Principal component analysis (PCA) transforms a vector x∈R
D
to a lower dimensional vector y∈R
d
(d
d
T
(x−
x
) in which
x
is the sample mean of x, and E
d
is a D×d matrix formed by the top d eigenvectors of the sample covariance matrix of x. Let x
1
and x
2
be any two samples of x, and y
1
and y
2
be the PCA transformed version of them. Show that d
A
2
(x
1
,x
2
)=∥y
1
−y
2
∥
2
2
Answers
The equation dA^2(x1, x2) = ||y1 - y2||^2 states that the squared Euclidean distance between the PCA-transformed vectors y1 and y2 is equal to the squared Euclidean distance between the original vectors x1 and x2. This equation shows that the PCA transformation preserves the pairwise distances between samples in the lower-dimensional space.
Let's consider the squared Euclidean distance between the original vectors x1 and x2:
||x1 - x2||^2
Expanding the above expression, we have:
(x1 - x2)^(T)(x1 - x2)
Now, let's express x1 and x2 in terms of their PCA-transformed counterparts:
x1 = x + Edy1
x2 = x + Edy2
where x is the sample mean of x, Ed is the matrix formed by the top d eigenvectors of the sample covariance matrix of x, and y1 and y2 are the PCA-transformed versions of x1 and x2, respectively.
Substituting the expressions for x1 and x2 into the squared Euclidean distance equation, we get:
||(x + Edy1) - (x + Edy2)||^2
Expanding and simplifying the expression, we obtain:
||Ed(y1 - y2)||^2
Since the matrix Ed is orthogonal (its columns are eigenvectors), the norm of the matrix Ed is equal to 1. Hence, the above expression simplifies to:
||y1 - y2||^2
Therefore, we have shown that the squared Euclidean distance between the PCA-transformed vectors y1 and y2 is equal to the squared Euclidean distance between the original vectors x1 and x2, confirming the preservation of pairwise distances in the lower-dimensional space.
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Related Questions
An operating system with _____ capabilities allows a user to run more than one program concurrently.
Answers
Answer:
networking
Explanation:
An operating system with multitasking capabilities allows a user to run more than one program concurrently. The correct option is d.
What is an operating system?A computer's operating system (OS) is a type of system software that controls computer hardware, and software resources, and offers standard services to programs.
It's an operating system that enables several users to access the applications that are running simultaneously on a single network server. The term “Terminal server” refers to a single network server. The program “terminal client” supports user sessions.
An operating system that supports multiple active processes at once is referred to as a multitasking operating system.
Therefore, the correct option is d. multitasking.
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The question is incomplete. Your most probably complete question is given below:
a. networking
b. hardware independence
c. memory management
d. multitasking
yall please help me in online school i only have 1 week to do it
its online by the way which is why it says computers and technology
Answers
Answer:
we cant see anything
Explanation:
Answer:
add meh back
Explanation:
pls
a binary number is an integer made up of only 0s and 1s. for example, 110111101 is a binary number. what is the smallest binary number divisible by 225?
Answers
The smallest binary number that is divisible by 225 is 1110001000.
A binary number is an integer that is made up of only 0s and 1s. It is a numeral system based on the binary system. The decimal system, which is based on 10, is what we use every day. The binary system, on the other hand, is based on 2. Any integer in the decimal system can be converted to the binary system with ease. Decimal numbers are translated to binary numbers by converting the decimal number to a binary number system by representing it in the powers of 2. The method of repeated division by 2 is used to convert decimal numbers to binary numbers. Given 225 is a 5 × 3 × 5 × 3. So, for any number to be divisible by 225, it must be divisible by 5 × 5 × 3 × 3. For the number to be divisible by 5, the last digit of the binary number must be 0.
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you are a server technician for your organization. you are creating a backup routine for your server systems. you are considering hierarchical storage management (hsm) rather than traditional tape media. what is an advantage of hsm?
Answers
The advantage of HSM (Hierarchical Storage Management) over traditional tape media is that the data is migrated to different storage tiers automatically to improve access speed and reduce cost.
What is HSM?Hierarchical Storage Management (HSM) is a storage technique that involves moving data between various storage tiers according to predefined policies. Data is moved automatically from primary storage (most expensive, fastest) to lower-cost storage media as it ages, according to a set of rules defined by administrators.
HSM systems normally transfer data from fast, high-cost disks to slower, low-cost disks, and even tape media. This decreases storage costs and enhances performance by preserving frequently accessed data on high-performance, costly storage systems.
HSM has the following benefits over traditional tape media:
Data is more easily accessible, as it is automatically transferred to different storage tiers to improve access speed and reduce cost. As a result, backup and retrieval times are much shorter.Data is less likely to be misplaced or lost, as it is not stored on physical tape.
As a result, security concerns are reduced.Individual files can be recovered more quickly, as they can be moved from lower-cost storage tiers to higher-cost storage tiers on the fly, and the HSM software automatically retrieves the necessary data blocks to complete the file.There are no restore problems due to corrupt or obsolete backup media, as HSM uses only current, readable media to store data
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mary wants to send a message to sam in such a way that only sam can read it. which key should be used to encrypt the message? answer sam's public key mary's public key sam's private key mary's private key
Answers
Sam"s public key is the correct option. A type of encryption known as symmetric encryption uses a single secret key to both encrypt and decrypt digital data.
Symmetric cryptography is one type of encryption (also known as secret key cryptography or private key cryptography). Symmetric cryptography is best suited for bulk encryption because it is much faster than asymmetric cryptography. Symmetric cryptography uses a shared key between both parties (which is kept secret). Asymmetric encryption uses a pair of public key and a private key to encrypt and decrypt messages when communicating, as opposed to symmetric encryption, which uses a single key that must be shared among the individuals who need to receive the message.
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What is the difference between electrical and electronic devices?
Answers
Answer:
A difference is that the electrical devices makes the electrical energy into the other forms of energies, such as heat, light, sound, gravitational, and nuclear. . . The electronic device controls the flow of electrons for performing the task.
Answer:
the different between electrical and electronics devices is the electricity and the power of inside of some devices which are considered most powerful electronics from, because the difference is the battery.
Explanation:
i hope it helps ;)
Can you think of ways that app designers can make the graphical user interface (GUI) better for users to navigate so that they can more easily change the settings on apps?
Answers
A few ways that app designers can make the graphical user interface (GUI) better for users to navigate and change settings more easily can be use clear and consistent labels, Group related settings together, etc.
What is GUI?A type of user interface known as the GUI, or graphical user interface, enables users to communicate with electronic equipment using graphical icons and aural cues like basic notation.
For users to explore and modify settings more conveniently, app designers can improve the graphical user interface (GUI) in the following ways:
Employ descriptive labels that are clear and consistent: App designers should use descriptive labels that are clear and consistent so that users can understand what each setting does.Assemble settings that are connected: In order to make it simpler for users to find what they're looking for, related options should be grouped together.Employ well-known icons and symbols: Instead than inventing new ones, designers should use well-known icons and symbols that users are already accustomed to.Thus, designing a user-friendly GUI for settings can greatly enhance the user experience and make it easier for users to navigate and customize the app.
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How can I log Into the instagram app if this pop up appears?
Answers
Answer:
tou sex die sojdifnfidjd7dhubdud
what is draft pls help me
Answers
Answer:
draft like as a rough draft it pretty much a set were you can play and the do the real thing
Victor has been murdered, and Art, Bob, and Carl are suspects. Art says he did not do it. He says that Bob was the victim's friend but that Carl hated the victim. Bob says he was out of town the day of the murder, and besides he didn't even know the guy. Carl says he is innocent and he saw Art and Bob with the victim just before the murder. Assuming that everyone - except possibly for the murderer - is telling the truth, encode the facts of the case so that you can use the tools of Propositional Logic to convince people that Bob killed Victor.
How can you find out using logic that Bob Killed Victor?
Answers
20 characters yes no
What is the output of the following program?
import java.util.Date;
public class Test {
public static void main(String[] args) {
Date date = new Date(1234567);
m1(date);
System.out.print(date.getTime() + " ");
m2(date);
System.out.println(date.getTime());
}
public static void m1(Date date) {
date = new Date(7654321);
}
public static void m2(Date date) {
date.setTime(7654321);
}
}
Answers
The output of the given Java program will be "1234567 7654321".
In the given Java program, the main method creates a Date object named "date" initialized with the value 1234567, representing a specific point in time. The program then calls the m1() method, which assigns a new Date object with the value 7654321 to the "date" variable within the method. However, this assignment does not affect the original "date" object in the main method.
Next, the Java program calls the m2() method, which modifies the value of the "date" object using its setTime() method, setting it to 7654321. This change affects the original "date" object in the main method.
Finally, the program prints the result of calling date.getTime(), which returns the time value of the "date" object. The first print statement displays 1234567, representing the original value of the "date" object. The second print statement displays 7654321, reflecting the updated value after calling m2().
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explain Machine Learning Quiz On Kernel Method?
Answers
Machine Learning Quiz on Kernel Method refers to a set of questions that are designed to test your understanding of the kernel method in the context of machine learning. The kernel method is a mathematical technique used in machine learning algorithms to transform data into a higher dimensional space, allowing for more accurate classification and prediction.
In a machine learning quiz on the kernel method, you may be asked questions about the different types of kernels (e.g. linear, polynomial, Gaussian), how to choose the appropriate kernel for a given dataset, and how to apply the kernel method in a machine learning algorithm.
To answer these questions, you will need to have a solid understanding of the kernel method, including its mathematical foundations and its applications in machine learning. You may also need to be familiar with different machine learning algorithms and how they use the kernel method to improve their performance.
In conclusion, a machine learning quiz on the kernel method is designed to test your knowledge and understanding of this important technique in the field of machine learning. By studying the kernel method and practicing with quizzes and exercises, you can improve your ability to apply this technique in real-world machine learning problems.
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Is the GPU shortage over? What do you think this means for other
chip-using industries? Why else do you think the prices are falling
on chip based products?
Respond to the question in full sentences.
Answers
The GPU shortage is not entirely over, but there have been some improvements in recent months. The GPU shortage has primarily been driven by a combination of factors, including the global semiconductor supply chain constraints, increased demand due to the growth of gaming and remote work, and the high demand for GPUs in cryptocurrency mining.
As for the impact on other chip-based products, the semiconductor shortage has affected various industries such as automotive, consumer electronics, and telecommunications. Manufacturers of these products have faced challenges in meeting the high demand, leading to delays and increased costs. However, as production capacity for semiconductors gradually ramps up and various governments invest in domestic chip production, the situation may improve in the coming months.
In summary, the GPU shortage is still ongoing but showing signs of improvement. The consequences of this shortage extend to other chip-based products, leading to production delays and increased costs across different industries. As semiconductor production increases and global efforts to resolve the issue continue, we can hope to see more stable supply chains and reduced shortages in the near future.
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how are web design & web development different from each other?
Answers
Answer:
Developers are people who build a website's core structure using coding languages, while designers are more visually creative and user-focused. Developers use their programming knowledge to breathe life into the designer’s creative vision.
You could think of developers as construction workers, and web designers as architects – both necessary, but different, skill sets.
I hope this helped :D
Explanation:
Find the inverse of the following matrices:
1.
3 -6 -1 4
2.
[1 2 3 7 6 5 ] 8 1 0
Answers
Answer:
Multiply by the unit squared
The matrices a) and c) are invertible and their inverses are [-2.5 0.5 3; 1.5 -1 -3; -0.5 0.5 1] and [0.5 1.5 5.5; 2.5 6.5 14.5; -2 -5 -11], respectively. The matrix b) is not invertible and we cannot find its inverse.
What is determinant?In order to determine whether a matrix is invertible, we need to calculate its determinant. If the determinant is not equal to 0, then the matrix is invertible and we can find its inverse. b then the matrix is not invertible and we cannot find its inverse.
The determinant of the matrix [2 1 2; 0 5 3; -1 1 0] is (2)(5)(0) + (1)(3)(-1) + (2)(0)(1) - (2)(1)(3) - (1)(5)(-1) - (2)(0)(0) = -3 + 5 = 2. Since the determinant is not equal to 0, the matrix is invertible. The inverse of the matrix can be found using the formula:
[2 1 2; 0 5 3; -1 1 0]^-1 = (1/2) * [5 -1 -6; -3 2 6; 1 -1 -2] = [-2.5 0.5 3; 1.5 -1 -3; -0.5 0.5 1]
The determinant of the matrix [3 -6; -4 8] is (3)(8) - (-6)(-4) = 24 - 24 = 0. Since the determinant is equal to 0, the matrix is not invertible and we cannot find its inverse.
The determinant of the matrix [1 3 2; -1 1 3; 2 2 -1] is (1)(1)(-1) + (3)(3)(2) + (2)(-1)(2) - (1)(3)(2) - (3)(1)(-1) - (2)(2)(3) = -1 + 18 - 4 - 6 + 3 - 12 = -2. Since the determinant is not equal to 0, the matrix is invertible. The inverse of the matrix can be found using the formula:
Therefore, the matrices a) and c) are invertible and their inverses are [-2.5 0.5 3; 1.5 -1 -3; -0.5 0.5 1] and [0.5 1.5 5.5; 2.5 6.5 14.5; -2 -5 -11], respectively. The matrix b) is not invertible and we cannot find its inverse.
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Impact of incentive programs on digital platforms (Uber/Rappi/Door Dash/Uber Eats/Lyft)
-How to segment users in an incentive program?
Answers
Incentive programs play a significant role in shaping user behavior and driving engagement on digital platforms like Uber, Rappi, DoorDash, Uber Eats, and Lyft.
These programs are designed to motivate users to take specific actions or achieve certain goals by offering rewards, discounts, or other incentives.
The impact of incentive programs on digital platforms can be analyzed from multiple perspectives:
1. User Acquisition and Retention: Incentive programs can attract new users to join the platform by offering sign-up bonuses, referral rewards, or first-time user discounts.
These incentives incentivize users to try out the service and increase the platform's user base.
2. User Engagement: Incentive programs can enhance user engagement by encouraging frequent usage of the platform.
3. Behavior Modification: Incentives can be used to shape user behavior in desired ways.
For instance, offering bonuses or higher earnings for drivers during peak hours can encourage them to be more available during busy periods, leading to shorter wait times for customers.
Segmenting users in an incentive program allows the platform to tailor incentives to different user groups based on their behaviors, preferences, or needs.
1. New Users vs. Existing Users: Segmenting users based on their status as new or existing can help design specific incentives to attract new users and retain existing ones.
2. Frequency and Usage Patterns: Segmenting users based on their usage frequency or patterns can enable the platform to incentivize less active users to increase their engagement.
3. Geographic Segmentation: Users in different regions may have varying needs and behaviors. By segmenting users based on their geographic location, platforms can offer location-specific incentives.
4. User Preferences and Behavior: Analyzing user preferences, such as preferred cuisine or ride type, can help segment users for targeted incentives.
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In a computer network, a _____ is an expansion card located within the system unit that connects the computer to a network.
Answers
Answer:
Explanation:
Technically, a NIC is a physical card that connects to an expansion slot in a computer. Many computers and wireless devices now include an integrated networking component called a network adapter. This may be an Ethernet controller and port attached to the edge of a motherboard or a small wireless networking chip located on the motherboard.
What are the benefits and risks of a client-server network?
Answers
Answer:
Ermm... i don't really know but probably
the benefits can be: multi device connection and can be upgraded.
The disadvantages: The server is expensive i think, a special staff like a network manager is needed, and if any single part of the system fails a whole lot of disruption can come.
hope this helps!
“Click” is a type of user input the onEvent code checks for in order to perform actions like going to another screen. List at least 3 other user inputs onEvent can check for.
Answers
Answer:
typing, commands, scrolling. hope this helps
what is a iteration in program code?
Answers
Answer:
it's when the code keeps repeating e.g while loop
Explanation:
What best describes proprietary file format?
A format that is closed but free of cost.
A format that is owned by a person or group.
A format that is not bound by copyright law.
A format that is open and free of cost.
Answers
Answer:
A format that is closed but free of cost.
Answer:
A
✔ free
format is not bound by copyrights, trademarks, patents, or restrictions.
A
✔ proprietary
format is considered to be intellectual property, which means it is owned by an individual or organization.
An open file format
✔ can be free or proprietary
A closed file format
✔ is unpublished
Explanation:
You are the network administrator for a small organization. recently, you contracted with an isp to connect your organization's network to the internet to provide users with internet access. since doing so, it has come to your attention that an intruder has invaded your network from the internet on three separate occasions. what type of network hardware should you implement to prevent this from happening again
Answers
The type of network hardware that you should to implement so as to prevent this from happening again is Firewall.
What is a Firewall?A Firewall is known to be a kind of network security machine that helps to monitors and run through any incoming and outgoing network traffic through the use of firm's formerly set up security policies.
Note that, a firewall is made as a kind of the barrier and as such, The type of network hardware that you should to implement so as to prevent this from happening again is Firewall.
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What is the significance of XML tags?
A.) They are self-descriptive.
B.) They are predefined.
C.) They are only computer readable.
D.) They are only human readable.
Answers
Answer:
your answer would be to ur question would be B
Answer:
It is self-descriptive
Explanation:
Plato Users
The best way to handle a problem is to ______.
a.
wait for someone to notice the problem
b.
avoid the problem so you don’t get blamed
c.
take care of the problem as soon as someone asks you
d.
take care of the problem as soon as you notice it
Answers
Answer:
D. take care of the problem ad soon as you notice it
For each order, list the order number, order date, item number, description, and category ach customer that did not place an order on October 15, 2015. for each item that makes up the order
Answers
Based on the statement, "For each order, list the order number, order date, item number, description, and category for each customer that did not place an order on October 15, 2015, for each item that makes up the order," the query intends to retrieve a report of orders made by customers for each product and category, excluding those on a specific date.
To accomplish this, a SQL script should be written.
Here is an example SQL query to extract the required information:
SELECT OrderNumber, OrderDate, ItemNumber, Description, Category
FROM OrdersWHERE OrderDate <> '2015-10-15';
The SQL statement retrieves all orders from the Orders table where the OrderDate isn't equal to 2015-10-15.
The SELECT statement extracts the OrderNumber, OrderDate, ItemNumber, Description, and Category columns from the Orders table.
Furthermore, if you provide additional details, I will be able to give a better response.
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Read the following scenario, and then decide if you should upgrade the computer. You have a desktop that you use primarily for writing essays for school and browsing the web at home. The computer is slowing down some, so you check the date on it. Your computer is 6 years old. It is amazing that it lasted this long. You probably need a better CPU and more RAM. What should you do?
Answers
Answer:
Upgrade
Explanation:
EDGE 2021
Answer:
B. Upgrade
Explanation:
Because you have a desktop, upgrading the CPU and RAM are an easy and inexpensive fix. Upgrading a laptop is more difficult and often requires purchasing a new computer.
I hope this helps<3
Have a nice day everyone<3
For your spring campaign, you're trying to influence consideration with your users. Which ad format would best support this goal?
Answers
To influence consideration with your users for your spring campaign, the best ad format to use would be video ads. Video ads can provide a more immersive experience for users and can showcase the benefits and features of your product or service in a visually engaging way.
Additionally, video ads can help build brand awareness and establish an emotional connection with your target audience, ultimately leading to increased consideration and conversion rates.
For your spring campaign, if you aim to influence consideration among users, the ad format that would best support this goal is the "Native Advertising" format. Native ads blend seamlessly with the surrounding content, making them less intrusive and more engaging for users, which can effectively drive consideration.
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a direct access table has the items 21, 32, 43, 54. what will be the output of hashsearch(table, 5)?
Answers
A direct access table has the items 21, 32, 43, 54.the output of hashsearch(table, 5) will be "Not Found".
A direct access table is an array where elements can be accessed directly using their keys as indices. A hash function is used to map the key to an index in the table. So, for the given direct access table, we'll need to know the hash function to determine the output of hashsearch(table, 5).
Assuming the hash function is h(x) = x % 10, let's perform the hashsearch:
Step 1: Compute the hash value for the given key.
h(5) = 5 % 10 = 5
Step 2: Check the table at index 5.
table[5] = ?
Since the table has the items 21, 32, 43, and 54, and their hash values are:
h(21) = 1, h(32) = 2, h(43) = 3, h(54) = 4
None of these hash values correspond to index 5, so the table[5] is empty.
In conclusion, the output of hashsearch(table, 5) will be "Not Found" or a similar indication that the element with key 5 is not present in the table.
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3. You'd prefer to read this email on a larger screen, so you open your laptop. Your laptop display is quite flat. What kind of screen do you think it is?
Answers
Answer:
.....
Explanation:
Answer:
plasma Screens
Explanation:
Used for very large screens and some laptops which display ones screen Flat.
in simple words please
What is a VRF system? What are the benefits over a split A/C system?
Answers
A VRF system is a type of air conditioning system that utilizes variable refrigerant flow technology to provide individual zone temperature control. This system provides better energy efficiency, greater flexibility, and quieter operation than traditional split A/C systems.
A VRF system, or variable refrigerant flow system, is a type of air conditioning system that allows for individual temperature control in different zones. The system uses a single outdoor condensing unit to circulate refrigerant through multiple indoor units, each of which can be controlled independently to maintain different temperatures in different rooms or zones. This provides greater flexibility and energy efficiency compared to traditional split A/C systems, which require separate condensing units for each indoor unit.
Compared to split A/C systems, VRF systems have several benefits. First, they provide better energy efficiency because they use variable refrigerant flow technology to precisely match the cooling or heating load of each zone, reducing the amount of energy wasted. Second, they offer greater flexibility because each zone can be controlled independently, allowing for personalized comfort settings. Finally, VRF systems operate more quietly than split A/C systems because they use smaller, quieter indoor units and have fewer outdoor units.
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