a bath while thinking about how he could determine if KingHiero‘s cro
Rudiy27

Answer:

the crown is false densty= 12556kg/m^3[/tex]

Explanation:

Hello! The first step to solve this problem is to find the mass of the crown, this is found using the weight of the crown in the air by means of the equation for the weight.

W=mg

W=weight(N)=31.4N

M=Mass

g=gravity=9.81m/S^2

solving for M

m=W/g

m=\frac{31.4N}{9.81m/S^2}=3.2kg

The second step is find the volume of crown  remembering that when an object is weighed in the water the result is the subtraction between the weight of the object and the buoyant force of the water which is the product of the volume of the crown by gravity by density of water

F=mg-\alpha  V g

Where

F=weight in water=28.9N

m=mass of crown=3.2kg

g=gravity=9.81m/S^2

α=density of water=1000kg/m^3

V= crown´s volume

solving for V

V=\frac{mg-F }{g \alpha } =\frac{(3.2)(9.81)-28.9}{9.81(1000)} =0.000254m^3

finally, we remember that the density is equal to the index between mass and volume

\alpha =\frac{m}{v} =\frac{3.2}{0.000254} =12556kg/m^3

To determine the density of the crown without using the weight in the water and with a bucket we can use the following steps.

1.weigh the crown in the air and find the mass

2. put water in a cylindrical bucket and measure its height with a ruler.

3. Put the crown in the bucket and measure the new water level with a ruler.

4. Subtract the heights, and find the volume of a cylinder knowing the difference in heights and the diameter of the bucket, in order to determine the volume of the crown.

5. find density by dividing mass by volume

7 0
3 years ago
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