Raftul cu initiativa Book Archive

Machine Theory

Subspace Learning of Neural Networks by Jian Cheng Lv, Zhang Yi, Jiliu Zhou

By Jian Cheng Lv, Zhang Yi, Jiliu Zhou

PrefaceChapter 1. Introduction1.1 Introduction1.1.1 Linear Neural Networks1.1.2 Subspace Learning1.2 Subspace studying Algorithms1.2.1 PCA studying Algorithms1.2.2 MCA studying Algorithms1.2.3 ICA studying Algorithms1.3 tools for Convergence Analysis1.3.1 SDT Method1.3.2 DCT Method1.3.3 DDT Method1.4 Block Algorithms1.5 Simulation info Set and Notation1.6 ConclusionsChapter 2. PCA studying Algorithms with Read more...

summary: PrefaceChapter 1. Introduction1.1 Introduction1.1.1 Linear Neural Networks1.1.2 Subspace Learning1.2 Subspace studying Algorithms1.2.1 PCA studying Algorithms1.2.2 MCA studying Algorithms1.2.3 ICA studying Algorithms1.3 tools for Convergence Analysis1.3.1 SDT Method1.3.2 DCT Method1.3.3 DDT Method1.4 Block Algorithms1.5 Simulation information Set and Notation1.6 ConclusionsChapter 2. PCA studying Algorithms with Constants studying Rates2.1 Oja's PCA studying Algorithms2.1.1 The Algorithms2.1.2 Convergence Issue2.2 Invariant Sets2.2.1 houses of Invariant Sets2.2.2 stipulations for Invariant Sets2

Show description

Read Online or Download Subspace Learning of Neural Networks PDF

Similar machine theory books

Digital and Discrete Geometry: Theory and Algorithms

This ebook presents finished assurance of the fashionable tools for geometric difficulties within the computing sciences. It additionally covers concurrent issues in info sciences together with geometric processing, manifold studying, Google seek, cloud info, and R-tree for instant networks and BigData. the writer investigates electronic geometry and its comparable positive tools in discrete geometry, delivering exact equipment and algorithms.

Artificial Intelligence and Symbolic Computation: 12th International Conference, AISC 2014, Seville, Spain, December 11-13, 2014. Proceedings

This booklet constitutes the refereed complaints of the twelfth overseas convention on synthetic Intelligence and Symbolic Computation, AISC 2014, held in Seville, Spain, in December 2014. The 15 complete papers offered including 2 invited papers have been rigorously reviewed and chosen from 22 submissions.

Statistical Language and Speech Processing: Third International Conference, SLSP 2015, Budapest, Hungary, November 24-26, 2015, Proceedings

This e-book constitutes the refereed complaints of the 3rd foreign convention on Statistical Language and Speech Processing, SLSP 2015, held in Budapest, Hungary, in November 2015. The 26 complete papers awarded including invited talks have been conscientiously reviewed and chosen from seventy one submissions.

Additional info for Subspace Learning of Neural Networks

Sample text

9 If w(0) ∈ S and w(0) ∈ / Vσ⊥ , then there exist constants θ1 > 0, Π1 ≥ 0, and d > 0 such that n j=l+1 zj2 (k) ≤ Π1 · e−θ1 k , for all k > N , where θ1 = ln σ + λp + 2ησλp σ + λp + 2ηλm+1 λp 2 > 0. Proof: Since w(0) ∈ / Vσ⊥ , there must exist some i(1 ≤ i ≤ m) such that zi (0) = 0. Without loss of generality, assume that z1 (0) = 0. 4, it follows that w(k) ∈ S for all k ≥ 0. 7, it holds that 1 + η λi (2 − w(k) 2 ) − wT (k)Cw(k) > 0, for k ≥ 0. 5, then w(k + 1) 2 ≤ 2σ < 2, σ + λp 2 · zj (k) z1 (k) 2 .

N). Next, we analyze the convergence of w(k) by studying the convergence of zi (k)(i = 1, . . , m) and zi (k)(i = m + 1, . . , n), respectively. 8899, 2 if w(0) ∈ S and w(0) ∈ / Vσ⊥ , then there exist constants θ1 > 0 and Π1 ≥ 0 such that n j=m+1 zj2 (k) ≤ Π1 · e−θ1 k , for all k ≥ 0, where 1 + ησ 1 + ηλm+1 θ1 = ln 2 > 0. Proof : Since w(0) ∈ / Vσ⊥ , there must exist some i(1 ≤ i ≤ m) such that zi (0) = 0. Without loss of generality, assume that z1 (0) = 0. 5) and for k ≥ 0. 1, S is an invariant set, then w(k) ∈ S for all k ≥ 0.

M), k→+∞ where zi∗ (i = 1, . . , m) are constants. Proof: Given any ǫ > 0, there exists a K ≥ 1 such that ΠKe−θK 2 (1 − e−θ ) ≤ ǫ. For any k1 > k2 ≥ K, it follows that k1 −1 |zi (k1 ) − zi (k2 )| = r=k2 [zi (r + 1) − zi (r)] k1 −1 ≤ η r=k2 σ − wT (r)Cw(r) zi (r) k1 −1 ≤ Π re−θr r=k2 +∞ ≤ Π re−θr r=K +∞ ≤ ΠKe−θK · = r e−θ r−1 r=0 ΠKe−θK 2 (1 − e−θ ) ≤ ǫ, (i = 1, . . , m). This shows that each sequence {zi (k)} is a Cauchy sequence. By Cauchy Convergence Principle, there must exist constants zi∗ (i = 1, .

Download PDF sample

Rated 4.89 of 5 – based on 18 votes