Depreciation in the income statement can be classified under Cost of sales or operating expenses or non-operating expenses. Is this correct and if yes, based on what aspect is the classification done ?

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It is  important to  appreciate that depreciation is part of the many functions within an entity. Depreciation can be a selling expense , administration expense, distribution costs and part of the cost of  production.

Where depreciation is reported depends on the assets being depreciated. for example , the depreciation on the sales staff motor van is considered part of the company's selling expense. Depreciation on the office building will be considered as part of administration expense.

 The depreciation on a manufacturer;s factory and production plant and equipment will be included in the cost of sales of the product made and when the product is sold , some of the depreciation will be included in the cost of goods sold and some of the depreciation will be included in inventory of the products not sold.

If it relates to direct operation  it should come under cost of sales or operating expenses, example - suppose your company doing   rental machines business   in that case your stock in trade is Machines, so those machines depreciation expense comes under cost of sales because its direct cost

If depreciation indirect  nature to operation it should be no operating expense 

It depends on for which purpose it is used, it may be for manufacturing, admin or selling purpose. Please refer Mr. Frank answer

Based on the nature of business, these classifications are done.

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Cost of Sales(a.k.a. cost of goods/products sold (COGS), and cost of services): For a manufacturer, cost of sales is the expense incurred for labor, raw materials, and manufacturing overhead used in the production of goods. While it may be stated separately, depreciation expense belongs in the cost of sales. For wholesalers and retailers, the cost of sales is essentially the purchase cost of merchandise used for resale. For service-related businesses, cost of sales represents the cost of services rendered or cost of revenues.