$--$To implement the K$-$Nearest Neighbors $($KNN$)$ algorithm for image classification using the CIFAR$-10$ dataset, you can use a built$-$in function from an existing library like scikit$-$learn or implement the algorithm independently.

For the first approach, you can use the KNeighborsClassifier function from the sklearn.neighbors module. You will need to load the CIFAR$-10$ dataset, preprocess it$,$ and then fit the model using the fit method. The predict method can then be used to classify new images.

For the second approach, you can implement the KNN algorithm from scratch. This involves calculating the Euclidean distance between a test image and all training images, sorting these distances, and then selecting the K nearest neighbors. The most common class among these neighbors is then assigned to the test image.

To improve the performance of your self$-$implemented KNN algorithm, you can experiment with different values of K$,$ use a more efficient distance calculation method, or use a more efficient sorting algorithm.

Your report should include an introduction to the KNN algorithm and its application in image classification, a description of the CIFAR$-10$ dataset and the classification tasks, details of the algorithms used, the results obtained, and the methods used to improve the performance of your algorithm. You should submit your work in the form of Jupyter Notebook $(.$ipynb$)$ and HTML files, along with the final report.

Your work will be graded based on your ability to implement the KNN algorithm using both the library function and self$-$coded method, your initial results, your efforts to validate and improve your algorithm, and the quality of your report.