اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدInitialization of Self-Organizing Maps: Principal Components Versus Random Initialization. A Case Study
92
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The performance of the Self-Organizing Map (SOM) algorithm is dependent on the initial weights of the map. The different initialization methods can broadly be classified into random and data analysis based initialization approach. In this paper, the performance of random initialization (RI) approach is compared to that of principal component initialization (PCI) in which the initial map weights are chosen from the space of the principal component. Performance is evaluated by the fraction of variance unexplained (FVU). Datasets were classified into quasi-linear and non-linear and it was observed that RI performed better for non-linear datasets; however the performance of PCI approach remains inconclusive for quasi-linear datasets.
قيم البحث
اقرأ أيضاً
Factorized layers--operations parameterized by products of two or more matrices--occur in a variety of deep learning contexts, including compressed model training, certain types of knowledge distillation, and multi-head self-attention architectures.
We study how to initialize and regularize deep nets containing such layers, examining two simple, understudied schemes, spectral initialization and Frobenius decay, for improving their performance. The guiding insight is to design optimization routines for these networks that are as close as possible to that of their well-tuned, non-decomposed counterparts; we back this intuition with an analysis of how the initialization and regularization schemes impact training with gradient descent, drawing on modern attempts to understand the interplay of weight-decay and batch-normalization. Empirically, we highlight the benefits of spectral initialization and Frobenius decay across a variety of settings. In model compression, we show that they enable low-rank methods to significantly outperform both unstructured sparsity and tensor methods on the task of training low-memory residual networks; analogs of the schemes also improve the performance of tensor decomposition techniques. For knowledge distillation, Frobenius decay enables a simple, overcomplete baseline that yields a compact model from over-parameterized training without requiring retraining with or pruning a teacher network. Finally, we show how both schemes applied to multi-head attention lead to improved performance on both translation and unsupervised pre-training.
Based on the classical Degree Corrected Stochastic Blockmodel (DCSBM) model for network community detection problem, we propose two novel approaches: principal component clustering (PCC) and normalized principal component clustering (NPCC). Without a
ny parameters to be estimated, the PCC method is simple to be implemented. Under mild conditions, we show that PCC yields consistent community detection. NPCC is designed based on the combination of the PCC and the RSC method (Qin & Rohe 2013). Population analysis for NPCC shows that NPCC returns perfect clustering for the ideal case under DCSBM. PCC and NPCC is illustrated through synthetic and real-world datasets. Numerical results show that NPCC provides a significant improvement compare with PCC and RSC. Moreover, NPCC inherits nice properties of PCC and RSC such that NPCC is insensitive to the number of eigenvectors to be clustered and the choosing of the tuning parameter. When dealing with two weak signal networks Simmons and Caltech, by considering one more eigenvectors for clustering, we provide two refinements PCC+ and NPCC+ of PCC and NPCC, respectively. Both two refinements algorithms provide improvement performances compared with their original algorithms. Especially, NPCC+ provides satisfactory performances on Simmons and Caltech, with error rates of 121/1137 and 96/590, respectively.
In this paper, we propose a new global analysis framework for a class of low-rank matrix recovery problems on the Riemannian manifold. We analyze the global behavior for the Riemannian optimization with random initialization. We use the Riemannian gr
adient descent algorithm to minimize a least squares loss function, and study the asymptotic behavior as well as the exact convergence rate. We reveal a previously unknown geometric property of the low-rank matrix manifold, which is the existence of spurious critical points for the simple least squares function on the manifold. We show that under some assumptions, the Riemannian gradient descent starting from a random initialization with high probability avoids these spurious critical points and only converges to the ground truth in nearly linear convergence rate, i.e. $mathcal{O}(text{log}(frac{1}{epsilon})+ text{log}(n))$ iterations to reach an $epsilon$-accurate solution. We use two applications as examples for our global analysis. The first one is a rank-1 matrix recovery problem. The second one is a generalization of the Gaussian phase retrieval problem. It only satisfies the weak isometry property, but has behavior similar to that of the first one except for an extra saddle set. Our convergence guarantee is nearly optimal and almost dimension-free, which fully explains the numerical observations. The global analysis can be potentially extended to other data problems with random measurement structures and empirical least squares loss functions.
Non-negative matrix factorization (NMF) has become a popular method for representing meaningful data by extracting a non-negative basis feature from an observed non-negative data matrix. Some of the unique features of this method in identifying hidde
n data put this method amongst the powerful methods in the machine learning area. The NMF is a known non-convex optimization problem and the initial point has a significant effect on finding an efficient local solution. In this paper, we investigate the most popular initialization procedures proposed for NMF so far. We describe each method and present some of their advantages and disadvantages. Finally, some numerical results to illustrate the performance of each algorithm are presented.
We study the problem of estimating a rank-$1$ signal in the presence of rotationally invariant noise-a class of perturbations more general than Gaussian noise. Principal Component Analysis (PCA) provides a natural estimator, and sharp results on its
performance have been obtained in the high-dimensional regime. Recently, an Approximate Message Passing (AMP) algorithm has been proposed as an alternative estimator with the potential to improve the accuracy of PCA. However, the existing analysis of AMP requires an initialization that is both correlated with the signal and independent of the noise, which is often unrealistic in practice. In this work, we combine the two methods, and propose to initialize AMP with PCA. Our main result is a rigorous asymptotic characterization of the performance of this estimator. Both the AMP algorithm and its analysis differ from those previously derived in the Gaussian setting: at every iteration, our AMP algorithm requires a specific term to account for PCA initialization, while in the Gaussian case, PCA initialization affects only the first iteration of AMP. The proof is based on a two-phase artificial AMP that first approximates the PCA estimator and then mimics the true AMP. Our numerical simulations show an excellent agreement between AMP results and theoretical predictions, and suggest an interesting open direction on achieving Bayes-optimal performance.
الأسئلة المقترحة
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
