KNN_Timeseries_Assignment(1)

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Week1 Assignment KNN Time Series Mohit Manjaria 9/24/2020 ALY 6020 Predictive Analytics Week1 Assignment KNN Time Series Mohit Manjaria Instructor: Marco Montes de Oca Winter 2021 January 28th 2021 Northeastern University Introduction In this assignment, a dataset of search interest of all categories for Predictive analytics term from January 2061 to January 2021 is selected for K-Nearest Neighbors Analysis. In this dataset, the numbers represent search interest relative to the highest point on the chart for the given region and time. A value of 100 is the peak popularity for the term. A value of 50 means that the term is half as popular. A score of 0 means there was not enough data for this term. Analysis In this part, time series forecasting with KNN regression will be performed. According to the auto-regressive model and model requirements that are given, three dimension, four dimension, five dimension and six dimension models with K values from 1 to 10 will be explored. Step 1: Installing libraries library (tinytex) library (neighbr) library (readr)
library (tsfknn) library (zoo) ## ## Attaching package: 'zoo' ## The following objects are masked from 'package:base': ## ## as.Date, as.Date.numeric library (ggplot2) Step 2: Importing the data and checking the data knnt <- read.csv ( "C:/Users/mohit/Downloads/multiTimeline.csv" ) head (knnt) ## Week Predictive.analytics...United.States. ## 1 1/31/2016 60 ## 2 2/7/2016 54 ## 3 2/14/2016 58 ## 4 2/21/2016 53 ## 5 2/28/2016 43 ## 6 3/6/2016 54 dim (knnt) ## [1] 259 2 summary (knnt) ## Week Predictive.analytics...United.States. ## Length:259 Min. : 9.00 ## Class :character 1st Qu.: 42.00 ## Mode :character Median : 52.00 ## Mean : 53.07 ## 3rd Qu.: 63.00 ## Max. :100.00 #KNN Model pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags = 1 : 2 , k= 1 ) pred $ prediction ## Time Series: ## Start = 260 ## End = 260
## Frequency = 1 ## [1] 34 pred $ neighbors ## [1] 259 #Plotting time series autoplot (pred, h= 1 ) #Calculating accuracy for k = 1 ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 11.00000 11.00000 32.35294 ro $ predictions ## h=1 ## [1,] 45 ro $ h_accu ## h=1 ## RMSE 11.00000 ## MAE 11.00000 ## MAPE 32.35294
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#Calculating Euclidean Distance install.packages(“philentropy”) library(philentropy) #knn.dist(knnt, dist.meth = “euclidean”, p = 2) #For n=2 or K = 3 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags = 1 : 2 , k= 3 ) pred $ prediction ## Time Series: ## Start = 260 ## End = 260 ## Frequency = 1 ## [1] 44.66667 pred $ neighbors ## [1] 259 218 206 #Plotting time series autoplot (pred, h= 1 ) #Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE)
## RMSE MAE MAPE ## 16.33333 16.33333 48.03922 ro $ predictions ## h=1 ## [1,] 50.33333 ro $ h_accu ## h=1 ## RMSE 16.33333 ## MAE 16.33333 ## MAPE 48.03922 #For n=2, k = 5 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags = 1 : 2 , k= 5 ) pred $ prediction ## Time Series: ## Start = 260 ## End = 260 ## Frequency = 1 ## [1] 50.6 pred $ neighbors ## [1] 259 218 206 149 256 #Plotting time series autoplot (pred, h= 1 )
#Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 20.00000 20.00000 58.82353 ro $ predictions ## h=1 ## [1,] 54 ro $ h_accu ## h=1 ## RMSE 20.00000 ## MAE 20.00000 ## MAPE 58.82353 #for n = 2, k = 7 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags = 1 : 2 , k= 7 ) pred $ prediction ## Time Series: ## Start = 260
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## End = 260 ## Frequency = 1 ## [1] 49.57143 pred $ neighbors ## [1] 259 218 206 149 256 176 16 #Plotting time series autoplot (pred, h= 1 ) #Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 15.00000 15.00000 44.11765 ro $ predictions ## h=1 ## [1,] 49 ro $ h_accu ## h=1 ## RMSE 15.00000 ## MAE 15.00000 ## MAPE 44.11765
#for n = 3, k = 1 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags = 1 : 3 , k= 1 ) pred $ prediction ## Time Series: ## Start = 260 ## End = 260 ## Frequency = 1 ## [1] 48 pred $ neighbors ## [1] 219 #Plotting time series autoplot (pred, h= 1 ) #Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 11.00000 11.00000 32.35294
ro $ predictions ## h=1 ## [1,] 45 ro $ h_accu ## h=1 ## RMSE 11.00000 ## MAE 11.00000 ## MAPE 32.35294 #for n = 3, k = 3 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags = 1 : 3 , k= 3 ) pred $ prediction ## Time Series: ## Start = 260 ## End = 260 ## Frequency = 1 ## [1] 49.33333 pred $ neighbors ## [1] 219 185 17 #Plotting time series autoplot (pred, h= 1 )
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#Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 10.66667 10.66667 31.37255 ro $ predictions ## h=1 ## [1,] 44.66667 ro $ h_accu ## h=1 ## RMSE 10.66667 ## MAE 10.66667 ## MAPE 31.37255 # for n =3, k = 5 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags = 1 : 3 , k= 5 ) pred $ prediction ## Time Series: ## Start = 260
## End = 260 ## Frequency = 1 ## [1] 43 pred $ neighbors ## [1] 219 185 17 259 257 #Plotting time series autoplot (pred, h= 1 ) #Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 17.60000 17.60000 51.76471 ro $ predictions ## h=1 ## [1,] 51.6 ro $ h_accu ## h=1 ## RMSE 17.60000 ## MAE 17.60000 ## MAPE 51.76471
#For n = 3, K = 7 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags = 1 : 3 , k= 7 ) pred $ prediction ## Time Series: ## Start = 260 ## End = 260 ## Frequency = 1 ## [1] 43.28571 pred $ neighbors ## [1] 219 185 17 259 257 227 155 nearest_neighbors (pred) ## $instance ## Lag 3 Lag 2 Lag 1 ## 33 33 34 ## ## $nneighbors ## Lag 3 Lag 2 Lag 1 H1 ## 1 35 32 45 48 ## 2 32 44 38 51 ## 3 37 42 42 49 ## 4 47 33 33 34 ## 5 32 41 47 33 ## 6 39 46 40 43 ## 7 28 26 21 45 #Plotting time series autoplot (pred, h= 1 )
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#Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 18.57143 18.57143 54.62185 ro $ predictions ## h=1 ## [1,] 52.57143 ro $ h_accu ## h=1 ## RMSE 18.57143 ## MAE 18.57143 ## MAPE 54.62185 #for n=2, k = 1, 3 #Combining several models with different k parameters pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags= 1 : 2 , k = c ( 1 , 3 )) pred $ prediction
## Time Series: ## Start = 260 ## End = 260 ## Frequency = 1 ## [1] 39.33333 pred $ neighbors ## [1] 259 218 206 nearest_neighbors (pred) ## $instance ## Lag 2 Lag 1 ## 33 34 ## ## $nneighbors ## Lag 2 Lag 1 H1 ## 1 33 33 34 ## 2 35 32 45 ## 3 29 29 55 #Plotting time series autoplot (pred, h= 1 )
#Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 13.66667 13.66667 40.19608 ro $ predictions ## h=1 ## [1,] 47.66667 ro $ h_accu ## h=1 ## RMSE 13.66667 ## MAE 13.66667 ## MAPE 40.19608 #for n=2, k = 1, 5 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags= 1 : 2 , k = c ( 1 , 5 )) pred $ prediction ## Time Series: ## Start = 260 ## End = 260 ## Frequency = 1 ## [1] 42.3 pred $ neighbors ## [1] 259 218 206 149 256 nearest_neighbors (pred) ## $instance ## Lag 2 Lag 1 ## 33 34 ## ## $nneighbors ## Lag 2 Lag 1 H1 ## 1 33 33 34 ## 2 35 32 45 ## 3 29 29 55 ## 4 32 41 72 ## 5 32 41 47 #Plotting time series autoplot (pred, h= 1 )
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#Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 15.50000 15.50000 45.58824 ro $ predictions ## h=1 ## [1,] 49.5 ro $ h_accu ## h=1 ## RMSE 15.50000 ## MAE 15.50000 ## MAPE 45.58824 #for n=2, k = 1, 7 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags= 1 : 2 , k = c ( 1 , 7 )) pred $ prediction ## Time Series: ## Start = 260
## End = 260 ## Frequency = 1 ## [1] 41.78571 pred $ neighbors ## [1] 259 218 206 149 256 176 16 nearest_neighbors (pred) ## $instance ## Lag 2 Lag 1 ## 33 34 ## ## $nneighbors ## Lag 2 Lag 1 H1 ## 1 33 33 34 ## 2 35 32 45 ## 3 29 29 55 ## 4 32 41 72 ## 5 32 41 47 ## 6 38 40 52 ## 7 37 42 42 #Plotting time series autoplot (pred, h= 1 )
#Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 13.00000 13.00000 38.23529 ro $ predictions ## h=1 ## [1,] 47 ro $ h_accu ## h=1 ## RMSE 13.00000 ## MAE 13.00000 ## MAPE 38.23529 #for n = 2, k = 3, 5 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags= 1 : 2 , k = c ( 3 , 5 )) pred $ prediction ## Time Series: ## Start = 260 ## End = 260 ## Frequency = 1 ## [1] 47.63333 pred $ neighbors ## [1] 259 218 206 149 256 nearest_neighbors (pred) ## $instance ## Lag 2 Lag 1 ## 33 34 ## ## $nneighbors ## Lag 2 Lag 1 H1 ## 1 33 33 34 ## 2 35 32 45 ## 3 29 29 55 ## 4 32 41 72 ## 5 32 41 47 #Plotting time series autoplot (pred, h= 1 )
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#Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 18.16667 18.16667 53.43137 ro $ predictions ## h=1 ## [1,] 52.16667 ro $ h_accu ## h=1 ## RMSE 18.16667 ## MAE 18.16667 ## MAPE 53.43137 #for n = 2, k = 3, 7 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags= 1 : 2 , k = c ( 3 , 7 )) pred $ prediction
## Time Series: ## Start = 260 ## End = 260 ## Frequency = 1 ## [1] 47.11905 pred $ neighbors ## [1] 259 218 206 149 256 176 16 nearest_neighbors (pred) ## $instance ## Lag 2 Lag 1 ## 33 34 ## ## $nneighbors ## Lag 2 Lag 1 H1 ## 1 33 33 34 ## 2 35 32 45 ## 3 29 29 55 ## 4 32 41 72 ## 5 32 41 47 ## 6 38 40 52 ## 7 37 42 42 #Plotting time series autoplot (pred, h= 1 )
#Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 15.66667 15.66667 46.07843 ro $ predictions ## h=1 ## [1,] 49.66667 ro $ h_accu ## h=1 ## RMSE 15.66667 ## MAE 15.66667 ## MAPE 46.07843 #for n = 2, k = 5, 7 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags= 1 : 2 , k = c ( 5 , 7 )) pred $ prediction ## Time Series: ## Start = 260 ## End = 260 ## Frequency = 1 ## [1] 50.08571 pred $ neighbors ## [1] 259 218 206 149 256 176 16 nearest_neighbors (pred) ## $instance ## Lag 2 Lag 1 ## 33 34 ## ## $nneighbors ## Lag 2 Lag 1 H1 ## 1 33 33 34 ## 2 35 32 45 ## 3 29 29 55 ## 4 32 41 72 ## 5 32 41 47 ## 6 38 40 52 ## 7 37 42 42
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#Plotting time series autoplot (pred, h= 1 ) #Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 17.50000 17.50000 51.47059 ro $ predictions ## h=1 ## [1,] 51.5 ro $ h_accu ## h=1 ## RMSE 17.50000 ## MAE 17.50000 ## MAPE 51.47059 #for n = 3, k = 1, 3 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags= 1 : 3 , k = c ( 1 , 3 )) pred $ prediction
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## Time Series: ## Start = 260 ## End = 260 ## Frequency = 1 ## [1] 48.66667 pred $ neighbors ## [1] 219 185 17 nearest_neighbors (pred) ## $instance ## Lag 3 Lag 2 Lag 1 ## 33 33 34 ## ## $nneighbors ## Lag 3 Lag 2 Lag 1 H1 ## 1 35 32 45 48 ## 2 32 44 38 51 ## 3 37 42 42 49 #Plotting time series autoplot (pred, h= 1 ) #Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE)
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## RMSE MAE MAPE ## 10.83333 10.83333 31.86275 ro $ predictions ## h=1 ## [1,] 44.83333 ro $ h_accu ## h=1 ## RMSE 10.83333 ## MAE 10.83333 ## MAPE 31.86275 #for n=3, k = 1, 5 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags= 1 : 3 , k = c ( 1 , 5 )) pred $ prediction ## Time Series: ## Start = 260 ## End = 260 ## Frequency = 1 ## [1] 45.5 pred $ neighbors ## [1] 219 185 17 259 257 nearest_neighbors (pred) ## $instance ## Lag 3 Lag 2 Lag 1 ## 33 33 34 ## ## $nneighbors ## Lag 3 Lag 2 Lag 1 H1 ## 1 35 32 45 48 ## 2 32 44 38 51 ## 3 37 42 42 49 ## 4 47 33 33 34 ## 5 32 41 47 33 #Plotting time series autoplot (pred, h= 1 )
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#Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 14.30000 14.30000 42.05882 ro $ predictions ## h=1 ## [1,] 48.3 ro $ h_accu ## h=1 ## RMSE 14.30000 ## MAE 14.30000 ## MAPE 42.05882 #for n=3, k = 1, 7 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags= 1 : 3 , k = c ( 1 , 7 )) pred $ prediction ## Time Series: ## Start = 260
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## End = 260 ## Frequency = 1 ## [1] 45.64286 pred $ neighbors ## [1] 219 185 17 259 257 227 155 nearest_neighbors (pred) ## $instance ## Lag 3 Lag 2 Lag 1 ## 33 33 34 ## ## $nneighbors ## Lag 3 Lag 2 Lag 1 H1 ## 1 35 32 45 48 ## 2 32 44 38 51 ## 3 37 42 42 49 ## 4 47 33 33 34 ## 5 32 41 47 33 ## 6 39 46 40 43 ## 7 28 26 21 45 #Plotting time series autoplot (pred, h= 1 )
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#Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 14.78571 14.78571 43.48739 ro $ predictions ## h=1 ## [1,] 48.78571 ro $ h_accu ## h=1 ## RMSE 14.78571 ## MAE 14.78571 ## MAPE 43.48739 #for n = 3, k = 3, 5 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags= 1 : 3 , k = c ( 3 , 5 )) pred $ prediction ## Time Series: ## Start = 260 ## End = 260 ## Frequency = 1 ## [1] 46.16667 pred $ neighbors ## [1] 219 185 17 259 257 nearest_neighbors (pred) ## $instance ## Lag 3 Lag 2 Lag 1 ## 33 33 34 ## ## $nneighbors ## Lag 3 Lag 2 Lag 1 H1 ## 1 35 32 45 48 ## 2 32 44 38 51 ## 3 37 42 42 49 ## 4 47 33 33 34 ## 5 32 41 47 33 #Plotting time series autoplot (pred, h= 1 )
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#Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 14.13333 14.13333 41.56863 ro $ predictions ## h=1 ## [1,] 48.13333 ro $ h_accu ## h=1 ## RMSE 14.13333 ## MAE 14.13333 ## MAPE 41.56863 #for n = 3, k = 3, 7 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags= 1 : 2 , k = c ( 3 , 7 )) pred $ prediction ## Time Series: ## Start = 260
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## End = 260 ## Frequency = 1 ## [1] 47.11905 pred $ neighbors ## [1] 259 218 206 149 256 176 16 nearest_neighbors (pred) ## $instance ## Lag 2 Lag 1 ## 33 34 ## ## $nneighbors ## Lag 2 Lag 1 H1 ## 1 33 33 34 ## 2 35 32 45 ## 3 29 29 55 ## 4 32 41 72 ## 5 32 41 47 ## 6 38 40 52 ## 7 37 42 42 #Plotting time series autoplot (pred, h= 1 )
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#Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 15.66667 15.66667 46.07843 ro $ predictions ## h=1 ## [1,] 49.66667 ro $ h_accu ## h=1 ## RMSE 15.66667 ## MAE 15.66667 ## MAPE 46.07843 #for n = 3, k = 5, 7 pred <- knn_forecasting (knnt $ Predictive.analytics...United.States., h= 1 , lags= 1 : 3 , k = c ( 5 , 7 )) pred $ prediction ## Time Series: ## Start = 260 ## End = 260 ## Frequency = 1 ## [1] 43.14286 pred $ neighbors ## [1] 219 185 17 259 257 227 155 nearest_neighbors (pred) ## $instance ## Lag 3 Lag 2 Lag 1 ## 33 33 34 ## ## $nneighbors ## Lag 3 Lag 2 Lag 1 H1 ## 1 35 32 45 48 ## 2 32 44 38 51 ## 3 37 42 42 49 ## 4 47 33 33 34 ## 5 32 41 47 33 ## 6 39 46 40 43 ## 7 28 26 21 45
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#Plotting time series autoplot (pred, h= 1 ) #Calculating accuracy ro <- rolling_origin (pred, h= 1 ) ro $ global_accu #(Evaluating Using RMSE, MAE, MAPE) ## RMSE MAE MAPE ## 18.08571 18.08571 53.19328 ro $ predictions ## h=1 ## [1,] 52.08571 ro $ h_accu ## h=1 ## RMSE 18.08571 ## MAE 18.08571 ## MAPE 53.19328
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Conclusion: As we can see from the models results, the higher the dimension the model is, the lower the error we get. References: https://cran.r-project.org/web/packages/tsfknn/vignettes/tsfknn.html https://cran.r-project.org/web/packages/philentropy/vignettes/Distances.html
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