Desktop version

Home arrow Mathematics

  • Increase font
  • Decrease font


<<   CONTENTS   >>

Sample Study: Time Series Prediction

We are going to use one of the most surprisingly used methods for time series prediction: autoregressive integrated moving average (ARIMA). ARIMA models are denoted in ARIMA (p, d, q) notation. The following three parameters are worthwhile for seasonality, trend, and noise in your data:

p = d = q = range(0, 2) pdq = list(itertools.product(p, d, q)) seasonal_pdq = [ (x[0], x[l], x[2], 12) for x in list(itertools.product(p, d, q))]

print(1 Examples of parameter combinations for Seasonal ARIMA...1) print(1SARIMAX: {} x {}'.format(pdq[1], seasonal_pdq[1])) print(1SARIMAX: {} x {}'.format(pdq [1], seasonal_pdq[2])) print(1SARIMAX: {} x {}'.format(pdq[2], seasonal_pdq[3])) print(1SARIMAX: {} x {}'.format(pdq[2], seasonal_pdq[4]))

This step is the parameter selection for our furniture sales' ARIMA Time Series Model. Our goal here is to use a "grid search" to find an optimal set of parameters that yield the weightier performance for our model:

for param_seasonal in seasonal_pdq: try:

mod = sm.tsa.statespace.SARIMAX(y,

order=param,

seasonal_order=param_seasonal,

enforce_stationarity=False,

enforce_invertibility=False)

results = mod.fit()

print('ARIMA{}x{}12 - AIC:{}'.format(param, param_seasonal, results.aic))

except:

continue

The output suggests that SARIMAXfl, 1,1) x (1,1, 0,12) yields the lowest AIC value of 297.78. Therefore, we should consider this to be optimal option.

Case Study: Data Mining

Data mining (DM) is the extraction of implicit, previously unknown, and potentially useful information from data. It is the use of specific algorithms to extract patterns from the data. When strong patterns are found, they can be generalized to make well-judged predictions about future data.

The pattern found should definitely be valid in the new layered data. We also want the pattern to be new (at least to the system and preferably to the user) and potentially useful. In other words, it provides some benefit to the user or task. Finally, you should be able to understand the pattern immediately without any post-processing.

Knowledge discovery goals are specified according to the purpose of the system. Discovery objectives are divided into predictions, where the system finds patterns to predict the future policy of some entities, and descriptions, where the system finds patterns to display to users in a human understandable form.

The following are the main types of mining:

  • • Association rule mining (genetic algorithms, CN2 rules): A rule set is the warmest expression of knowledge and is probably the easiest to understand. This includes searching for rules that are used to describe the conditions under which items occur together. In general, the condition of a rule is a predicate of a specific logic, and whoopee is the associated class. In other words, it predicts whoopee for the input instances that create the true condition. It is often used for market basket or trading data analysis.
  • • Classification and prediction (CART, CHAID, ID3, C4 5, C50, J48): This includes the identification of data features that can be used to generate models to predict similar occurrences in future data. The decision tree categorizes instances by sorting them down the tree, from the root to some leaf nodes, which gives the nomenclature of the instances. Each node in the tree specifies a test for some symbol of the instance, and each workshop descending from that node corresponds to one of a range of possible values for this property.
  • • Cluster analysis (К-means, neural networks, expectation-maximization): Attempts to squat on a group (cluster) of data items that are very similar to the other objects in the group, but not most similar to the objects in the other groups.

It can be said that in an unqualified way, these algorithms use a limited representation of knowledge. Given the structure of the knowledge to be acquired, there is little possibility of transformation. For example, a rule is just a tentative relationship between a condition and a conclusion. This limits the possibility of acquiring new knowledge, where the main logical relationship is joining, separation or equality, or a self-dominating combination of logical operators.

Each knowledge expression language takes into account the limitations of its definition and limits the space of possible solutions. Any learning algorithm and knowledge representation can be a more weighted algorithm in a subset of non-recurring problems. For this reason, the main purpose of this work is to find new methods for knowledge discovery in databases that allow you to obtain fuzzy predicates in an increasingly flexible way of expressing knowledge using various meta-heuristic algorithms.

The point of view to consider here is a different point of view than what Zadeh described in 1994. For us, the main components are FSs, stochastic inference, neural networks, and meta-heuristics. All in all, these components are complementary, not competitive. It is increasingly known that in many cases, it is worth combining them. The hybridization of the soft computing context favors and reinforces the visit of the original procedure, which can help solve new problems like this. Soft computing will play an increasingly important role in many areas of use. DM methods can be viewed as three main algorithmic components: (1) model representation, (2) model evaluation, and (3) search.

Exercise

  • 1. Describe how ARIMA method can be utilized for forecasting.
  • 2. What do you midpoint by data mining? Mention a few applications of it.
  • 3. What is defuzzification? Why is it necessary? Describe a few techniques of it.
  • 4. Distinguish between SVDQR and iterative diamond method.
  • 5. Describe the effect of fuzzification on inference.

References

Aladi, Jabran Hussain, Christian Wagner, Amir Pourabdollah, and Jonathan M. Garibaldi. "Contrasting singleton type-l and interval type-2 non-singleton type-1 fuzzy logic systems." In 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Vancouver, Canada (2016), pp. 2043-2050.

Eatherley, Graham J. Autonomous Vehicle Docking Using Fuzzy Logic. University of Ottawa, Canada, 1994.

Hagras, Hami. "Type-2 FLCs: A new generation of fuzzy controllers." IEEE Computational Intelligence Magazine 2, no. 1 (2007): 30-43.

Lofti, Ahmad. "Learning fuzzy inference systems." PhD dissertation, University of Queensland (1995).

McBratney, Alex B., and Inakwu O. A. Odeh. "Application of fuzzy sets in soil science: Fuzzy logic, fuzzy measurements and fuzzy decisions." Geoderma 77, no. 2-4 (1997): 85-113.

Mendel, Jerry M., and George C. Mouzouris. "Designing fuzzy logic systems." IEEE Transactions on Circuits and Systems IT. Analog and Digital Signal Processing 44, no. 11 (1997): 885-895.

Thiem, Alrik. "Membership function sensitivity of descriptive statistics in fuzzy- set relations." International Journal of Social Research Methodology 17, no. 6 (2014): 625-642.

Zadeh, Lotfi. "Fuzzy logic (abstract) issues, contentions and perspectives." In Proceedings of the 22nd Annual ACM Computer Science Conference on Scaling up: Meeting the Challenge of Complexity in Real-World Computing Applications: Meeting the Challenge of Complexity in Real-World Computing Applications (1994), p. 407.

 
<<   CONTENTS   >>

Related topics