Near-Optimal Sample Compression for Nearest Neighbors

Abstract

We present the first sample compression algorithm for nearest neighbors with non-trivial performance guarantees. We complement these guarantees by demonstrating almost matching hardness lower bounds, which show that our performance bound is nearly optimal. Our result yields new insight into margin-based nearest neighbor classification in metric spaces and allows us to significantly sharpen and simplify existing bounds. Some encouraging empirical results are also presented.

Penentuan Rute Pengiriman Barang Dengan Metode Nearest Neighbor

“…langkah pertama memasukkan tujuan ke dalam rute pengiriman, hal pertama yang harus dilakukan adalah mengurutkan nilai terkecil yang telah diperoleh mulai dari yang terbesar hingga yang terendah [17]. Pada komputasi NN memiliki kinerja yang sangat cepat [18]. NN ditemukan oleh Solomon pada tahun 1987 yang konsepnya adalah mengunjungi lokasi terdekat dari masing-masing lokasi yang sedang dikunjungi [19].…”

Robust randomized optimization with k nearest neighbors

“…In particular, we employ smoothness concepts from Chaudhuri and Dasgupta [10] and Kpotufe [20]. A related line of work in the literature are the Bayes consistent 1-nearest neighbour methods [14,15,18,19]. These works are focused upon classification, rather than optimisation, and as such do not make the smoothness assumptions required by [10] and the present work.…”

The Inverse Voronoi Problem in Graphs I: Hardness

“…Surveying the research in this applied area is beyond the scope of our research. We refer to Biniaz et al [5] and Gottlieb et al [16] for some of the latest algorithmic results on this topic. Considering each class as a Voronoi cell, the inverse Voronoi problem is asking precisely whether there exists a consistent subset with one element per class.…”