Visual methods have been widely studied and used in data cluster analysis, \textit{e.g.}, the VAT algorithm for visual analysis of cluster tendency. Given a pairwise dissimilarity matrix $\bm{D}$ of a set of $n$ objects, methods such as VAT generally represent $\bm{D}$ as an $n\times n$ image $\mathrm{I}(\tilde{\bm{D}})$ where the objects are reordered to highlight cluster structure as dark blocks along the diagonal of the image. A major limitation of such visual methods is their inability to highlight cluster structure in $\mathrm{I}(\tilde{\bm{D}})$ when $\bm{D}$ contains clusters with highly complex structure. In this paper, we address this limitation by proposing a Spectral VAT algorithm, where $\bm{D}$ is mapped to $\bm{D'}$ in an embedding space by spectral decomposition of the Laplacian matrix, and then reordered to $\bm{\tilde{D'}}$ using the VAT algorithm. We propose a strategy to automatically determine the number of clusters in $\mathrm{I}(\bm{\tilde{D'}})$, as well as a visual method for cluster formation from $\mathrm{I}(\bm{\tilde{D'}})$ based on the difference between diagonal blocks and off-diagonal blocks. In addition, we propose a sampling-based extended scheme to enable visual cluster tendency assessment and data partitioning for large data sets. Extensive experimental results on several synthetic and real-world data sets demonstrate the effectiveness of our algorithms.