Data analysis of weather forecasting
- 1. DATA ANALYSIS ON WEATHER FORECASTING Prepared by, Trupti Shingala
- 2. Introduction: Dataset We have used weather forecast dataset having 366 observations from rattle package in R. Used following Independent variables from the dataset: Max_Temperature , Min_Temperature, WindSpeed3pm,WindSpeed9am, Pressure3pm, Humidity9am, Humidity3pm,RainToday, RainTomorrow.
- 3. Data Clean and Goals ļ Replaced the missing value with the field mean for numerical data. ļ Implement various algorithms on the data to help derive conclusion on classification and clustering of data.
- 4. Algorithms used Classification: ļ K-nearest neighbors ļ Naive Bayes ļ DecisionTree- Rpart Clustering: ļ K means clustering
- 5. Classification and RegressionTree ļ The decision trees produced by CART are strictly binary, containing exactly two branches for each decision node. ļ CART recursively partitions the records in the training data set into subsets of records with similar values for the target attribute. ļ The CART algorithm grows the tree by conducting for each decision node, an exhaustive search of all available variables and all possible splitting values. ļ Formula = Rain_Tomorrow ~ min_temp+ max_temp+windspeed9am+windspeed3pm+h umidity3pm+pressure3pm
- 6. DecisionTree
- 7. Decision Tree ļ To determine if the tree is appropriate or if some of the branches need to be subjected to pruning we can use the cptable element of the rpart object: ļ The xerror column contains of estimates of cross- validated prediction error for different numbers of splits (nsplit).The best tree has three splits. ļ Now we can prune back the large initial tree using the min Cp value.
- 8. The error rate of the decision tree after pruning is 16%
- 9. K-MEANS CLUSTRING ļ k-means clustering is a method of vector quantization, originally from signal processing, that is popular for cluster analysis in data mining. ļ The goal of K-Means algorithm is to find the best division of n entities in k groups, so that the total distance between the group's members and its corresponding centroid, representative of the group, is minimized. ļ Formally, the goal is to partition the n entities into k sets Si, i=1, 2, ..., k in order to minimize the within-cluster sum of squares (WCSS), defined as:
- 10. K-means Algorithm Step #1 A typical version of the K-means algorithm runs in the following steps: 1. Initial cluster seeds are chosen (at random). ā These represent the ātemporaryā means of the clusters. ā Imagine our random numbers were 60 for group 1 and 70 for group SEED1 SEED 2
- 11. K-means Algorithm Step #2 2.The squared Euclidean distance from each object to each cluster is computed, and each object is assigned to the closest cluster.
- 12. K-means Algorithm Step #3 3. For each cluster, the new centroid is computed ā and each seed value is now replaced by the respective cluster centroid. ā¢ The new mean for cluster 1 is 62.3 ā¢ The new mean for cluster 2 is 68.9
- 13. K-means Algorithm Step #4 ā #6 4.The squared Euclidean distance from an object to each cluster is computed, and the object is assigned to the cluster with the smallest squared Euclidean distance. 5.The cluster centroids are recalculated based on the new membership assignment. 6. Steps 4 and 5 are repeated until no object moves clusters.
- 14. Applications ļ market segmentation ļ computer vision ļ geostatistics ļ astronomy ļ Agriculture ļ It often is used as a preprocessing step for other algorithms, for example to find a starting configuration.
- 16. For k=3
- 17. PLOTTING CLUSTER FOR K=2 FOR K=3
- 18. NaĆÆve Bayes Classifier ļ Computes the conditional a-posterior probabilities of a categorical class variable given independent predictor variables using the Bayes rule.
- 19. NaĆÆve Bayes Classifier(Cont..) ļ Naive Bayes classifiers assume that the effect of a variable value on a given class is independent of the values of other variable.This assumption is called class conditional independence. ļ An advantage of the naive Bayes classifier is that it requires a small amount of training data to estimate the variable values necessary for classification.
- 20. NaĆÆve Bayes Classifier(Cont..) ļ Here, we implemented NaĆÆve Bayes on RainToday and RainTomorrow attributes with another attributes of MinTemp, MaxTemp, Temp9am,Temp3pm, Pressure9am, Pressure3pm.
- 21. NaĆÆve Bayes Classifier(Cont..) ļ Perform naĆÆve Bayes on categorical data only. Here in predict model if type is row then the conditional a-posterior probabilities for each class are returned. ļ Else the class with maximum probability is returned
- 22. NaĆÆve Bayes Classifier(Cont..) Pred No Yes No 300 66 Yes 0 0 ļ Output
- 23. ļ Perform naĆÆve Bayes using Laplace smoothing. It is technique that used to smooth categorical data. ļ The default (0) value of laplace disables Laplace smoothing. NaĆÆve Bayes Classifier(Cont..)
- 24. NaĆÆve Bayes Classifier(Cont..) Pred No Yes No 258 34 Yes 42 32 Pred No Yes No 271 38 Yes 29 28 ļ RainToday ļ RainTomorrow
- 25. ļ It is a Lazy Learning Algorithm ļ Whenever we have a new point to classify , we find its K nearest neighbors from the training data ļ It Defers the decision to generalize the past training examples till a new query is encountered ļ K-NN uses distance function to calculate the distance between points from the center ļ Our Goal is to specify for which value of K the weather data is most accurate K - Nearest Neighbor
- 26. ļ Given a query instance xq to be classified, ļ Let x1,x2ā¦.xk denote the k instances from training examples that are nearest to xq ļ Return the class that represents the maximum of the k instances ļ For eg: if we take K=5 In this case query Xq Will be classified as Negative since 3 of its Nearest neighbors are classified as negative K - Nearest Neighbor
- 27. K-Nearest Neighbor ā Transitional Conclusions ļ For K = 1 we have following Table result & error rate for rain tomorrow ļ For K = 2 we have followingTable result & error rate for rain tomorrow
- 28. ļ For K = 5 we have following Table result & error rate for rain tomorrow ļ For K = 10 we have following Table result & error rate for rain tomorrow K - Nearest Neighbor
- 29. K-Nearest Neighbor ā Conclusions and Error Rate ļ The error rate changes every time since the training and the test dataset are not stable ļ The error rate is 21%
- 30. Comparison of Algorithms Accuracy of the following algorithms are: 1. KNN ā 79% 2. K-means ā 80.5% 3. Decision tree ā 84%