ITC516 Data Mining and Visualisation For Business Intelligence

not change with change in time. This kind of a random process is time invariance meaning it does not change with shift in time. A weak stationarity occurs whereby the mean and variance of a time series remain does not change over a given time frame. Strong stationarity implies that in a stationary process, the probability distribution of the random variable tossed at each time instant is exactly the same along time, and that the joint probability distribution of random variables at different time instants is time shifting invariant.

White noise is a term used to describe sounds that mask other sounds that may occur naturally in a given environment. White noise is a stationary random process because it has a flat spectral density, which means that its amplitude remains constant throughout the audible frequency range and does not vary with time.

Random walk is not a stationary random process because the variance of random walk increases with time. It’s not stationary because if you assume pt=bpt−1+atpt=bpt−1+at, then the variance of this process is σ2ptσpt2 = σ2at/(1−b2)σat2/(1−b2).This violates the condition required to be stationary.

MA(1) process  is a strongly random stationary process as both P(Xt1,...,Xtn)P(Xt1,...,Xtn) and P(Xt1+k,...,Xtn+k)P(Xt1+k,...,Xtn+k) are multivariate (1-dependent)

Autocorrelation function for the MA (1) process ……………(Processes, n.d.)

At lag Ꝋ

[Xt·Xt] = [X·êŠef-1] + [Xt·ef]

  r(0) =  Ꝋef-1[Ꝋef-1=ef] + ef[Xt·ef]+ef[Ꝋef-1+ef]

  r(0) = Ꝋ²f²+ f²

At lag 1

[Xt·Xt-1]=Xt -1· Ꝋef]+[Xt-1·ef]

r(1)= Ꝋf² +0

r(1)= Ꝋf²

^È·₀₌ r(0)/ r(0)=1

È·₂₌ r(1)/r(0)

= Ꝋ È·_2/Ꝋ²È·²

⁼ Ꝋ/  +1

An ARMA model is an auto-regressive model used to describe weakly stationary random process ina   time series in terms of two polynomials. In these two polynomials,the first polynomial represents auto regression, while the second polynomial is for the moving average.

The lag operator is denoted by B and used to express the dwaddled values of the process but for our case we shall use Z so that we come up with the expression :ZXt = Xt−1, 2ZXt = Xt−2, Z3Xt = Xt−3,. . ., ZdXt−d. • If we define Φ(Z) = 1 − X p j=1 φjZj = 1 − φ1Z − φ2Z2 − . . . − φpZp the AR(p) process is deined by the following equation: Φ(Z)Xt = ωt;t = 1, . . . , n. • Here, Φ(D) is  the specific  polynomial of the process and its roots determine whether the process is defined as being  stationary or no(AR, MA and ARMA Models • The Autoregressive Process of Order p or AR ( p ) Is Defined by the Equation, n.d.)t.

For example, a process Xt is said to be invertible if

Xt = X ∞ j=1 ajXt−j + ωt with the restriction that P∞j=1 a2j < ∞

Problem segmentation is a marketing response to the recognition that the end user is crucially solving a market problem. This general problem perspective contributes to management strategy needs related to product and service quality and the formation of competitive positions of great importance and value. This provides a solution to the problem of the degree of aggregation in the data that an enterprise perpetually uses for decision-making.

A Bottom-up algorithm for time series begins by creating the first possible approximation of the time series so that n/2 parts are used to approximate the n length time series. After this, the cost of merging each pair of adjacent segments is calculated separately and then the two algorithms are joined together to form a complete algorithmic design meaning  that  in this method, each  module is formed and then tested separately, a process known as  unit testing before integrating them to come up with a solid solution.(Zifan et al., 2007) The process of unit testing is performed by leveraging specific low-level functions then integrating them together to come up with a unit.

public int dp (int n) {

    int[] output = new int[n + 1];

    output [1] = 1;

    output [2] = 1;

    for (int i = 3; i <= n; i++) {

        output[i] = outpu t[i - 1] + output[i - 2]

    return output[n];

If we check this algorithm it starts from lower values going to the top values.

After this,the cost of putting together every pair of adjacent segments is computed, and then the algorithm begins to merge the lowest cost until a stopping criteria is obtained.

The term "stopping criteria" refers to the conditions that must be met in order to stop execution of the algorithm. Execution time, total number of iterations, non-improving iterations, and optimal (lower bound for minimum, upper bound for maximum) solution found are some of the most common stopping conditions.

 The procedure is stopped in step 2 of the algorithm if any of the sets become complete due to predefined set size limits. The number of design variables and a desired level aspects are used to calculate the maximum size of a package. The number of points that the computation comes up with before stopping is proportional to n because the random points are drawn from a uniform distribution. S* is normally a much smaller number of local minimum points than the other two combinations because there can only be one minimum for each starting point of the computation. Moreover, the algorithm should be stopped if the number of local minima found goes beyond the Bayesian estimated value of the local minima.

Cost computation is the execution time per time step during simulation. This involves the calculation of the total cost of an amount of output and job done either at a given time or at a unit time. Cost estimates are made based on the form of production. The basic expenses are calculated according to their purpose in them. There are different forms of cost computation:

Plan cost calculations are compiled for a planned period using progressive input norms for labor and production means; the progressive standards reflect continued technical progress and improvement in production and labor organization. Report expense calculations are based on accounting statistics and are used to characterize the real amount of spending.

Normative cost calculations are a type of current planning calculation that is prepared in a variety of industries in conjunction with the normative method of recording expenditures. The current actual standards which characterize essentially the level of expenses attained, serve as the foundation for these calculations.

Projected cost calculations are a subset of long-term planning cost calculations; they are required, along with other indices, to determine the efficiency of capital investments and new machinery

The median filter is normally a tool for reducing noise in an image, just like is commonly done using the mean filter although it often does a better job than the mean filter since it preserves useful details in the given image.

Mean filtering is a simple and easy to implement method of smoothing out images by reducing the intensity variation between one pixel and the next.

• The median is a more pronounced average than the mean so a single pixel that is very unrepresentative in a neighborhood will not affect the median value greatly.
• Median filter does not create new unrealistic pixel values when the filter straddles an edge since the median value must actually be the value of one of the pixels in the neighborhood. The median filter is therefore a much better tool at preserving sharp edges in an image than does the mean filter.

Original data: 0,1,3,1,0,0,1,0,1,5,6,0,2,4,4,5,5,4order the data: 0,0,0,0,0,1,1,1,1,2,3,4,4,4,5,5,6

0	1	1	3
1	6	2	0
0	4	5	0
2	5	4	4
0	4	0	1

For two events that is A and B, if we are aware of the conditional probability P(B|A) and the probability P(A), then the Bayes’ theorem explains that we can calculate the conditional probability P(A|B)(Durga et al., 2015) as explained belowBayes’ theorem is often applied in statistics as follows.

[1−Bel(B|A)]Pl(B|A) < Bel(B|A)[1−Pl(B|A)] Bel(A¯ ∩ B) Pl(A¯ ∩ B) | {z } 1/R4

• P(A) – the probability that one is positive by 1%
• P(B) – the probability that one is chosen1/10000
• P(A|B) – the probability that one is negative by 1%
• P(B|A) – the probability that the test is accurate 98%.

Substituting the below

References

AR, MA and ARMA models • The autoregressive process of order p or AR ( p ) is defined by the equation. (n.d.).

Durga, M., Bharathi, S., Murthy, P. B., & Devasena, T. (2015). Characterization and phytotoxicity studies of suspended particulate matter (SPM) in Chennai urban area. Journal of Environmental Biology, 36(3), 583–589.

Processes, S. R. (n.d.). Lecture Notes 7 Stationary Random Processes • Strict-Sense and Wide-Sense Stationarity • Autocorrelation Function of a Stationary Process • Power Spectral Density • Continuity and Integration of Random Processes • Stationary Ergodic Random Processes. 1–27.

Zifan, A., Moradi, M. H., Saberi, S., & Towhidkhah, F. (2007). Automated Segmentation of ECG Signals using Piecewise Derivative Dynamic Time Warping. International Journal of Biological and Medical Sciences, 1(3), 181–185.

Online exams can be a pain in the head. But, you needn’t worry since our online exam help is here at your disposal. No matter how tough the questions are, we have the right team of experts to help you out. The team guides you through all the questions are you struggling to find an answer to. We will provide you with credible study and research material as well, depending on the question. Besides online exam help, we also provide unmatched quality essay writing services and custom writing assistance. You can also hire qualified ghostwriters from our team and get rid of all academic burdens easily.